Leibniz with Professor Martha Bolton

Syllabus

Texts

Assigned and recommended readings will be papers, letters, and published articles of Leibniz, as well as some secondary sources. Readings will be on electronic reserve although there will also be class handouts. Many of the readings are taken from a collection of writings of Leibniz which is available at the bookstore, G. W. Leibniz, Philosophical Essays, tr. Roger Ariew and Daniel Garber. Purchase is optional; all assigned readings will be available electronically.

Requirements

You are expected to attend all meetings of the class and to do all reading assignments thoroughly and promptly. Assignments should be read at least once for the class meeting in which they are to be discussed. You are strongly encouraged to participate in class discussion. This helps you and everyone in the class to learn by exploring them yourself. There will be one short paper (roughly 5 pages) assigned during the semester and a long paper (roughly 12-15 pages) due at the end of course. There may be additional out-of-class written assignments, quizzes, or in-class exercises.

Learning goals

The course is intended to provide a good understanding of some of the central doctrines of Leibniz’s metaphysics and theory of cognition, the reasoning by which we supports them, their strengths and weakness, historical context and significance. It is also meant to develop skill in analyzing and evaluating arguments, as well as developing, supporting, and expressing views of one’s own.

Schedule

January 28: The alphabet of thought and method of demonstrating truths
- ‘Of an Oragnum or Ars Magna of Thinking’ (1679)
- ‘Preface to Universal Characteristic’ (1678-9)
- Optional: ‘Samples of the Numerical Characteristic’ (1679)
- Suggested: Catherine Wilson, Leibniz’s Metaphysics, pp. 7-44
January 30: Method of demonstration and the existence of God
- ‘The Nature of Truth’ (1686)
- ‘That a Most Perfect Being Exists’ (1676)
February 4: The infinite analysis theory of contingent truth
- ‘On Contingency’ (1686?)
- ‘On Freedom’ (1689?)
February 6: More consequences of the ‘predicate in notion’ theory of truth
- ‘Primary Truths’ (1689)
February 11
- ‘Discourse on Metaphysics’ (1686): special attention to 1-16
February 13
- See February 11
February 18: Fatal necessity and the structure of the concept of an individual substance.
- Excerpts from Leibniz’s first two letters to Arnauld (May 1686; 14 July, 1686)
February 20: Critique of Descartes’ doctrine of corporal substance, substantial forms, corporeal substances
- Excerpts from letters to Arnauld 28 Nov/8 Dec 1686 and 30 Apr 1687; 9 Oct 1687;
- Notationes generales
February 25
- See February 20
February 27: Expression, perception, soul, body (Short paper assignment)
- Letter to Arnauld 9 Oct 1687
- Suggested: Chris Swoyer, ‘Leibnizian Expression’, Journal of the History of Philosophy 33 (1995), 65-94
March 4
- ‘Meditation on the Principle of the Individual’ (1676)
- ‘Substance and Individuation in Leibniz’, Cover and Hawthorne, pp. 184-99
March 6: What God does and what created substances do
- ‘Discourse on Metaphysics’ 8, 14, 26;
- Robert Adams’ Leibniz: Determinist, Theists, Idealist, pp. 94-9
March 11: The notion of force in physics and metaphysics (Short paper due)
- ‘On the Correction of Metaphysics and the concept of Substance’ (1694)
- ‘On Body and Force against the Cartesians’ (1702)
- Suggested: ‘Specimen Dynamicum, Part 1’ (1695)
- Suggested: Stuart Brown’s ‘The proto-monadology of the De Summa Rerum‘
March 13: Pre-established harmony, miracles and occasionalism
- ‘New System, etc.’ (1695);
- ‘First Explanation of the New System, etc’ (1696);
- Letter to Damaris Masham (1704);
- Letter to Arnauld 30 Apr 1687
March 16-23: Spring break
March 25: How the soul ‘knows’ what to do
- ‘Letter . . . containing an explanation of the Difficulties which M. Bayle, etc.’ (1698)
- ‘Reply to the Comments in the Second Edition of M. Bayle’s . . .’ (1702)
March 27
- See March 25
April 3: Monads, force, extension
- Selections form letters to De Volder (1703-1706)
- Suggested Jeffrey McDonough, ‘Leibniz’s Philosophy of Physics’, Stanford Encyclopedia of Philosophy, on-line
April 8: Monads and the status of corporeal substances
- Glenn Hartz, ‘Why Corporeal Substances Keep Popping Up in Leibniz’s Later Philosophy’
- Brandon Look, ‘Idealism and Corporeal Substance in Leibniz’s Metaphysics’
- Optional ‘Richard T. Arthur, ‘Presupposition, Aggregation and Leibniz’s Argument for a Plurality of Substances’
April 10 Law of change in a monad: two principals of final causality?
- Donald Rutherford, ‘Leibniz on Spontaneity’
Apr, 17
- ‘What is an Idea?’ (1678);
- ‘Discourse in Metaphysics’, 26-9;
- ‘Monadology’ 43;
- Robert Adams, Leibniz, etc., pp. 177-183; optional pp. 84-91
April 22: Concepts are expressions of ideas; blind thought, no thought without sensible signs
- ‘Meditations on Knowledge, Truth and Ideas’ (1684)
April 29: Arguments for perceptions of which the soul is unaware; theory of consciousness
- New Essays concerning Human Understanding (1702-04) excerpt from Preface, Book 2.1
May 1 same
May 6 Same

Final paper due on regularly scheduled exam date for this class period.

January 23rd, 2013 – Lecture: The alphabet of thought and method of demonstrating truths

Leibniz lived between 1646 to 1716
In the part of the world we now call Germany, there was terrible religious war and plague.
Public debates were held where the public tried to decide which was “the religion.”
The people who were Calvinist may have had comfort or distress based on radical predetermination.
- The idea, starkly, is if you’re saved, you don’t worry about.
- Conversely, in the Roman Catholic religion, works are important.
- This is one brand of Protestantism, and it was stark and hard to live with.
- There are lot of religious debates over this.
There was a flourishing of counter-Reformation art, commissioned by the church.
There are a lot of treatises on self-help and logic, critical thinking.
This was a counter-Reformation strategy, these self-help manuals.
This has to do with the social contract theory.
The Eighteenth Century is what we called the “Enlightenment Era”, and Leibniz bridges the past and the Enlightenment.
Leibniz’s life
- His father was a university professor.
- This father instilled a love of learning in him.
- Yet, Leibniz was largely self-taught. He taught himself Latin at the age of 7.
- Leibniz is the co-discoverer of infinitesimal calculus and a logician.
- He is extremely interested in formal structures, languages and symbol systems
- He constructed a wooden calculating machine that you could “turn.”
- He was very good at seeing abstract “relations” between things.
- He first adopted the views of the scholastics, of Aquinas and Aristotle.
  - Aquinas adopts Aristotle to apply it to Roman Catholiscism.
- When 16 years old, he replaces Aristotelian system with mechanism.
  - Mechanism is the view that everything that happens in the corporeal world is just matter in motion.
  - This means matter can be represented in geometry.
  - The hope is that motion can be represented in mathematical formulas.
- Leibniz starts out just accepting Aristotelianism, and ends up converting to mechanism.
- German was a collection of principalities with princes who trade with one another.
- His teachers recognize his brilliance, and offer him a job, but he declines it and goes into public office.
- He was sent to Paris on a diplomatic mission. This was a revolution for Leibniz.
- He learns mathematics from Cartesians and he reads about Galileo and Hougins (pendular motion).
- He comes alive intellectually here in this “Paris period” (1672-1676), and he was eventually called back.
- This laid the foundations for his philosophy and his mathematics and his motions, all formulated here.
- He was working on what he calls the “foundation of cognition.”
- Career
  - He goes back to England speaks with Spinoza (exiled Jewish naturalist), Oldenburg
  - Goes back to Germany and settles in Hanover.
  - He has a variety of employers in and around the court.
  - Engineering projects, diplomatic projects.
  - He came up with the idea of distracting France by pointing out Egypt.
  - He is the court historian.
  - He comes up with a geological history of his region.
  - One thing for which he is famous is that he was working with the ancestors of George Ludwig, and he discovers that languages change.
  - While he is doing this research, he finds documents that establish a connection between George Ludwig and the British monarchy.
  - When the Brits ran out of monarchs, this made Ludwig become George the First of England.
- Aside from his career, he had private projects.
- He wanted to reconcile Protestantism with Catholicism.
- He is very interested in codes and code-breaking (with Wallace).
- Interested in physics, theology – Jesuits, protestants, – many other things.
- He is intellectually engaged in almost everything that is going on.
Leibniz’s thoughts
- Cognition
  - Humans and animals both participate in cognition, but humans also participate in knowledge.
  - Prof. Bolton doesn’t believe that her cat has beliefs, and that if her cat does, the cat is unwarranted in holding the,
    - Well, she does, but only because she’s so fond of her cat.
  - How does what goes on in a mind or a soul, a cognitive being, sense perception, related to its environment, so that there is actual intaking of information? Not just atoms.
  - We also have information about what is, what could be, what might be, what ought be, what is necessarily true, etc.
  - There is “mind-world” and “super world” cognition.
  - He comes up with the thought that we think of many things that are complex, but if we think of complex things, there must be simple things that they are made of.
  - Our thoughts must be composed of simple thoughts.
  - What are the simples? If you could only find the simples, you’d have a powerful instrument.
  - He has this vision that there is an alphabet of human thought.
  - He becomes discouraged, but he has plenty of projects trying to find it.
- Classical metaphysical thoughts
  - Is there anything that remains? Stays the same?
  - If god exists, then god remains.
- The mains philosophical works are:
  1. Meditations on Knowledge, Truth, and Ideas (1684)
  2. Discourse on Metaphysics (1686)
  3. Specimen of Dynamics (1695)
  4. ‘New System of the nature and Communications of Substances’

January 28th, 2013 – Reading

Leibniz’s ‘Of an Oragnum or Ars Magna of Thinking’ (1679)

The supreme happiness is the greatest increase in one’s own perfection.
Vigor shares the same relationship over health as disease is under health.
The most powerful human faculty is thinking.
- Assisted by either remedies of body or mind.
Remedies of bodies are applied to corporeal organs directly.
Remedies of mind are those modes of thinking that make other thoughts easier.
The greatest remedy of mind is the modes of thinking which infinite others arise – like the numbers 1 through 10 can generate all other numbers.
Thoughts must be “built on” something – there must be a point where you have “the most simple” thought(s).
Another example is that all numbers can be built on using everything and nothing, 0 and 1, using the binary system.

Leibniz’s ‘Preface to Universal Characteristic’ (1678-9)

God made all using weight, measure, and number. Mechanism.
Those things that cannot be weighed because they have no force or power.
Also things that “lack parts,” and thus cannot be measured.
There is nothing that can’t be numbered, however. This is how everything is investigated.
Since Pythagoras, people have thought there to be mystery in numbers.
Because they lacked understanding, they slipped into superstition and futility.
This nonsense still fills books, and also, the belief that numbers can discover amazing things remains.
The Universal Characteristic is a language in which “all notions and things are nicely ordered.”
Yet no one has discovered a language which does what numbers do.
When he was young, Leibniz saw that no one could devise a certain alphabet of human thoughts.
Leibniz spends quite a while calling other people stupid for not having thought of this because he did it when he was a youth.
When the characteristic numbers of notions is determined, it will do for the mind what glasses did for the eyes.

When we have a true characteristic number of things, then at last, without any mental effort or danger of error, we will be able to judge whether arguments are indeed materially sound and draw the right conclusions.

Leibniz’s ‘Samples of the Numerical Characteristic’ (1679)

Observes that while sometimes an argument leads to the correct conclusion, it is not because of sound argument or true premises.
Every categorical proposition has two times: the subject and the predicate.
The quality of the proposition is affirmation or negation.
The quantity of the proposition is universality or particularity.
In every proposition, the predicate is said to be in the subjection.
For example, “Every man is an animal” means “The concept of animal is contained in the concept of man.”
Leibniz does some weird and goofy number assignment and negative stuff here.

January 28th, 2013 – Lecture

Remember that Leibniz escapes from nothern Germany to Paris, and he is called back to Germany to write ‘Of an Organum or Ars of Thinking.’
He’s interested in what can be done for personal happines and the happiness of society in general.
He’s thinking that improving our power of thinking would go a long way to improve happines.
He’s thinking that if you can take the “smallest” truth and use it to build other truths, it would be more efficient.
So he comes up with this argument – either you can see this thing, or you can see this thing through something else.
What’s the distinction between:
1. concieving of something and
2. concieving of something through another “thing”
If you want to concieve an even number, you concieve of a number through something else, the specific type of number it is.
- You think of a number,
- And of a number divisible by two.
Suppose I think of a triangle, do I think solely of a triangle or do I think of it through another concept.
The concept of an odd number is that of a number and of a number not divisible by two.
To be precise, concept A (involves, includes, contains) concept B.
Leibniz is thinking that if you cannot concieve of justice without virtue, this is relevant.
He’s got an argument that since we concieve some things through other things, there has to be concepts which are ultimately simple, that they aren’t built from others, that they are independant conceptions.
From these basics, we can build the comples.
How does he show that there are these simple concepts?
Leibniz is thinking that you can always ask whether a concept is “simple” or “complex.”
If nothing is concieved as itself, nothing can be concieved at all.
You cannot think of a compound concept without actually thinking about the sum of it’s parts.
A point about Leibniz’s argument:
- Could it be that there are complex concepts, but that they come in “familys.”
- That any member of any given family could be used to build another, forming a “circularity.”
- For instance:
  - A point is simple.
  - A line is motion of a point.
  - A plane is the motion of a line.
- And additionally:
  - A plane is simple.
  - A line is the intersection of two planes.
  - A point is the intersection of two lines.
- This is the distinction between “wholists” and “atomists.”
Leibniz thought that maybe the only thing “concieved throught itself” is god.
One of his thoughts is that everything is composed of limits on the infinite.
- He never fully sketched this idea out.
- He was “attracted” to this idea.
Leibniz is thinking that is you have the simple concepts and you assign them “symbols”, then, just by mechanically generating all the allowable symbols, you could generate all the concepts.
So Leibniz has the idea that given symbols of all concepts, you would have the symbols to generate all propositions, and you’ll be able to determine whether the propositions were true.
He has this thought of forming an artificial languages.
The concept containment theory of truth
- He is making assumptions about propositions.
- Aristotle’s logic is that there are basic propositions which build all other propositions. There are four:
  1. All A is B ? the concept of A contains the concept of B.
  2. No A is B ? the concept of A contains the concept of not B.
  3. Some A is B ? the concept of A and the some concept of something X contains the concept of B.
  4. Some A is not B ? the concept of A + X contains the conceopt of not B.

