How Do Philosophers Use Logic?

One of philosopher’s favorite activities is distinguishing between things. Where we have some concept like “moral action” or “beautiful objects”, we investigate their nature by distinguishing kinds of moral action or types of beautiful objects.

In everyday conversation, one of the best and most often practiced ways of making progress in a field or an activity is to reason, that is to assert something and then make other statementswhich in some way support it. In the context of Humanistic or religious debate, when a person commits themselves to a belief about humanity’s purpose or the meaning of existence, giving reasons which structurally support the claim is an effective way of persuading another or exploring one’s own views.

The Set Up

These structures, in a philosophical context, are called arguments, and not only do they have a logical structure but they also have components, which are expressions of what philosophers callpropositions. Consider the following, and perhaps familiar, argument:

  1. If the building-blocks of life are irreducibly complex, then there is a Creator.
  2. The building-blocks of life are irreducibly complex.
  3. Therefore, there is a Creator.

Philosophers have given formal names and definitions to the structure and components to this argument, which they also take to be distinguishable. To tease out one from the other, it’s helpful to replace the string “the building blocks of life are irreducibly complex” with the some symbol, for instance p, and “there is a Creator” with another shorter symbol, say m. This yields the following,

  1. If p, then m.
  2. p.
  3. Therefore, m.

Now this gets very interesting: If you fill in the p and m symbols with a different sentence – any sentence! – you’ll find that even though the argument is completely logical and valid you may or may not agree with the reasoning. But how could this be if all these forms of reasoning follow the same structure? For instance, consider the following replacement of p and m:

  1. If the year is 2014, then the President of the United States is Barack Obama.
  2. The year is 2014.
  3. Therefore, the President of the United States is Barack Obama.

Imagine a person, perhaps it’s even yourself, that wants to grant or accept the truth of the reasoning in the Presidential argument but not in the Creator argument. What tools does the person have for rejecting one but not the other if they follow the same structure? They both seem to contain the same method of reasoning, but one must be making someother mistake!

Soundness and Validity

This is where philosophers distinguish valid from sound, which you’ve probably encountered already in day to day conversation.

Soundness is a relatively easy to understand. An argument is said to be sound only when it’s premises are actually true. In other words, the following argument is not sound:

  1. If Bertrand Russel is alive, then the Internet is pink.
  2. Bertrand Russel is alive.
  3. Therefore, the Internet is pink.

What? That’s exactly right: This argument is not sound. Beginning with (1), a reasonable person will deny that Bertrand Russel’s living presence has nothing to do with the color of the Internet, which is an absurd idea in itself. Of (2), a gloss of his Wikipedia page will show that Bertrand Russel has been deceased for some time. Because