In every true proposition the concept of the predicate is somehow contained in the concept of the subject.

Anything that satisfies the subject satisfies the predicate.

January 30th, 2013 – Reading

Leibniz’s ‘That a Most Perfect Being Exists’ (1676)

Simple concepts are perfect forms and they are impossible to access.
Only “universal propositions” can be stated about that which cannot be demonstrated.
“Necessary identical propositions are identical.”
- An indentical proposition is something akin to “A is A.”
As many simple forms as you want can exist in the same subject.
Existence is one of these simple forms, one of the perfections.
Therefore, a most perfect being must exist.
- Q.E.D. stands for “quod erat demonstrandum”, which means “which had to be demonstrated.”
An argument:
- What is necessary, necessarilly exists.
- Whatever necessarilly exists, exists.
- Therefore, a necessary being exists.

Stanford Encyclopedia of Philosophy – Leibniz: The Existence of God

Leibniz thinks that perfection is a “simple quality which is positive and absolute, or, which expresses without any limits whatever it does express.”
From this, it follows that “there can be no inconsistency among perfections, since a perfection, in being simple and positive, is unanalyzable and incapable of being enclosed by limits.”
Compounding any and all simple truths will never be incompatible.
Therefore, it is possible that all simples are compatible.
This argument is not sufficient to demonstrate that god necessarilly exists.

January 30th, 2013 – Lecture: Method of demonstration and the existence of God

There are two things: things you think of through others and things you think of through itself.
There has to be simple concepts, otherwise we couldn’t think of anything.
You can’t think a thought of something without “bottoming out” on a simple concept eventually.
By relating simple concepts, you get all other concepts that there are.
Then, a proposition is made out of concepts.
All basic propositions are “subject/predicate” propositions, joined by “is” and “is not.”
All other propositions can be formed from basic propositions.
They are all universal, negative, existential, affirmitive.
We can get all basic propositions from the alphabet of human thought.
When you have subject concept and predicate concept, decompose the two, and you’ll find that every concept in the subject is in the predicate, the “simple concepts” that for the two concepts will be identical.
- Is everything that is true “vacuously true”?
  - No – because every simple concept is ground in god.
Leibniz is thinking that the connection between “Every A is B” is loose enough that facts about the world are possible.
Leibniz is worried about this problem, this is a preface, an anticpation.
If you grant “simple concepts”, all of the above follows.

Leibniz’s ‘That a Most Perfect Being Exists’ (1676)

Ontological argument
Subject to a lot of objections
Anselm and Leibniz, revived by Descartes
Leibniz grants what a lot of critics deny: that existence is an attribute.
Existence, for Leibniz, is something that is ascribed to a thing (as opposed to presupposed when you prescribe anything else).
He does not grant that existence is perfection.
Necessary existence is different from mere existence, it is eternally unshakable.
It’s quite an extraordinary way of being, and it is a perfection.
When we form this definition that god is the most perfect being, we put words together, and have concepts.
You can do this in a way that you don’t define anything because of contradiction.
“A regular 12-sided polygon” – geometrically impossible but “valid” definition.
When we toss out a definition, we may only be talking formally, but you’re talking nonsense.
In “Ars Magna”, the second part, he says we can’t trace back the “simples” all the way, but we can get far enough.
We’ve got to halt and no reason on the basis of some definition.
If this definition of god is something that’s possible, it shows that it exists.
He undertakes showing that is possible that a necessary being exists.
He’s going to use the apparatus of the concept containment of truth.
This is very abstract.
Argument:
1. Perfections are undefinable or have concepts that are unanalyzable.
  - The first thing is: he defines perfection as absolute positive quality.
  - Also indefinable and unanalyzable.
  - Once you have the notion of unlimited extension, you can specify parts of it.
  - There are endless ways of specifying an unlimited concept, but when you do, you are inevitable limiting it.
  - All perfections are limitless attributes, no limitation built-in to them.
  - By virtue of this, they are simple.
  - If you’ve got a proposition about a perfection, the subject is unalazable, it is “immune” to demonstration.
2. A necessarilly true proposition that is indemonstrable is an indentity.
  - If you’ve got an indemonstrable proposition that is necessarilly true, it’s got to be that the subject concept has to be in the predicate concept.
  - Every A is AB
3. Suppose it’s not possible that A and B are perfections and that A and B belong to the same thing.
  - Let’s consider this supposition as expressed by the following: “A is B-incompatible.”
  - This is not an identity.
  - It’s undefinable, unalazable.
  - Can’t be demonstrated.
  - But a necessarilly true proposition is an identity, so this isn’t a necessary truth.
4. “A is B-incompatible” is not an identity and not demonstrable. So it’s not necesarilly true.
  - This also works with “A is B-compatible.” This seems to break the argument?
  - All Leibniz wants to show is that it’s not impossible.
  - So “A is B-incompatible” is possible true.
Homework: Use Leibnizian logic to prove:
- All cockerspaniels are dogs.
- All triangles have three angels.
- Water is liquid at room temperature.

February 4th, 2013 – Reading

Homework

All cockerspaniels are dogs.
- Subject: cocker spaniels
- Predicate: all are dogs.
- “In every true proposition the concept of the predicate is somehow contained in the concept of the subject.”
- Cockerspaniels are a complex idea experienced through the concept of dog, along with the other properties of cockerspaniels.
- Symbolically, cockerspaniels can be represented as $$ , q_1, q_2, … , q_n $$ where qs are qualities unique to cockerspaniels and “dog” is the set of all concepts in dog.
- The concept of dog is a complex idea experienced through other ideas, but it does not need to be defined here. Let $dog$ be the set of all dog qualities.
- Because $dog$ $ $ $$ , q_1, q_2, … , q_n $$, all cocker spaniels are dogs.
Water is liquid at room temperature
- We experience water through the simpler concepts of: $chemical compound, 2 hydrogen 1 oxygen$
- You cannot prove this with Leibnizian logic because you need causation.
- The concept of liquid is not “contained within” the concept of water.

Leibniz’s ‘On Contingency’ (1686?)

Existence does not differ from essence for god.
It is essential for god to exist.
God is a necessary being.
Creatures are contingent in that their existence does not follow from their essence.
- This is what it must be to be mortal.
- Leibniz think that god’s essence $ $ god’s being.
Necessary truths are those that can be demonstrated through analysis of terms.
- This is “Leibnizian logic” – see cocker spaniels exercise.
- Example: An equation expressing an identity ultimately results from substitution of terms.
- “Everything true is an identity”
We does say that both god and creatures exist.
Necessary propositions are no less true than contingent ones.
One can always give a reason for every non-identical proposition.
- In necessary propositions, reason necessitates.
- In contingent propositions, it inclines.
Of things that exist, they have more “reason to exist” that things which do not exist.
In contingent propositions, there comes a point where only god can further understand the infinite analysis.
One can ask whether this proposition is necessary: Nothing exists without there being a greater reason for it to exist that for it to not.
Not all possibles attain existence, otherwise nothing novel could be imagined, yet they obviously can be.
There are an infinite number of series of possible things, and one series cannot be contained within another. Therefore:
1. God always acts with the mark of perfection and wisdom.
2. Not every possible thing attains existence.
“The proposition that has the greater reason for existing exists.”
- Existing means “being true.”
- Exists means “is true”
- This proposition is necessarily true.

February 4th, 2013 – Lecture: The infinite analysis theory of contingent truth

Even without the proof of the possibility of god, the argument discussed last time has some “moral weight.”
It’s not valueless, even if nobody has proved the possibility of a being with all perfections.
While we’re waiting, people should work on trying to prove the possibility of god, and Leibniz thinks he has.
“We’re entitled to assume the possibility of any being until someone shows the contrary.”
If something exists rather than nothing, something is possible.
We ought to have a bias in favor of the possible because of reality.
He often remarks with regards to Euclid that it was the closest to science in the 17th century, that he couldn’t prove that a line was the shortest distance between two points.
Leibniz is just barely out of university when he wrote what we’re reading.
They’re also unpublished.
These are comparable to the false start in papers.
One of the things that the professor likes about reading Leibniz’s early work is that you can try to figure out how his mind is working and how he forming and revising his opinions.
Towards this end, homework.
- Triangle
  - The concepts which we have through names, lexical ones, are very complex.
  - Relative to the alphabet of human thought, that is.
  - There are lots of ways of decomposing the analysis of the whole thing, triangle.
  - This depends on how many “simples” there are in the concept.
  - Leibniz remarks on this from time to time.
  - When he talks about a definition or an analysis, he is thinking about something that is coextensive with it.
- Water
  - You have to engage in an analysis of water.
  - Can we go outside on what we know just on the basic of concepts.
Leibnizz thinks we need to proceed by analyzing terms, and if we’re doing this in the English language, we’re using definitions.
We are trying to do these analyses in English, and Leibniz is well aware that it is not a perfect language, for that reason, if we try to use English, we’ll run into problems.
To actually implement of proof that Leibniz calls demonstration, we would really need an ideal language.
The more logical and precise your language, the further you can get with these proofs.
There are these “hitches” and “things to take into account” given our knowledge.
He continues to use this as the standard of demonstration.
When he talks about demonstration, he is talking about a high gauge notion which irrecvibly shows something.
There are arguments which aren’t demonstration that are still valuable.
You have to start from where you are, and you’re not an ideal point, you’ll have to use arguments which aren’t solid.
But keep track of your assumptions and check them – this is how you make progress.

Leibniz’s ‘On the Nature of Truth’ (1686)

This is later than the Paris period, and he’s still thinking his way through the concept cointainment theory of truth.
There are three illustrations of Leibniz’s difficulties.
He’s trying to figure out how to make it work.
He starts out by saying every proposition is either true or false, but not both.
There is no proposition that is indeterminate.
If a proposition p is false, then the contradictory of p is true. $ p $ and ¬p are contradictory.
- Law of non-contradiction
- Interestingly, this law cannot be proved, because you’d have to use propositions.
A true proposition is one which the concept of the predicate is contained the concept of the subject, meaing there is a connection, and it is objective, built into reality.
This containment can be express or virtual, which means in the context “potential.”
This connection is either necessary of contigent.
- Necessary if it follows from definitions and consequences.
- Contigent if different things are true at different times. (This is only one kind)
  - Also, it’s not necessarily true or false, it’s a propositions that’s possibly true or false, but happens to be true.
  - The impossibility of that thing is not necesarilly true.
  - They vary in time.
  - There is no necessary connection.
  - We assume they follow from free decress of god.
  - Always have to do with things that exist, are natural, about things that do exist other than god and the assumption is that they exist because god wills that they exist.
- The principle of sufficient reason: For every true proposition, there is a reason for it being true rather than otherwise.
  - Nothing happens which a reason cannot be given for it happening rather than otherwise.
  - No proposition is true without there being a reason.

Homework

Look at the last paragraph of ‘On the Nature of Truth’
Principle of Sufficient Reason
- See how Leibniz is toying with whether it’s necessary or continent.
‘On Contingency’
‘On Freedom’
‘Primary Truths’ (read but we will not talk about)

February 6th, 2013 – Reading

Principle of Sufficient Reason

Wikipedia

The principle of sufficient reason states that nothing is without a ground or reason why it is.

For every entity x, if x exists, then there is a sufficient explanation for why x exists.
For every event e, if e occurs, then there is a sufficient explanation for why e occurs.
For every proposition p, if p is true, then there is a sufficient explanation for why p is true.

We have said that the concept of an individual substance [Leibniz also uses the term haecceity ] includes once for all everything which can ever happen to it and that in considering this concept one will be able to see everything which can truly be said concerning the individual, just as we are able to see in the nature of a circle all the properties which can be derived from it. But does it not seem that in this way the difference between contingent and necessary truths will be destroyed, that there will be no place for human liberty, and that an absolute fatality will rule as well over all our actions as over all the rest of the events of the world? To this I reply that a distinction must be made between that which is certain and that which is necessary.

Stanford Encyclopedia of Philosophy

The principle of sufficient reason, namely, that nothing happens without a reason.

all truths rest upon two great principles:
1. the Principle of Contradiction (which says that a truth is necessary just in case its negation is a contradiction)
2. and the PSR

Leibniz’s ‘On Freedom’ (1689?)

How freedom and contingency can coexist is one of the oldest human worries.
The worry is increased when you add Christianity to the affair.
When Leibniz considered that nothing happened by chance, he was close to the view that everything was absolutely necessary.
Some think that it’s enough to be un-coerced, even if we’re subject to necessity.
There are certain possibilities that will never be.
There are fictions that have no place is this universal series god selected.
- Unless the universe contains everything.
- This would eliminate all beauty.
All creatures have impressed upon them a certain mark of divine infinity.
There is no portion of matter so tiny that it does not contain a sort of world of creatures of infinite number.
Even though in contingent truths, the predicate is in the subject, it can never be demonstrated as an equality or identity.
- God alone can see it though.
- This is derived from his intellect.
Two ways remains for us to know continent truths:
1. Experience: when we perceive a thing sufficiently distinly through the sense.
2. Reason: when something is know from the general principle that nothing is without a reason, or that there is always some reason why the predicate is in the subject.
God made everything in the most perfect way, an he does nothing without a reason, and nothing happens anywhere unless he who understands understands its reasons.
God knowns infinite and contigent truths not by demonstrastion, as this would imply contradiction, but rather by divine intuition.
- This intution is not experiential, but rather one of a priori.
Having accepted the notion that necessity everyone accepts, which is that those things whose contrary implies a contradiction.

Leibniz’s ‘Primary Truths’ (1689)

The primary truths are those which assert the same thing of itself or deny the opposite of its opposite.
- A is A
- Not-A is not-A
- “Everything is as it is.”
- “Everything is similar or equal to itself.”
- “Nothing is greater or less than itself.”
All remaining truths are reducded to primary truths with the help of definitions.
- Through resolution of other notions.
- A proof indepedant of experience.
- “The whole is greater than its part.”
- “The part is less than the whole.”
- Something esaily demostrated from the definition of less or greater.
  - Arguement:
  1. The part is equal to a part of the whole.
  2. What is equal to a part of a whole is less than the whole.
  3. Therefore, the part is less than the whole.
Therefore the predicate is always in the subject.
This is truth for every affirmitive truth, universal or particular, necessary or contigent.
Things that follow from this:
- Nothing is without reasons.
- There is no effect without cause.
- When in the givens everything on one side is the same as the other side.
- There is even a reason for eternal things.
- There cannot be two individual things that differ in number alone.
- There are no purely extrinsic demominations.
- Every individual substance contains in its perfect notion the entire universe.
- All individual created substances are different expressions of the same universe.
- No created substance exerts a metaphysical action or influx on any other thing.
- Assuming the distinction between soul and body allows us to explain their union.
- There is no vacuum.
- There is no atom.
- Every particle of the unverse contains a world of an infitiy of creatures.
- There is no determinate shape in actual things.
- Corporeal substance can neither arise nor perish except through creation or annihilation.
- Animate things neither arise nor perish, but are only transformed.

February 6th, 2013 – Lecture: More consequences of the ‘predicate in notion’ theory of truth

The infinite analysis will always yield a reason a true proposition is true.
We have the principle of sufficient reason.
A couple of questions:
1. Whether the PSR has a sufficient reason.
  - There’s a kind of reason for thinking there is a reason for the PSR.
  - It’s a truth, Leibniz says.
  - All truths have SR.
  - So what’s the SR for the PSR?
  - God does nothing without a reason?
  - If it is contigent, god could have created the PSR false.
  - But surely it’s necessary.
  - If you grant the concept containment theory of truth, then you have to analyze the terms.
2. How you’ll bring together the PSR, god creates the world, how the PSR governs god, and how a lot of things are contigently true.
Leibniz attempts to clean up his PSR by distinguishing existence and propositions.
The thing is that “x exists* is a proposition.
Leibniz wants to say:
1. God exists essentially-necessarily.
2. Creatures exist contigently.
3. There are truths that are necessary.
4. There are truths that are contigent.
But what are common between necessary and contingent beings and necessary and contigent truths?
Two questions come up:
1. Is it necessary for god to choose the best?
  - The best of the alternatives.
  - The greater of the opposite.
2. Is it necessary that nothing exists without there being a greater reason for it to exist than not?
  - The only reason that will appeal to an infinitely powerful and knowing agent is that one of the possible alternatives is the best.
  - Here’s a problem: Adam exists. Adam sins. God created this. How does is this resolved?
  - Everything for Leibniz, nothing is isolated in it existence.
  - Leibniz will fill this in in the material world, with the fact that matter is infnitely divisable and extenable.
  - One motion has material consequences for everything else in the world.
  - Everything in the world is also influenced by everything in the world.
  - If you want a full account of why someone sneezes, you have to describe the whole universe.
  - The things that are present in material things that are diversified infinitely.
The necessity of the consequence does not determine the necessity of the consequent.
If Zero Dark Thirty won the Oscar, it got the most number of votes. If it wins, it is necessary it does. But it’s not necessary it does.

Leibniz’s ‘On Freedom’

One of the reasons Leibniz is so interested in matters of fact being contigent in the actual world is that he wants to preserve accountability.
He wants to preserve freedom.
What counts as freedom?

Definitions

Concept Containment Theory of Truth: In every true proposition, the concept of the predicate is contained in the concept of the subject, either the analysis is finite or inifite, but in either case the connection between concepts is the reason for the propositions truth.
Principle of Sufficient Reason: For every true proposition there is a reason for it, being true rather than false.

February 11th, 2013 – Reading

‘Discourse on Metaphysics’ (1686)

1. On Divine Perfection, and That God Does Everything in the Most Desirable Way

God is an absolutely perfect being
- This is the best way we can describe god
- We also need to consider what it actually means.
- There are several different perfections in nature.
  - God possesses them all together.
What is a perfection?
- Things that are not capable of a highest degree are not perfections.
- The “greatest of all number/figures” imply a contradiction, so not perfection.
- On the otherhand, knowledge has “all knowledge”, so it’s a perfection,
- Power and knowledge are perfections, insofar as they belong to god.
God:
1. Posseses infinite and supreme wisdom
2. Acts in the perfect manner in:
  - Metaphysical matters,
  - Moral matters

2. Against Those Who Claim That There Is No Goodness in God’s Work, or That the Rules of Goodness and Beauty Are Arbitrary

Leibniz is far removed from those who maintain there is no good or perfect
- It can’t be so because god is their author, would have considered them afterwards, and found them good.
- Scriptures are an anthropomorphic expression only to make understand the excellence of god’d work.
- Through considering the works you can discover the creator.
  - Therefore, his works carry his mark
  - The contrary opinion is dangerous
- In saying that things are not good by virtue of any rule of goodness but by the whim of god, you destroy god’s love and glory.
- Where will his power remain if it is simply despotic?
  - Besides, all acts presuppose a reason for willing.
- Descartes thought that god “could have” willed that a triangle have four sides.

3. Against Those Who Believe That God Might Have Made Things Better

Nor can Leibniz approve of those who maintain that god could have made the world better.
- The consequences of this opinion is contrary to the glory of god.
  - A lesser evil is relatively good
  - A lesser good is relatively evil
- Showing that an architect could have done better is to find fault with his work.
- If their right, the “the series of imperfection descends to infinity”
  - This view is backed by scripture
- Leibniz thinks that there is nothing so perfect that there is not something more perfect.
In this way way, the “moderns” believe that they can safeguard god’s freedom.
- To think that god does something without having a reason does not conform to his glory.
- Imagine god has a choice between A or B, chooses A, without considering B.
  - Being as all praise must be based on some reason, this is absurd.
- God does nothing for which he does not deserve to be praised.

4. That the Love of God Requires Our Complete Satisfaction and Acquiescence with Respect to What He Has Done without Our Being Quietists as a Result

The genral knowlege of this truth is the foundation of the love that we owe god
- He who loves seeks his satisfaction of the object loved and in his actions.
- It is difficult to love god when we are not disposed to will what god wills.
- Those who are not satisfied with god are not much different from rebels.
To act in accordance to god, it is not sufficient to be patient.
- We must be satisfied with everything that comes according to his will.
- We must not:
  1. Be quietists
  2. Stand ridiculously with arms folded
- We must:
  1. Act in accordance with what we presume to be the will of god
  2. Contribute to the general good

5. What the Rules of the Perfection of Divine Conduct Consist in, and That the Simplicity of the Ways Is in Balance with the Richness of the Effects

Therefore it is sufficient to have the confidence that god does everthing for the best.
- To know in detail the reasons that could have moved him surpasses the power of the mind.
However, it is possible to make general remarks
- He who acts perfectly is similar to an excellent geometer.
- The most perfect of all beings occupies the least volume that least interfere with one another.
On the simplicity of the ways of god
- Nothing costs god anything
- Since god only has to make decrees in order that a real world come into being
- The simplest system is always preferred in astronomy.

6. God Does Nothing Which Is Not Orderly and It Is Not Even Possible to Imagine Events That Are Not Regular

The volitions or acts of god are divided into two groups:
1. Ordinary
2. Extraordinary
  - The extraordinary is only extraordinary relative to god to those creatures who have seen an established order
In whatever manner god created the world, it would have been regular an in accordance with certain general order.
- God chose the most perfect world.
  - In that it is simplest in hypotheses and richest in phenomena
  - Just like a line in geometry whose construction is easy and whose properties and effects are remarkable and widespread.

7. That Miracles Conform to the General Order, Even Though They May Be Contrary to the Subordinate Maxims; and about What God Wills or Permits by a General or Particular Volition

Nothing happens which is not in order.
- Miracles are therefore part of that natural order.
- There are the same type of operation as the subordinate maxims we call the nature of things.
- God can have as much a reason to break these maxims as the make the maxims maxims.
General and particular volitions
- God does everything following his most general will.
  - This is in conformiaty with the most perfect order
- But he can also have particular volitions
  - These can be exceptions to his general will
- The most general are without exception, as they are most within his will.
God wills everything that is a particular object of his volition
- Objects of his general volition are the acts of other creates
- If the action is good in itself, we can say that god wills it and sometimes commands it.
  - Even if it doesn’t take place.
- If the action is evil in itself and becomes good only by accident, then we can say that god permits it.
  - But he does not will it.
- He concurs with it because of the laws of nature he has established and because he knows how to draw greater good from it.

8. To Distinguish the Actions of God from Those of Creatures We Explain the Notion of an Individual Substance

It is difficult to distinguish the actions of god and creatures
- Some believe god does everything.
- Some believe god does only what is needed to conserve the energy of creatures.
When there are several predicates associated with a subject and the subject is attributed to no other, it is called an individual substance.
- We must considering what it is to attributed truly to a certain subject.
Every true predication has some basis in the nature of things.
- When the predicate is not contained in the subject, it must be contained virtually.
- The subject term must alwayus contain the predicate term.

The notion of an individual substance or of a complete being is to have a notion so completel that is is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed.

The quality of being a kind is not enough to determine enough to constitue an individual, nor is it a quality that anything is exclusively.
- But when god sees Alexander the Great, he sees the basis and reason for all predicates.
- He knows a priori what will happen to him and what did and what is.
- When we considering the connection of things, we can say that Alexander’s soul contains vestiges of everything that has happened to him and marks everyhing that will happen to him and even marks of everything that will happen in the universe.

February 11th, 2013 – Lecture

Discourse on Metaphysics

Leibniz starts out in the first four sections laying out basic claims about god.
First of all, he tells us the way he understands god and what he is.
- Absolutely perfection.
What is perfection?
- It is a nature or attribute capable of highest degree.
- Movement is not a perfection because there isn’t a fastest motion.
- Knowledge is a perfection because there is a knowledge of everything.
God has each of these perfections without limitations.
He goes on deny theistic voluntarism.
- Theistic volutarism about x is that god willed that x.
Descartes held the outstanding view that what is true and false is due to the will of god.
- If you try to think through this doctrine it is mind boggling.
He wants to say that the world god created is good not because god willed it to be good but because he created it and it was indepedantly good, in and of itself.
- Is the world good because god will the world be good or is the world good because god made a good world?
Leibniz has an argument based on the PSR that if god were to will that justice be good, it would be, but for a reason, and what better reason than justice actually already being god.
Two goals:
1. Maximal diversity of the world
2. Maximal simplicity of the simples. Leibniz has to create a world where the simple concepts are as intecllectually appealing as possible.
The divergence of these is perfection.
There are subordinate laws that generally hold in this true, but no and then there may be exception based on god’s will that violates one of these laws.
- This violation makes the Universe better than it would be otherwise.
What does god will when he actually wills that the world exists?
- It’s delicate because there are bad things.
- Does god will bad things?
- What should we say about what decrees should exists with regard to the actual world in view of all the bad things?
- Leibniz answer:
  - Insofar as god will something in particular volitions, god always wills that these things happen.
  - But about the general laws of nature, there is distinction between what god wills and what he concurs with.
  - To the extent that something is good, he wills it.
  - To the extent that something is bad, he concurs with it, because the world wouldn’t be as good without this one bad.
  - There is nothing god could have done, because he isn’t volutarist about the possibles.
  - Questions:
    1. This presupposes that you can get out some good and some bad out of any event, “teasing it out”
    2. Think of god’s will. Omnipotent. If she wills it, it happens. If god wills you do something, where is there room for you to be bringing that about? God’s will will do it anyway. Anything you do to bring about it, it’s going to come about anyway.
  - What god wills is good. So if you know what god wills, you know what’s good and will want to do it anyway.
  - Nicole: Without access to knowledge of the will of god, so you cannot say that “you did this wrong thing” because of the will of god, because you didn’t have access to that.
    1. God is not concerened with freedom or responsibility.
    2. God may still be the one making us want god’s will.
  - Nicole: There’s a possibility of the world being predetermined without a god.
  - For Leibniz, god is sustaining, propping up the world.
  - There are places where Leibniz commits himself to a view that Descartes liked, that once the world exists, there’s no guarentee on it continuing. “Existential inertia.”
  - To get the world up to this moment is contigent on god continually recreating and willing the world.
  - This makes it more difficult to distinguish the productivity of the world and the productivity of god.
- There are two conflicting doctrings:
  1. Continual recreation, and
  2. Continual concurance
- Leibniz wants contiual recreation
- He also wants to have humans be in a reasonable sense, agents.
- Section 8 is about in what sense can god do things and in what sense can creatures do things.
- There is a meaningful sense to say two things:
  1. We are agents who choose things.
  2. God is the ultimate agent who chooses everything.
Aristotle’s Categories
- A substance is something to which other things are attributed which cannot be attributed to anything else.
  - There are some things are exist in others
  - Some things are neigther said of nor exist in others.
- In the world we have these things, which are referred to as some things, and never referred to as other things.
- Leibniz calls this a nominal definition.
  - He worries that we can produce a definition that produces and conceals a contradiction.
- Leibniz’s project is to show how this model can be contained within the concept containment theory of truth.
- “Green is predicated of grass.”

February 13th, 2013 – Lecture

Concept containment definition of individual substance: X is an individual substance if and only if the concept of X contains the basis and reason for everything that can be truly said of X.
‘Discourse on Metaphysics’ part 9
1. Principle of the Identity of the Indiscernables: No two substances are exactly alike
  - As far as there properties go, there are no two objects that at every level of granulaity are identical.
  - God would have no reason to create two identicals.
  - Leibniz believes that every proposition contains only concepts.
  - Say that there is a Y that is identical to X, everything that can be said of X can be said of Y, except that X is not Y, but they’re identical so this is equivilent to X is not X, which is a contradiction.
2. Substance begins only by creation and cease to exist only by annihilation
3. Substance cannot be divided into 2 substances or form by combining 2 substances.
4. Mirroring thesis: Each substance is a mirror of the universe and of god.
5. Each is bears in some way the character of god, wisdom, and power
  1. Is analogous to god’s perception of the infinite
  2. Is such that every other is accommodating it.

Notable paradoxes

If we know about an individual substance that has a complete concept, then certain things have to be true about everything that satisfy that concept.

February 18th, 2013 – Reading: Excerpts from Leibniz’s first two letters to Arnauld (May 1686; 14 July, 1686)

Remarks on Arnauld’s Letter about My Proposition That the Individual Notion of Each Person Includes Once and for All Everything That Will Ever Happen to Him [May 1686]

Arnauld: god was free to create Adam or not, but assuming that he wanted to create him, everything that has happened to humankind had to happen, or ought to happen, by fatal necessity.
- Absolute and hypothetical necessity
- Arnauld is speaking only of hypotheical necessity
The other reply to this is that god is resolving to create Leibniz cannot fail to create a nature capable of thought.
Arnauld admits in good faith that what can be deduced from the notions of individual is the same process as deducing the notions of a spehere from its properties.

February 18th, 2013 – Lecture: Fatal necessity and the structure of the concept of an individual substance.

Leibniz’s points:
1. When god creates Adam
  - He does it determinately, and absolutely.
  - When god creates Adam, it is part of a whole.
2. It’s one thing to consider truths about kinds of things, it’s abstract.
  - Once you get an individual, there’s one and only one thing which that concept can apply to.
  - So, Adam, is completely individual and can be inditical to no other.
  - This fits in to Leibniz’s view of infinite analysis and identity.
3. Arnalud: Either the connection Adamn and Adam’s posterity is intrinsicdependant of free decrees of god. Or the connection is intrinsic and necessary. (This bothers him because god would not have a choice.)
  - If god creates Adam and god freely decrees certain laws and freely decrees certain particular events, then Adam’s posterity exists.
  - Leibniz stresses the connection between Adam and Adam’s posterity, as it is “packed into” Adam.
  - So you just look at the concept
Adam has a complete concept which contains all the predicates which are true of Adam and everything that happens after he dies, the connection between them contigent laws, but everything is there in the concept.
Argument, consider Adam-r
- There is no reasons to say Adam-r = Adam.
- So Adam is not identical to Adam-r
The original meaning of a priori was something you know from it’s cause, it was in Leibniz’s time which it became known as the “before senses” version.
Super-esssentialism: For all predicates P, if i is P, then necesarilly i is P.
Moderate-essentialism: For such predicates P, if i is P, then necesarilly i is P and for some predicates Q, if i is Q, necesarilly i is Q.
Super-intrinsicalism: If there were a thing x which differs in any predicate from i, x would not be equal to i.

February 20th, 2013 – Reading: Excerpts from letters to Arnauld 28 Nov/8 Dec 1686 and 30 Apr 1687; 9 Oct 1687;

February 20th, 2013 – Lecture: Critique of Descartes’ doctrine of corporal substance, substantial forms, corporeal substances

This was written on the board, on page 85 of the reading. Where a C-body is a cartesian body.
1. Every C-body is composed of C-bodies, so a C-body is an aggregate.
2. An aggregate is a collection of things in some relation (its unity is in some way mental).
  - Several things collected together as one thing.
3. An aggregate is real only if its constituents are true unities (substances).
4. So if an aggregate is composed of aggregates, which are composed of aggregates endlessly – the decomposition set contains nothing but aggregates, and it is unreal.
5. So a C-body is unreal.
Heaps of stones
- Classic example of vagueness
- Take one stone away, do you still have a heap of stones?
- Well, yeah, if it’s big enough.
- But then what about if you do it again?
- And again?
- When you only have two?
- When you only have one?
- When you have none?
Bodies may be like heap of stones, indeterminate about their number.
Unless you can percieve something like substanial forms.
Either bodies are merely extended on par with rainbows and heaps, or they have substantial forms and souls.
What’s wrong with material things that are extended?
Descartes maintains that bodies are subtances and are extended in three-dimensions.
- Minds are entirely different things.
A substance could have in its instance nothing but extension.
Descartes has an extremely difficult time explaining what a human being is.
“You’ve got some extension and you attach a human mind to it and you have a subtantial form.”
Arnauld is a Cartesian, he think Descartes is right about the mind and body.
If a body is a substance, it has to be connected to a substantial form.
A soul is a substance, so it has to be connected to a substantial form.
In his second letter, Arnauld focuses on two questions:
1. World apart thesis
  - The body can’t have causal influence on the soul and vice versa
2. Something that’s merely extended can’t be a substance.
  - A Cartesian body can’t be a substance.
  - Leibniz:
```
soul = substantial form + body = substance
```
  - He never refers to the soul as a simple substance.
  - There is a kind of duality here, the soul as a substantil form.
  - He points out that it satisfies the defintion.
    1. Immaterial,
    2. Not composed of parts,
    3. Can’t be destroyed,
    4. Can’t be corrupted
    5. Contains all past and future states
    6. All states of the universe
  - Substances as parts of substances.
  - What he calls substances on the right side of the formula above is “corporeal.”
  - He expressed uncertainty about what are corporeal.
  - A block of marble is not substanial forms.
  - Human beings have substantial forms, but animals may or may not.
  - Intrinsic unity and unity by accident: individual things arranged in a useful way, dependant on relations.
  - Every extended thing is divided into parts, which may or may not be seperated.
  - Arnauld – Substance: A substance is an entity which is not a mode or state.
  - Leibniz – The essense of an aggregate consists in modes or states of its constituents.
  - So there are no aggregates unless there are substances, which are not aggregates.
Read for monday the assignment for wednesday

February 25th, 2013 – Reading: Chris Swoyer, ‘Leibnizian Expression’, Journal of the History of Philosophy 33 (1995), 65-94

Leibniz on Expression

I set out the relevant data for this project, including Leibniz’s terse characterizations of expression, his examples of it, and, what is often neglected by those commentators who do explore the notion, his views about the role of expression in human reasoning.

Leibniz’s Characterizations of Expression.

I. That is said to express a thing in which there are relations that correspond to the relations of the thing expressed.

One thing expresses another, when there is a constant and ordered relation between what can be asserted of the one and what can be asserted of the other.

it is sufficient for the expression of one thing in another [sufficit enim ad expressionem unius in alio] that there should be a certain constant relational law, by which particulars in the one can be referred to corresponding particulars in the other.

Leibniz’s Examples of Expression

But these are too brief.
Leibniz’s favorite example is the perspectival projection of a figure onto a plane. Examples:
- When a circle is projected onto an ellipse, the latter is an expression of the former
- In analytic geomtry, numbers and figures represent geometric figures.
- In algebra, numbers and figures represent magnitudes.
- A map expresses the geographical region that it depicts.
- A miniature model of a machine expresses the machine
- Perception is an expression of that which is perceived
  - our ideas of color, warmth, and other sensory qualities are really expressions of the motions of minute figures
- General concepts express things.
  - the idea of a circle expresses the circle itself
- Words express the things that they signify
- Numerals express numbers
- Speech expresses thought
- each monad expresses the entire universe

Leibniz on the Role of Expression in Human Reasoning.

What is common to all these expressions is that we can pass from a consideration of the relations in the expression to a knowledge of the corresponding properties of the thing expressed.

For example, the idea of a circle expresses a circle, and although it “is not similar to the circle, truths can be derived from it which would be confirmed beyond doubt by investigating a real circle”

V. Characters are certain things by which the relationships among other things are expressed and which are easier to manage than the things themselves.

We need valid symbols to derive truths about what is smbolized.
This stems from the role of expression in Leibniz’s philosophy.

All of our reasoning is nothing but the combining and substitution of characters, whether those characters are words, marks, or even images

Perspectival Projection As The Paradigm Of Expression

These explicit sources are not enough for inquiry.

Perspectival projections

Thus, a circle can be represented by an ellipse (that is, an oval curve) in a perspectival projection, and indeed by a hyperbola, which is most unlike it, and does not even return upon itself; for to any point of the hyperbola a corresponding point of the circle which projects the hyperbola can be assigned by the same constant law.

And his response to Arnauld in passage (2) runs more fully:

One thing expresses another, in my language, when there is a con- stant and ordered relation between what can be asserted of the one and what can be asserted of the other. It is in this way that a projec- tion in perspective expresses a geometric figure.

In Theodicy,

There must always be an exact relation between the representation and the thing [it expresses]…. The projections in perspective of the conic sections of the circle show that one and the same circle may be represented by an ellipse, a parabola, a hyperbola, and even another circle, a straight line and a point.

In New Essays,

… [A]n ellipse, and even a parabola or hyperbola, has some resem- blance to the circle of which it is a projection on a plane, since there is a certain precise and natural relationship between what is projected and the projection which is made from it, with each point on the one corresponding through a certain relation with a point on the other.

our sensory ideas express the motions of the particles that cause them,
Correlating relation: a relation that establishes such a correspondence.
- Like a function, a mapping of the points of the original figure to their counterparts in the figure that expresses it. Bijective.

The Method of Projection and Section.

Just like when an artist paints something, the representation being dependant on the angle of view, distorting the original form into something dependant on the viewer’s capacity to be tricked,
- In the same way, an circle view obliquely is a ellipse.
For those paintings done in accordance with the rules of perspective, we have little trouble “being tricked.”
- While some of the original is distorted, some of the original structure is also preserved, then.
So which of the original features is preserved and which of them are destroyed/distorted?
When Leibniz tells us that there is an “exact” or a “precise and natural” relation between the points of the two figures in a perspectival projection, he is also noting the much deeper relation- ship that holds between a conic section and its perspectival projections

Morals for an Account of Perspectival Expression

Perspectival expression: The expression of one geometrical figure by a perspectival projection of it onto another.
Features that are preserved by a transformation are said to be invariant under it.

Surrogative reasonging:

       1. Correlating relation
R(a,b) ----------------------> R(a*, b*)
             preserves R           | 
                                   | 2. Surrogative reasoning
                                   |
3. Inverse of Correlating Relation v
Q(b,a) <--------------------- Q(b*, a*)
             preserves Q

Steps of surrogative reasoning:
1. We can encode information about the original situation as information about the relationships among the corresponding items in the expression. a* bears R to b*
2. Because information about the original relationships is pre- served by the corresponding relationships among items in the expression, much of the original information is also preserved by inferences about the constituents of the expression.
3. In a perspectival projection, preservation of structure runs both ways, and so we can make the return trip to a conclusion about relationships among the original items of interest.

An Account of Perspectival Expression

Perspectival expression: “the points in the original figure stand in a given projective relation (or have a given projective attribute) just in case the surrogates of those points in the expression stand in the counterpart of that relation (or have the counterpart of that attribute). Hence, the essential feature of a perspectival expression is that the pattern of projective relations and attributes among the constituents of the represented phenomena is mirrored by the pattern of such relations and attributes among the constituents of the expression of it.”
In passage I, Leibniz tells us that one thing expresses a second when it contains “relations which correspond to the relations of the thing expressed.”
In passage II, Leibniz tells us that one thing expresses another “when there is a constant and ordered relation between what can be asserted of the one and what can be asserted of the other.”
In passage III, Leibniz tells us that it is sufficient for the expression of one thing in another that there be a “constant relational law, by which particulars in the one can be referred to corresponding particulars in the other.”

A General Account of Leibnizian Expression

This section provides:
1. A simple a natural generalization of Leibnizian expression
2. Shows how this account conforms with Leibniz’s explicit characterizations
3. Explains how it relates to surrogative reasoning

Generalizing the Account of Perspectival Expression

Isomorphism is too much to expect from an expression
- For example, a circle does not have enough of it’s relations preserved when projected into a parabola.
- Only those attributes that affect the truth value of what’s being reasoned about matter.
Since one thing may have two different names, language is not a function.
- Perhaps expression if from the expression to the object, then.
Leibniz talks about an ideal language where things are onto, one-to-one.
The key to expression is preservation of structure, and not direction.
- one thing expresses a second just in case there is a structure-preserving mapping from either to the other.
- Consequences of this:
  - one thing can express another even if they have only a little structure in common.
  - figures that are not conic sections, e.g., squares, can express a circle, since there are mappings from the points of a square to those of a circle that preserve genuine relations
  - does not require that the correlating relations in all expressions have these features (total, onto, one-to-one functions)

February 25th, 2013 – Lecture

The soule, however, is nevertheless the form of its body, because it is an expression of the phenomena of all other bodies in accordance with the relationship on its own. Leibniz to Arnauld, 14 July 1686, Mason 65-6

If the body is a substance and not a simple phenomenon like the rainbow, or an entity united by accident or by aggregration like heap of stones, it cannot consist of extension, and one must necessaily conceive of something there that one calls substancial form, and which corresponds in a way to the soul. Leibniz to Arnauld, 14 July 1686., Mason 65

In order that this conclusion might be valid, one would first have to define ‘substance’ and ‘substanial’ in the following terms: I call ‘substance’ and ‘substantial’ that which has a true unity. But as this definition has not yet been accepted, and since there is no philosopher who is not as entitled to say: I call ‘substance” that which is not modaility of state, and who cannot consequently maintain that it is paradoxical to say that there is nothing substancial in a block of marble, since this block is not the state of another substance; and that one might say is that it is not a single substance but many substances mechanically joined together. Arnauld to Leibniz, 4 March 1687, Mason 107-8

9 October, 1687, last responded letter to Arnauld
- It has always been a sideline for Arnauld.
- It’s really Leibniz’s business.
- At this point in time, he became preoccupied with his own affairs.
- Maybe he didn’t find anything to respond to.
- Leibniz in 1688, wrote two more letters.
  1. The right laws of motion, short letter
  2. A final one going back to his metaphysical system
- This one does not introduce a lot that is new.
```
"substantial form" + "body" = "aggregate of corporeal substances"
```
- You cannot have a whole real body unless it’s parts are real.
- Each substantial form having a different concept
- You need to give reality to it’s parts.
- Every body is composed of parts and every part has substantial forms and they consitute corporeal substances.
- Infinite corporeal substances.
- There can be no causal interaction between created substances.

Concommitance

time 1                       time 2
state of soul -------------> state of soul
              laws of soul
              laws inherent

state of body -------------> state of body
              laws of motion
              its causes

Moral accountability is dependant on being able to reflect on themselves.

        true unity = corporeal substance
               |
+--------------|-------------------------------+
|              v            +----------------+ |
| substantial ------------> | whole composed | |
|    form                   |   of parts     | |
|                           +----------------+ |
+----------------------------------------------+

The heap question
- There is no fact of the matter about it, no objective truth.
- Leibniz is saying put all of those substantial forms into the corporeal substance, see complete concept.
- We know that the complete concept of any substance of the substantial form has the reason that you have that identity to that substance at that time.
  - Now that we have a substantial form that animates the corporeal substance

February 26th, 2013 – Reading: Leibniz’s theory of expression and cognitive representation

‘That is said to express a thing in which there are relations [habitudines] which correspond to the relations of the thing expressed. But there are various kinds of expression; for example, the model of a machine expresses the machine itself, the projective delineation on a plane expresses a solid, speech expresses thoughts and truths, characters express numbers, and an algebraic equation expresses a circle or some other figure. What is common to all these expressions is that we can pass from a consideration of the relations in the expression to a knowledge of the corresponding properties of the thing expressed. Hence it is clearly not necessary for that which expresses to be similar to the thing expressed, if only a certain analogy is maintained between the relations. It is also clear that some expressions have a basis in nature, while others are arbitrary, at least in part, such as the expressions which consist of words or characters. Those which are founded in nature either require some similarity, such as that between a large and a small circle or that between a geographic region and a map of the region, or require some connection such as that between a circle and the ellipse which represents it optically, since any point whatever on the ellipse corresponds to some point on the circle according to a definite law. Indeed, a circle would be poorly represented by any other figure more similar to it in such a case. Similarly every entire effect represents the whole cause, for I can always pass from the knowledge of such an effect to a knowledge of its cause. So, too, the deeds of each one represent his mind, and in a way the world itself represents God. It may also happen that the effects which arise from the same cause express each other mutually, as for example, gesture and speech. So deaf people understand speakers, not by the sound, but by the motion of the mouth.’ ‘What is an Idea?’ (1678) G 7.326-4; L 205T 2.
- The model expresses the machine.
- The way that things are arranged.
- Some are natural, which means they depend on natural laws, or natural ways of thinking about things.
- On the other hand, some correlate to signs and convetionality.
‘One thing expresses another (in my terminology) when there is a constant and ordered relation between what can be said of the one and what can be asserted of the other. This is the way that a perspectival projection experesses its ground-plan. Expression is common to all [substantial] forms, and it is a genus of which natural perception, animal sensation and intellectual knowledge are species. In natural perception and in sensation, it is enough for what is divisible and material and dispersed into many entities to be expressed or represented in a single indivisible entity or a substance which is endowed with true unity. . . . But this representation is accompanied by consciousness in the rational soul, and then it is called thought.’ Letter to Arnauld, 9 Oct. 1687; G 2.71, Mason, 144
‘It is sufficient for the expression of one thing in another that there should be a certain constant relational law, by which particulars in the one can be referred to corresponding particulars in another.’ ‘Metaphysical consequences of the Principle of Sufficient Reason’ (1715), MP 176-7
- There is a constant relational law betwen the constants.
‘It is true that the same thing may be represented in different ways; but there must always be an exact relation between the representation and the thing, and consequently between the different representations of one and the same thing. The projections in perspective of the conic sections of the circle show that one and the same circle may be represented by an ellipse, a parabola and a hyperbola, and even by another circle, a straight line and a point.’ Theodicy, 357 (1710); H 339
‘The doctrine of shadows is simply that of perspective in reverse and results from it if we replace the eye by the luminous source, the object by the opaque body, and the projection by the shadow.’ ?Precepts for Advancin the Sciences and Arts’ (1680), Leibniz Selections, Philip Wiener, 41
‘. . . the simplicity of a substance does not prevent the plurality of modifications which must necessarily be found together in the same simple substance; and these modifications must consist in the variety of relations which the substance has with things outside. In the same way there may be found, in one centre or point, though it is perfectly simple, an infinity of angles formed by lines which meet in it.’ Principles of Nature and Grace (1714), AG 207
‘There are successive perceptions, but there are also simultaneous ones, for, when there is a perception of the whole, at the same time there are perceptions of its actual parts, and it is even the case that each part has more than one modification. There is a perception all at once, not only of each modification, but also of each part. These perceptions, however much they are multiplied, are different from one another, even though our attention cannot always distinguish them, and that is what makes confused perceptions, of which each distinct one contains an infinity because of its relation to everything external. Finally, that which is composition of parts outside is represented only by the composition of modifications in the monad; without this, simple beings could not be distinguished internally from one another, and they would have no relation to external things.’ To Masson (1715); AG 228-9
‘Each soul is a world in perspective, representing things outside according to its point of view, and confusedly or distinctly according to the organs that accompany it, . . . ‘ To Sophie Charlotte (1706); G 7.566-7
‘. . . although each created monad represents the whole universe, it represents more distinctly the body which is particularly affected by it and of which it is the entelechy. And as this body expresses the whole universe by the connection between all matter in the plenum, the soul also represents the whole universe in representing the body which belongs to it in a particular way.’ Monadology 61 (1714); AG 221
‘And since God’s view is a always true, our perceptions are always true; it is our judgments, which come from ourselves, that deceive us.’ Discourse on Metaphysics, 14 (1686); AG, 47
‘[N]othing can limit [a monad] to representing only a part of things, though it is true that its representation is merely confused as to the details of the whole universe and can be distinct for a small part of things only . . . It is not in the object but in the modification of their knowledge of the object that the monads are limited. They . . . are limited and distinguished one from another by the degrees of their distinct perceptions.’ Monadology 60; AG 220

February 27th, 2013 – Lecture: Expression, perception, soul, body

Occasionalism: Minds cause their states, but bodies are mostly passive, causally inert. Some occasionalists, even mind cannot change themselves.
- Wikipedia: Occasionalism is a philosophical theory about causation which says that created substances cannot be efficient causes of events. Instead, all events are taken to be caused directly by God.
If you have a three dimensional scene,
If you pick an angle from every point on the scene, draw a straight line.
If you take a plane and “stick it between” the lines to your point, you have a 2D representation of a 3D scene.
It can be so good you think you’re seeing the scene, and illusion.
These cases, expressions is a symettrical relation, if there is a correspondence, there’s going to be a reverse correspondence too.
A lot of the examples of expressions Leibniz gives are not this strong.
If you think of the combustion engine, there are going to be features of the machine which will not be able to be expressed in the model.
Very like loss of precision in computer science.
X is perceiving if and only if X is an individual substance and X expresses something material, divisible, and multitude.
There’s a substantial form, your substantial form, which expresses perfectly the body that you animate.
Look a map expresses the territory it maps, no way that it cognizes the territory.
I have true unity, which expresses this territory. According to Leibniz, this cognizes the territory.

February 27th, 2013 – Short Paper Assignment

The paper should be five pages in length (a little longer is acceptable) Some topics to write about are suggested below. The suggestions are starting points. You decide how you want to develop them. This may involve narrowing or focusing the topic. Remember – you only have five pages for this. The paper must make a clear point or claim, and it must make a strong case for this claim.

You may write on a topic not mentioned below provided that it involves material we’ve discussed. Please consult with me before beginning to write on such a topic. Even if you choose one of the listed topics, you may want to let me know how you intend to focus it.

According to Leibniz, there is no reason for doubting that God can form a concept of Adam so complete that everything that happens to Adam and the Universe can be derived from it. ‘It follows that he would not have been our Adam, but another, if he had experienced other events.’ (‘Remarks on Arnauld’s Letter’, etc., p. 73; G 2.42) What is the reasoning by which Leibniz purports to show that this conclusion follows? Comment on the argument and/or consider some implications, e.g. whether Adam could have refused the apple, whether it is necessary that Adam took the apple.
Arnauld complained that Leibniz’s argument that extension alone is not sufficient to constitute a substance (contra Descartes’ account of corporeal substance) depends on an arbitrary definition on an individual substance. Discuss the question whether or not this is a good objection.
Corporeal substances have a claim to be true unities in part because they are indestructible. Why is this important to Leibniz? Why do corporeal substances have this property? Consider some implications regarding what there is in the material world. You might consider, e.g., whether Leibniz can explain the fact that in some species, a worm can be cut into two and both half of it live; or, whether he can explain the fact that a cutting taken from a pear tree and grafted onto an apple tree grows and produces pears; or some other facts about living things. Do you think that the doctrine of corporeal substances is in some way problematic?

March 4th, 2013 – Passages on relational predicates and the metaphysical status of relations

“Therefore there seem to pertain to relations all the extrinsic denominations, i.e. those denominations which rise and perish without any change of the subject, simply because something changes in something else. Thus, a father becomes father as soon as his child is born, even though he, who happens to be in the East Indies, does not undergo any change. Thus, the similarity, which I share with someone else, is born and comes to light without any change in myself, but with a change in the other.” A 6.4.308, tr. Mugnai
NB: An “extrinsic denomination” of X is a predicate applied to X from something else, Y; e.g. X is the father of Solomon; X is greater than 3; X is similar to Plato.
“. . . there are no extrinsic denominations, and no one becomes a widower in India by the death of his wife in Europe unless a real change occurs in him. For every predicate is in fact contained in the nature of a subject.” A 6.4.1503 (1683-86?), tr. Mugnai
“It follows further that there are no purely extrinsic denominations which have no foundation at all in the denominated thing itself. For the concept of the denominated subject necessarily involves the concept of the predicate. Likewise, whenever the denomination of a thing is changed, some variation has to occur in the thing itself.” “Primary Truths” (1689?), L 268
- Leibniz is tying that there are no extrinsic denominations to the concept containment theory of truth.
- Titius expresses everything in the Universe, including “having son” at moment one not at “moment two.”
Philalethes-Locke: “. . . a change of relation can occur without there having been any change in the subject. . . [Titius, who is today a father] ceases to be so tomorrow, only by the death of his son, without any alteration made in himself.” Theophilus-Leibniz: “That can very well be said if we are guided by the things of which we are aware; but in metaphysical strictness there is no wholly extrinsic denomination (denominatio pure extrinseca), because of the real connection of things.” NE 227 (1702-04)
“In addition to the substances, which are the underlying objects, there are the modifications of the substances, which are subject to creation and destruction in their own right. And finally, there are the relations, which are not created in their own right but result from the creation of other things.” Notes on Temmik (1715-16), Massimo Mugnai, Leibniz” Theory of Relations, 155, tr. Mugnai
“It may be that dozen and score are merely relations and exist only with respect to the understanding. The units are separate and the understanding takes them together, however scattered they may be. However, although relations are the work of the understanding they are not baseless and unreal. The primordial understanding is the source of things; and the very reality of all things other than simple substances rests only on the foundation of the perceptions or phenomena of simple substances.” NE 145
“Relations and orderings are to some extent beings of reason, although they have their foundations in things; for one can say that their reality, like that of eternal truths and possibilities, comes from the Supreme Reason.” NE 227
“The reality of relations is dependent on mind, as is that of truths; but they do not depend on the human mind, as there is a supreme intelligence which determines all of them from all time.” NE 265

March 4th, 2013 – Reading

‘Meditation on the Principle of the Individual’ (1676)

Someone who understands an effect perfectly will also understand the cause of that effect.
- In this way, an effect involves its cause.
- There is a necessary connection between a complete cause and the effect.
- There is an obstacle however! Consider the argument:
  1. Whether two parallelograms or two triangles are put together, it will always produce the same square.
  2. Neither square can be distinguished from the other square.
  3. Therefore, not all complete causes have a 1 to 1 relation, they’re not functions.
- Leibniz solves this problem by raising the point of how no two objects in his metaphysics can be identical.
  - There will be some difference that retains the mind of the method in which change was produced.
  - This can be discerned.
This argument proves that matter is not homogenous.
- Our inmost mind is present both to itself and to matter, therefore nothing can be introduced to them which cannot be understood by us in some way.

‘Substance and Individuation in Leibniz’, Cover and Hawthorne, pp. 184-99

March 4th, 2013 – Lecture

To have a position in space is to exist at a particular distance from other things in time.
What Leibniz says about relations in general holds true for spatial and temporal positions.
The soul of Alexander expresses everything in the Universe, and we now know what this means.
What’s a relation?
- Non-identity is a relation
Two issues:
1. What is the metaphysical status?
2. Something.
Near the end of Leibniz’s life, there was a famous discussion about space.

Relations

A relational predicate: P is a relational predicate of S if P implies
1. That something other than S exists.
2. That thing (1) have a certain relation to S.
The motivation for the complete concept containment is from Aristotle.
- That something that is predicated on something individually cannot be predicated on anything else.
- Substances
The thought is that there are nine categories of axioms.
Of the nine, they cannot exist unless they exist in some substance.
Another part of Aritstotle’s doctrine is that some accident must exist in some substance, must exist in only one.
An accident:
- Aristotle: A thing that is said of or exists in another.
- Leibniz: Somethings that is predicated on another.
If you get the complete concept of an individual, the predicates of the individual are unique to that individual.
Accidents:
1. Quantity
2. Quality
3. Relations
4. Dispositions
Aristotle says a couple of interesting things about relations
1. A relation, unlike quality or quality, is an eccident of a particular subject, but it is directed to another subject, so it implies the exist of another.
  - “Of” something or “than” something
  - “Towardness”
2. A subject that has a relation can cease to have that relation without anything happening to that subject.
  - Socrates is taller than Simius, and then he is shorter than Simius, but nothing has happened to Socrates.
  - A thing can undergo a change with regards to its relational accidents without anything happening to that thing.
  - Cambridge change
  - No strictly extrinsic denominations
This shouldn’t come as a surprise (no extrinsic denominations)
You can go from knowledge of the expression, you can learn truths about the things expressed.
- Provided you know the relations to be preserved are.
There are two parts to the relation,
1. The soul expresses perfectly the S-body.
  - The body is surrounded perfectly by the S-body
The connection of all things is spatial continuity
When the son of Titius dies, there is something in Titius’ soul which expresses that change.
Leibniz denies that space is anything but an ordering relation
He agrees with Newton’s empirical evidence for absolute acceleration.
- But not absolute space and time.
Leibniz holds that space is relation of order
- What are we talking about when we talk about space?
  - We observe that many of the things that exist at the same time have an order of coexistence.
  - Say we have bunch of bodies that are simulteanosly existing, and some of them, maintain the same distances from each other.

March 11th, 2013 – Short Paper Assignment: Leibniz, Corporeal Substances, and Biology

The breadth and precision of the work of Gottfried Wilhelm Leibniz is astonishing. Writing between the mid-1650s and early 1700s, Leibniz’s vast contributions to mathematics and philosophy are overwhelming. As an early modern, Leibniz wrote just on the cusp of the bulk of the Scientific Revolution. There are accepted scientific discoveries taught to every child of the 21st Century that Leibniz never had access to. As a consequence of this, Leibniz’s theory could not have been conceived with many of what are now prominent scientific theories in mind. It is impossible to determine how Leibniz would have accommodated or changed his system had he known of the tremendous advances humanity has made since his time, but it perfectly possible to see how his theory stands against new knowledge. A quality of a good theory is being able to predict and account for new information. Leibniz’s conception of corporeal substances is of particular interest to this endeavor, as much has been discovered since Darwin about the nature of humankind and their animal, plant, and bacterial co-inhabitants. Leibniz developed a system to explain what it meant to be alive, to be animated, and why humankind appear to be different from other life 100 years before the fundamental theory of biology, evolution by natural select, had been seriously proposed. It was many hundred more before it was widely accepted and explored by the scientific community and the public. There are facts about the natural world which integrate nicely into Leibniz’s thought, but there are also facts and theories which stand in direct conflict with Leibniz’s view. Leibniz is renowned for his lifelong attempts at the irenicism of Catholicism and Protestantism, and in similar spirit, this paper will set out to point out and reconcile the differences in a modern understanding of science and biology with Leibniz’s conception of corporeal substance.

In order to explore Leibniz on corporeal substance, one must begin with an understanding of his account of substance. This begins with Leibniz’s Concept Containment Theory of Truth, that is, that a true proposition is a predicate which contains within it the concept of the subject. From this, Leibniz concludes that something is a substance if and only if its concepts contains the basis and reason for everything that can be truly said of that thing. This means that it contains all predicates which could possibly be said of that thing in the past, present, and future. This leads Leibniz to the following conclusions about substances:

No two substances are exactly alike (Principle of the Identity of the Indiscernables);
Every substance begins only by creation and cease to exist only by annihilation;
No substance can be divided into 2 substances or be formed by combining 2 substances;
Every substance is a mirror of the universe and of God (Mirroring Thesis); and
Every substance bears in some way the character of god, wisdom, and power

It is from this platform that one can understand Leibniz’s criticism of Cartesian corporeal substance. Leibniz holds that Cartesian bodies, Descartes’ account of corporeal substance, are unreal. Because every Cartesian body (C-body) is composed of C-bodies, Leibniz holds, a C-body is an aggregate. An aggregate can only be real if it’s components are real, but a C-body contains nothing but aggregates. Therefore, C-bodies are unreal. This means bodies are examples of vagueness for Leibniz, just like heaps of stones.

To solve this, Leibniz uses souls. The soul is the substance formed when when a substantial form and a body have true unity (as opposed to the accidental unity of rainbow and bodies). Leibniz points out that souls meet the definition for substances, as they are immaterial, not composed of parts, cannot be destroyed, cannot be corrupted, they contain all past and future states, and all states of the universe. He states that human beings definitely have substantial forms, but he is unsure about other animals. This is important for Leibniz because God needs a timeless way to discern and plan the course of the entire universe from every given substance, and bodies are vague and not timeless.

Armed with a crash course in the metaphysical status of bodies in Leibniz, the reader is prepared to analyze some facts discovered some facts about biology since Leibniz’s death. There is at least one discovery which Leibniz would likely rejoice in!

One-hundred trillion. That’s the number of bacteria present in every human in what is known as the “human micro biome.” The Stanford microbiologist Dr. David Relman says that humans are “like coral” in that they are an “an assemblage of life-forms living together.” There are ten times more bacterial cells in humans than human cells (the latter are much bigger). Every human has one to two and half kilograms of bacterial mass at any given time. Dr. Relman adds that it’s “humbling” (Kolata). This is a perfect example of how C-bodies are unreal in the metaphysical sense, and how they may be very like rainbows and heaps of rocks. It would be consistent with Leibniz’s point to ask a question like, is a human without a micro biome still human? The answer is, of course, intuitively quite obvious, but clearly become increasingly problematic. This supports Leibniz because it makes physical bodies vague aggregates, which require some metaphysical grounding.

But using this as evidence for Leibniz’s claims is problematic. Leibniz’s claim is that C-bodies are infinitely divisible, yet there is a fairly rigid definition of what is “alive” in biology. Cells are considered to be the “atom” in biology, where those sub-cellular parts that make a cell are not considered to be a living things on their own. A defender of Leibniz would respond that cells are, in fact, easily divisible. Cells are composed of 20 amino acids, five nucleotide bases, a few sugars, and some lipids (McKay); and that the parts not being alive is irrelevant, cells are still infinitely divisible. This type of argument is forever at the risk of committing “god of the gaps”-type argument from ignorance fallacy, where Leibniz’s opponent respond that these components actually have some other finite indivisibility, be it atoms, sub-atomic particles, quantum bosons, photons … This argument, however, is one which Leibniz’s metaphysical theory can be said to have predicted. Leibniz is right, and consistent with the evidence, bodies are vague. But Leibniz may be mistaken that bodies are infinitely divisible.

There is a technique in horticulture known as “grafting,” and it involves taking vascular tissue from one plant and inserting it into another plant so that they may form one plant. It is used when one plant has a desirable roots and trunk, and another plant with desirable stem, leaves, flowers, or fruits. It’s useful because a farmer can, for instance, take advantage of the fast growing qualities of one plant and the pretty flowers or tasty fruit of another. There are many other uses, ranging from repair to improving sturdiness to as a mere curiosity attraction (Hottes).

This is relevant to Leibniz because he holds that no substance can be divided into two or combined to form one. Leibniz also holds that any given substance can only come into being by creation. Perhaps for plants this is easily written off as, well, plants must not have substantial forms. It is intuitive, though not clear, that plants do not warrant souls. This would mean that grafting is not the combining or dividing of substances, and becomes unproblematic.

What happens as the argument moves closer to humankind, who Leibniz explicitly says have substantial forms, souls, and corporeal substance. Sponges are animals which do not have nervous, digestive, or circulatory systems, instead they rely on water to distribute nutrients and remove waste. Unlike all plants, sponges share the same kingdom as humankind: Animalia. And they have this curious way of reproducing. They can “bud”, an asexual means of reproducing where fragments of the animal fall off by means of being hit by a wave or akin, and those fragments go on to form an entirely distinct sponge (Ruppert, E. E., Fox, R. S., and Barnes, R. D.). This is a problem for Leibniz because sponges are animals which share many characteristics with humans, and if they are granted souls or substance, then it would be the case that a substance could be formed from the division of another.

But perhaps even though sponges are animals, they are still too simple to warrant souls. A defender of Leibniz may say that while sponges are classified zoologically as being similar to humans, there are relevant, explicit differences in complexity that distinguish sponges from humanity. From this, there are rational bases for believe that humankind have substantial forms while sponges do not. What is worrying about this for Leibniz is that it’s possible to move all the way up the tree of life and find instances of what appears to be substances being created by division of existing substances. Leibniz’s definition of substance has to answer to a growing list of asexual reproduction in and out of the animal kingdom, e.g. the splitting of worms, Timema insects using solely asexual reproduction for (evidently) millions of years, parthenogenesis in hammerhead sharks, the list grows.

But even if the critics of Leibniz grant that human beings are absolutely unique in all of life on Earth in being complex enough to warrant having substantial form, there are still problems. The primary means of explaining the complexity of life on Earth is the fundamental theory of biology, which is change over time by means of natural selection. This process implies two things: (1) There must have been some point of creation, which formed the substance on which change over time operated on, and (2) That there was some point in natural history in which the life that was to be humans did not have the prerequisite complexity to warrant substantial form. Leibniz theory of souls works if the story described in Genesis is assumed. Working under the premise of the modern understanding of science, a Leibnizian needs to be able to describe how a soul could be “gained” or “injected” into a sufficiently complex life form, after a long period of development.

Everything in the Universe contains marks and traces of everything else in the Universe, Leibniz holds. And on the subject of life on Earth, modern science corroborates his claim, as all creatures share the same language of life, DNA. Furthermore, a modern understanding of science would confirm Leibniz’s claims about the vagueness of bodies, in that it is unclear at what point one has a body and when one does not have a body. What needs explaining, however, is how this shared heritage can be while humankind remain unique in having substantial form. It is a testament to Leibniz’s genius that hundreds of years of rapid advancement of science and understanding of the natural world have not vanquished his theory. Instead, his system raises perplexing questions which inspire further research in both philosophy and natural science.

Works Cited

Bolton, Martha. “Leibniz (01:730:416).” Rutgers University Lecture, Spring 2013.
Hottes, A.C. Practical plant propagation: an exposition of the art and science of increasing plants as practiced by the nurseryman, florist and gardener. New York: De La Mare Company, Inc, 1925.
Kolata, Gina. “In Good Health? Thank Your 100 Trillion Bacteria.” Print, online, June 13, 2012.
McKay, Chris. “What Is Life and How Do We Search for It in Other Worlds?” Print, online, September 14, 2004.
Ruppert, E. E., Fox, R. S., and Barnes, R. D. Invertebrate Zoology. New York: Brooks / Cole, 2004.
Stanford Encyclopedia of Philosophy. “Gottfried Wilhelm Leibniz.” Online, 2013.

March 11th, 2013 – Lecture: The notion of force in physics and metaphysics

You could have two identical things different in space and time and that would be enough to make them different.
Nothing ever changes unless some intrinsic change in everything in the universe has a mark and trace of the change.
Every individual substance expresses the whole Universe.
- It contains a “pointer.”
Spatial and temporal relations have relations.
You can’t get things in different spaces in different times unless you have something to put them there.
There’s something in each of those things that makes them in those times and places.
PII: Often he argues from the PSR
- Two ways to go from PSR to PII:
  1. Look again at the argument in the third letter that Leibniz wrote to Clarke
Newton and Clarke think space has an absolute frame of reference
- Clarke thinks the material world is finite
```
                N
    x+--------+  y+--------+ 
     |possible|   |possible|
     |world a |   |world b |  
   W +---+    |   |   +----+ E
         |    |   |   |
         |    |   |   |
         +----+y  +---+x
                S
```
- God would have no means to prefer a to b, therefore space cannot be absolute by PSR.
- Divine preference argument: If there indiscernables in the actual world, then there is another possible world where they are switched. God could have no reason to choose one rather than the other. But PSR.
No Reason Argument: There is no reason for saying that A and B are individually different, so they aren’t individually different. Objections:
1. Why couldn’t it run the other way around?
2. The mere fact that something has no reason is not enough to suggest something. Perhaps there is no fact of the matter, no objective truth.
Premises
1. PSR
2. Exactly alike
3. Sufficnient reason to say alike
4. No possible differences

April 3rd, 2013 – Lecture: How the soul ‘knows’ what to do

The natures of soul and bodies means there are no possible connections.
All souls are self-contained.
There are no external forces or contributions.
All go along with perceptions and volitions.
On the other hand, the body obey mechanistic physics.
Logical positivists were bent on eliminating unverifiable, unfalsifiable claims.
- There are forms that are logically valid or not.
- There is science.
- And then any other discourse, either with forms or science, is meaningless.
- So values, emotive expressions, are meaningless.
If you go back to Aristotle, he’s an empiricist, and a metaphysics is an abstract science.
The scholastics mix up metaphysics and natural science.

We have to go back to these substanstial forms Aristotle
The scholastics confused a physics that appealed to forms.
Different kinds of forms, different powers.
Since this is a long story, since they had no grips on the forms and the source of the phenomea that was observed, they couldn’t say anything about the forms, but they caused the phenomena.
- If this has an error of circularity about it, that’s the point.
Leibniz is advocating this metaphysical theory about the phenomena we all agree up.
- Very abstract theory with physical evidence.
- Most general of the empirical scientists.
When you get to the positivists, metaphysics took an idealistic turn.
For science, it put matter into a secondary position.
Science is what we can count on, and metaphysics follows (or other way around).
Examples of positivist: Schlick, Karl Hempel (last of the great), Quinne, Oppenheim
He held German metaphysics responsible for the horrors of WWII.
There’s a big debate about the relevance of philosophy to physics
- Some say that philosophy has nothing to say about physics.
- Some say that philosophy and metaphysics has a big role to play in the armchair.
- Physics should be talking about something that is real.
Leibniz is in a pretty clear position, whereas the connection between metaphysics and science is unclear now.
- When we’re talking about the rules, laws of nature, that govern the world, we’re talking about necessary truth.
So we have the pre-establish harmony, what puzzles you most?
2 clocks always tell the same time.
1. They causally effect each other.
2. There’s a maintenance person who regularly adjests them.
3. Perfectly made each on its own tells the right time.

April 8th, 2013 – Handout

Analysis of the passage (L 530) in which Leibniz lists the constituents of a corporal substance: ‘If you think of mass as an aggregate . . . into one machine.’
- The first sentence is badly edited; it should read: ‘If you take the mass [massa] as an aggregate containing many substances, you can still conceive in it one preeminent substance, if indeed that mass constitutes an organic body animated by its primary entelechy.’
- The entire passage raises a question about the constitution of a monad.
  - Is the primitive passive power which joins with an entelechy to form the monad a mass in which many subordinate monads concur—so that the entelechy is joined with a mass which comprises many monads?
```
$Entekchy  + aggregate of monads$ = monad
```
    implies that the monad is an embodied entelchy. On this view, there is one substance.
  - Or, does the primitive power exclude other monads so that it pertains to that one entelechy alone?
```
$ Entelechy 
+ primary passive power exclusive of monads, 
  but related to the agg of monads
$ = monad
```
    implies that monad is a simple substance, comprising no other ends or monads; its passive power is somehow related to the agg of other monads. On this view, there are two substances: a simple substance which is a constituent of a compound substance.
- Robert Adams points out that Leibniz seems to have shifted from one view to the other when drafting this paragaraph:
  - When drafting the second sentence, he originally wrote:
    
    ‘For the rest, (a) to form the Monad or complete simples substance, I conjoin with the entelechy nothing but the [primitive passive force of the whole mass].
  - He deleted that and replaces it by;
    
    ‘For the rest, (b) I arrange in the monad or the simple substance, complete with an entelechy, only one [primitive passive force which is related to the whole mass of the organic body]. ‘
- The part in brackets in (a) suggests that the ent joins with the whole mass, which is the aggregate containing many substances—this comports with the 1-substance view.,
```
$Ent + body=aggregate$ 
```
  makes a monad; monads are embodied entelechies; an entelechy alone is not yet a substance.
  - This is the 1-substance view.
- But the part in brackets in (b) comports with the 2-substance view. A monad, alone, is a substance formed from an entelechy and a primary passive power which is distinct from the aggregate and found only in that monad–=a lthough the primitive passive power is somehow related to the aggregate.
```
$Ent+PPF exclusive of all monads$ 
```
  - makes a monad; monads are not embodied ents.
- But they comprise passivity which is related to the aggregate of monads which concur in the organic machine.
```
$Dominant monad + organic machine, infinitely composed of org machines$ make a corporeal substance, or animal. 
```
  - Leibniz may have hesitated, but he came down for the theory that monads are simple substances, and corporeal substances have mass which is the concurrence of many monads.
  - This would seem to commit Leibniz to the existence of corporeal substances, which enjoy substantial unity in virtue of one of their constituents, viz, the dominant monad.
  - But it also would seem to imply that corporeal substances are reduced to aggregates of monads.
    Yet aggregates do not have true unity. Is this a problem?
To De Volder (1704 or 1705); AG 181

I don’t really eliminate body, but reduce [revoco] it to what it is. For I show that corporeal mass [massa], which is thought to have something over and above simple substances, is not a substance, but a phenomenon resulting from simple substances, which alone have unity and absolute reality. Leibniz
To De Volder, 1704 or 1705, AG 182; (‘[[‘ indicates material in Leibniz’s copy not sent to De Volder)

Indeed, everywhere and throughout everything I place nothing but what we all acknowledge in our souls on many occasions, namely, internal and spontaneous changes. And so, with one stroke of mind, I draw out the entirety of things. Moreover, I also put corporeal forces where I put bodies, namely, among the phenomena, if they are understood as adding something over and above simple substances or their modifications. In just the same way, a rainbow is not improperly said to be a thing, even though it is not a substance, that is, it said to be a phenomenon, [[a real or well-founded phenomenon that doesn’t disappoint our expecations based on what precedes]]. And indeed, not only sight but also touch has its phenomena. [[And corporeal masses [massa] are like entities of aggregation, things whose unity derives from perceiving it. Leibniz

April 8th, 2013 – Lecture

Presentation from Lucas

A problem in the literature

A problem in the literature: is Leibniz a realist or an idealist? On the one hand, he seems committed to the claim that matter is a phenomenon, whereas only spiritual substances are real. But on the other hand, it is hard to square these claims with his deep attachment to natural sciences.

Thesis

Leibniz is both, he’s a realist because he’s an idealist, and an idealist because a realist. In other words: the distinction doesn’t fit into his thinking.

Argument

Considering the sciences of life as an influence for his metaphysics (especially the theme of unity, infinity and the pre-established harmony).

Examples

Being freed from the trivial schools, I discovered the Moderns and remember walking alone in a garden near Leipzig, called Rosendal at 15 and deliberating if I would keep the substantial forms. Letter to Rémond 14 January 1710 G III 606

In every machine, a principle of motion is needed. I think that in the animal motion comes from an already existing motion, as in an already rotating pendulum, or from the chyle, which mixed with blood, permits fermentation. Machina Animalis 1677 LH III 5 f. 12

Accordingly, it is one thing to describe the motion of a mill, but quite another to describe the different possible uses of this mill, e.g. cutting the wood. (…) All these operations ought to be explained separately, once the reason of the prime motion, or in other words, life is understood. Machina Animalis LH III 5 f. 12 1677

We can cut them [viz. the animals] open and examine them how and when we please Directiones ad rem medicame pertinentes LH III 1 31671

We will thus rightly assert that an animal is not only a Hydraulico-Pneumatic machine, but also in a certain respect a Pyrotechnic one. Corpus hominis et unicuscujusque animalis machina est quoedam LH III 1 2 1682

Since moreover we will at length demonstrate [that] force is one thing, motion quite another, and motion indeed inheres in an extend mass which is called in common bodies the substantial form, in living bodies the Soul, in Man the Mind, whence in animals the origin of sense as well as appetite, and the union of the soul and the body, and the way in which either the Soul acts in the body, or is acted upon by the body will be able to be explained with unexpected clarity Corpus hominis et unicuscujusque animalis machina est quoedam LH III 1 2 1682

The Bodies of Animals are Machines of perpetual motion, or, to put it more clearly, they are machines comparable to a certain fixed and singular species of perpetual organic motion that is always maintained in the world. Thus for as long as there are spiders there will be weaving machines, for as long as there are bees there will be honey-producing machines, and for as long as there are squirrels there will be dancing machines. Corpus hominis et unicuscujusque animalis machina est quoedam LH III 1 2 1682

Putrefaction can only consist in small works invisible to the naked eye Letter to Thomasius G I 19 1669

This is clear from the experiences done with a microscope. Indeed, there are maybe more than 800,000 little animals visible in a drop of water, and each of these animals is quasi as far from being a prime element as we are Project of a Letter to Malebranche June GP I 355 1679

I prefer a Leeuwenhoek who tells me what he sees to a Cartesian who tells me what he thinks Letter to Huygens, May 2nd GM 641 1691

On this point I have been helped by the transformations observed through microscopes by Swammerdam, Malpighi, and Leeuwenhoek, who are among the best observers of our day. They have made it easier for me to accept that no animal or other organized substance begins, though we think they do, and that when it seems that an animal starts to exist there is really only a development, or a kind of augmentation. And I have noticed that Malebranche and other able men have had views not far from this. New System §5 1695

It seems that one or other these two things must be concluded: that either in the efformation and organization of the bodies of Animals, as well as the other phenomena, everything comes to pass fortuitously and happens to be as it is, without the guidance and direction of any mind or understanding; or else, that God himself doth all immediately, and, as it were with his own hands, form the body of every Gnat and Fly, Insect and Mite, as of other Animals in generations True Intellectual System of the Universe, Chap. III, Sec. XXXVII, 2 1678

The physicist can explain his experiments, now using simpler experiments already made, now employing geometrical and mechanical demonstrations without any need of the general considerations which belong to another sphere, and if he employs the co-operation of God, or perhaps of some soul or animating force, or something else of a similar nature, he goes out of his path quite as much as that man who, when facing an important practical question would wish to enter into profound argumentations regarding the nature of destiny and of our liberty Discourse of Metaphysics §10 1686

Our body is a sort of world full of an infinity of creatures that would also deserve to exist Letter to Lady Masham G III 356 1704

That is why I define the Organism, or the Natural Machine, as a machine in which each part is a machine, and hence the subtlety of the artifice goes ad infinitum – nothing is so small that it be neglected – whereas the parts of our machines are not machines Letter to Lady Masham G III 356 1704

My two main meditations revolve around two things, to know unity and to know infinity. Letter to Sophie Charlotte G III 260 1696

Any organized body being plura entia, there would have to be many beings to render the bodies animated. Leibniz to Arnauld October 9th 1687

The Monad is nothing but a simple substance that compose the aggregates; simple, in other words without any part. Monadology §1 1714

Every portion of matter may be conceived as a garden full of plants and a pond full of fishes. But each leave of the plant, each member of the animal, each drop of its humors is again such a garden or such a pond. Monadology §67 1714

They [viz. the Monads] don’t have windows from which something could enter or leave. Monadology §7 1714

The living is a divine machine. 5th letter to Clarke GP VII 417-418 1714

A present pregnant of the future Monadology §22 1714

Extension was enough to Descartes; to Leibniz, life is needed Emile Boutroux, edition and introduction to the Monadology, Delagrave 2005

April 15th, 2013 – Passages

Freedom, such as is required by the schools of theology, consists in > > intelligence, which includes a distinct knowledge of the object > of > deliberation; in spontaneity, in virtue of which we > determine > ourselves; and in contingency, that is, in the > exclusion of > logical or metaphysical necessity. Intelligence > is, as it were, > the soul of freedom, and the rest is as its > body and basis. The > free subject determines itself by itself; > and this according to > the motive of the good perceived by the > understanding, which > inclines it without necessitating it; and > all the conditions are > contained in these few world. > Theodicy 288; G 6.288, tr. > Rutherford
In order to better understand this point, we must realize that a > > genuine spontaneity is common to us and all simple substances, and > > that in the intelligent or free substances this becomes a > dominion > over its actions. . . T 290-1; G 6.298, tr. > Rutherford
[E]veryone who accepts immaterial indivisible substances attributes > > to them a simultaneous multitude of perceptions, and > spontaneity > in their reasonings and their voluntary acts. I am > therefore only > extending that spontaneity to their confused and > involuuntary > thoughts, and showing that their nature is to > contain relations to > everything that is external. Reply > to the Comments in the Second > Edition of M. Bayle’s,etc., WF > 118
Change [transitio], or variation, itself . . . is nothing but a > > complex of two states which are immediate and opposite to each > > other, together with a force or [seu] reason for the change, which > > reason itself is a quality. MP 134
The laws of appetite [are] the laws of the final causes of Good and > > Evil. PNG 3
Souls act according to the laws of final causes, through appetites, > > ends and means. Bodies act according to the laws of efficient > > causes, or of motions. And the two realms, that of efficient > > causes and that of final causes, are in mutual harmony. Mon > 79; AG > 223
- This suggest that laws of final causes that pertain only to souls.
- Laws of efficient causes that apply only to bodies.
- But there are laws of final causes that apply to bodies, namely natural telological ones.
. . . with confused perception and a corresponding appetite (which, > > with some, you might term instinct) [the soul] imitates divine > > infinity, in such a way that nothing happens in the body that > the > soul does not in fact, perceive, nothing concerning which > [the > soul] does not exercise [its] appetite . . . even if we > are > unaware. Animadversiones . . . Stahli, D 2.2.135; > RF, 28
. . . let us say that everything in bodies happens mechanically, or > > in accordance with laws of motion, and that everything in the > soul > happens morally, or in accordance with appearances of good > and > evil, in such a way that even in our instinctive and > involuntary > actions, there is in the soul an appetite for good > or an aversion > to evil which drives it, even though our > reflection is not able to > pick it out in the confusion. > To Sophie Charlotte (1704), WF 224
Leibniz explains what is required for an appetite of the soul to be > > executed by the body: [I]t is necessary that the appetites and > > consequently the perceptions from which they arise attain in > > perfect detail everything which brings this about in the organs. > > For this reason: . . . will is not always sufficient to make > the > body act according to its desire, when the exact perception > of the > means is not conjoined with it . . . Thus it is > necessary that end > and means should always be joined together > in the soul, as causes > and effects are in the body, in order > that the desired effect > should be executed. To > Hartsoeker, G 3.509-10
[I]t is true that the appetite cannot always completely reach the > > whole perception toward which it tends, but it always obtains > > something of it, and reaches new perceptions. Mon 15
. . . as I should prefer to define it, perfection is degree or > > quantity of reality or essence . . . To Eckhard (1677); L > 177
. . . there are no perceptions which are matters of complete > > indifference to us; NE 162

April 15th, 2013 – Lecture

Intelligence is the soul of freedom
The subject of freedom “chooses itself for itself.”
Rutherford is worried that spontinaeity is wonderfully general.
Applies to everything all the time.
Monadic spontienaty is a necessary but not sufficient condition for Leibniz.
It occurs when there is an absence of something that is not always abset.
Freedom from external causes, monad is always free from external causes.
Somehow Rutherford is thinking that Leibniz needs to add to spontinaiety some further constraint, some other kind, not always absent, because we don’t always act freely.
- When we do, something is absent that isn’t always.
- Spontaneity can’t be freedom because it’s present in all cases.
- Some sort of break from what a monad can do.
- Absent when a monad acts volutarily.
Rutherford is seeking this in the area where sponteoity is excluding external constraints, that causal area, two sorts of circumstances, or conditions under which, a monad causes itself to undergoe a change, where a monad acts freely.
Spontenaity is a necessary condition of freedom, not sufficient.
There are many monads that are not intelligent.
- This involves the capacity to think of yourself as yourself.
- There are many monads that are not able to think of themselves.
- Bale’s dog thinks and feels and whatever it might be, anticipating future states, but it cannot think of itself as doing that.
- We, on the other hand, have a self-reflective quality about ourselves.
- This is a condition when we have a freedom of action.
Distinct knowledge of the object under consideration.
It is not always the case that a disctinct monad perfectly understands all the possibilities.
Leibniz is stressing the importance of intelligence.
Freedom and intelligence gives us freedom over our actions.
Leibniz is placing a lot of clues about the importance.
We do think that free action requires freedom from certain constraints.
Rutherford is wanting a freedom from causal constraints.
Leibniz thinks distinct knowledge is the key.
Rutherford’s project is to assume that Leibniz hasn’t laid out a full view.
Rutherford wants to suggest that Leibniz has the resources to make the distinction.
Part of his take on this, there is within a monad, a distinction between a monad is active and monad is passive.
There’s a little section where Rutherford talks about change, the constitution of the for model of substance.
I’ll come back to it.
It articulates some of the things that Rutherford’s proposal has to do.
There is a force or reason to take something from one state to another.
When we get an account of how change occurs in the monad we need to be able to explain what goes on in a monad in these two ways.
This brings Rutherford to what he calls “teleology.”
Final cause of A‘s doing X why A does X in terms of an end doing X is likely to produce.
It’s common to describe freedom in terms of people’s actions, “final cause” in Leibniz’s time, and those are ends from the point of which things act, when an act is described by final actions it is described in terms of “goodness.”
- If you’re going to talk about final causes, you’re assuming that changes often occur that being about good ends, then you need some explantion about why changes bring about good ends.
- When you explain things by final cause, you assume that there are explantions.
  - Leibniz would say that god made the world this way.
  - “The eyes operate in order that we see things and that is good.”
In monads there is nothing but perception and appetite.
- Perceptions are states of the monads that express something something.
- Appetites are derivative forces, driving the soul from perception to perception to perception (?).
- The perception that a monad has at a given moment
- When in acting we realize something good,
Leibniz need not deny that appetites take a monad from a past perception to a future perception, but I think he means to say that the ends towards the appetite are for and the impediments it meets (present states that precede future states), doesn’t occur in body.
- There is a kind of law that proper to souls and a kind of law that are proper to bodies.
Force F operates in accord with N-telelogical laws if and only if the effectiveness of F in bring about a change from S₁ to S₂ is explained by the objective goodness of S₂.

April 17th, 2013 – Passages

With regard to the preestablished harmony between the modifications > > of the soul and those of the body, and the execution of our > > appetites by the bodily organs, it is necessary that the appetites > > and consequently the perceptions from which they arise, should > run > in perfect detail with all of that which happens in the > organs, in > that these appetites be executed. This would appear > to us if it > were possible to analyze our confused perceptions. > Otherwise, it > would not be an appetite which is perfect and > complete with regard > to the whole of its object, but only > something approaching it. And > because our understanding and > consequently our will is not capable > of this detail, our simple > will (if it goes to the end without > going to means and means > for the means) is not an appetite the > body is obliged to follow > and to execute. Execution by the body > happens only in unimpeded > interior voluntary movements, where > confused appetite seconds > the will or distinct appetite in perfect > detail. However our > interior involuntary motions do not cease to > answer to our > confused and unconscious appetites, but these > movements depend > as little on the empire of the will as these > appetites depend > on our understanding, so that the will is not > always sufficient > to set the body in motion according to its > desire, when the > perception of exact means is not joined with it. > Letter > to Hartsoeker, 30 October 1710; G 3.509-10
- Set some goal, but you can’t go directly to the goal, you have to do something to get there.
- If you don’t have the means to get there, you wont get there.
- What are the means by the soul may or may not get there?
- It cannot be anything but the types of perceptions …
. . . fundamentally pleasure is a sense of perfection, and pain a > > sense of imperfection, each being notable enough for one to become > > aware of it. For the minute [sc. confused] perceptions of some > > perfection or imperfection, which I have spoken of several > times > and which are as it were components of pleasure and of > pain, > constitute inclinations and propensities but not outright > > passions. So there are insensible inclinations of which we are > > unaware. NE 194
- Pleasure is a distinguished sense of perfection
- While pain is a distinguished sense of pain.
- “Inclinations and propresenties”, insensible inclinations which we are unaware of.
What usually drives us are those minute insensible perceptions which > > could be called sufferings that we cannot become aware of, if > the > notion of suffering did not involve awareness. These minute > > impulses consists in our continually overcoming small > > obstacles—our nature labors at this without our thinking about it. > > This is the true character of that disquiet which we sense > without > taking cognizance of it. . . for we are never without > some > activity and motion, simply because nature continually > labors to > be more completely at ease. NE 188
- Here the emphasis is on aversions.
- Our insensible perceptions are attached to aversions, the activity is to remove the source of the disquiet or of the semi-suffering.
- There are many impulses of this of the soul at any moment.
- So that the soul will be more at each.
- There are these little urges that are desiderous in nature, but there is still something that is in this sense bad. (???)
It is true that the appetite cannot always completely reach the > > whole perception toward which it tends, but it always obtains > > something of it, and reaches new perceptions. Mon 15; AG > 215
Re. the antecedent will of God (will prior to arriving at a definite > > volition) and the subsequent will of God (his definite eternal > > volition): Now this consequent will, final and decisive, > results > from the conflict of all the antecedent wills, of those > which tend > towards good, even as of those which repel evil; and > from the > concurrence of all these particular wills comes the > total will. So > in mechanics compound movement results from all > the tendencies > that concur in one and the same moving body, and > satisfies each > one equally, insofar as it is possible to do all > at one time. T > 22, H 137

April 17th, 2013 – Lecture

Everything that is is good.
- Anything that’s bad is a privation.
- Absence of “potential good.”
Voluntary is something that happens because of distinct cognition.
- The army, the workers, of the will, is the involuntary.
- They’ll do what they’re inclined to do.
We should be looking at the third condition, the circumstance that is sometimes present in the soul, and sometimes not present in the soul.
```
soul
```
———-> +—–+ -> | | —> / |body | -> / | | +—–+ \<—–
We do will things and our voltions have varying degrees of success.
Leibniz is set against any soul body interaction.
Pre-established harmony.

April 22nd, 2013 – Passages

‘Perception is the expression of many things in one, or in a simple substance: if it is combined with the reflection of the percipient, it is called thought. We judge perception to apply not only to us but also to other living things or organic beings, and thought to be not only in us but also (and indeed most perfectly) in God. This quality of the percipient is treated in logic. “Nova Methodus Discendae Docendaeque Jurisprudentiae”, A 6.1, p. 286
‘So ‘understanding’ in my sense is what in Latin is called intellectus, and the exercise of this faculty is called ‘intellection’, which is a distinct perception combined with a faculty of reflection, which the beasts do not have. Any perception which is combined with this faculty is a thought, and I do not allow thought to beasts any more than I do understanding. ‘ NE 173
Locke challenges Leibniz to name a proposition which is innately known: “I would name . . . the propositions of arithmetic and geometry, which are all of that nature; and among necessary truths no other kind is to be found.” NE 86
With regard to ideas of contingent things: “But there is no term which is so absolute or so detached that it does not involve relations and is not such that a complete analysis of it would lead to other things and indeed to all other things.” NE 288
A. Within a human mind, there are sets of ideas so related to thoughts of propositional truths that an ordered set of ideas $1,2,3,…$operating in accord with a tendency to produce thoughts of propositions framed by an ordered set of connectives $c, d, e, . . . $ has this relation R to acts of thinking a proposition P just in case $1, 2 ,3, . . .$ and $c, d, e, . . . $ contain all the ideas and proposition framing tendencies that are essentially individually necessary and jointly sufficient to cause thoughts of P.

B. In God’s understanding sets of ideas are related to truths in such a way that an ordered set of ideas $A, B, C, . . .$ and an ordered set of connectives $c, d, e, . . .$has R* to a truth just in case $A, B, C, . . . $and $c, d, e, . . .$ contain all and only the ideas and connectives from which the truth results.

April 22nd, 2013 – Lecture

One is abbreviations, so something stands for some content, you can then replace every instance with that abbreviation.
- You come to think of abbreviations as shorthand for the actual concept.
- One strategy:
  - Say you want to think of 50, and you write:
```
|||||||||| |||||||||| |||||||||| |||||||||| ||||||||||
```
  - This requires having 50 things in your mind.
  - But if 10 stands for ||||||||||,
```
10 10 10 10 10
```
  - Etc
- Other strategy:
  - If you want to think of a circle, draw one, and you have a model that certain facts will be true about and those things will be true of the abstract circle.
The problem is: How do we think about things that are complex.
He’s talking about propositional knowledge, Leibniz thinks there’s a big different between propositional and
Implications of Leibniz’s perception:
1. Implications cannot be mistaken (it’s the judgements that are mistaken).
2. It’s impossible to perceive something that does not have parts.
  - The only way things register perceptively is through parts.
  - This is significant because we can think about monads.
  - This means we must have a way of knowing things that is not perceptual (intellectual).
  - From the letter to Arnauld, he’s explaining what expression is, and he’s talking about geometric expressions, and then he says that perception is universal (or something … )
  - We do not have perception of things without parts, true unities, propositions.
  - Intellect is linked with the ability to reflect.
How do states of the soul express things that are represented by thoughts?
- What’s the metaphysical status of things like circles, numbers, etc.
  - Ideas are something that is in our mind.
  - Traces and
- How do we get into contact with them?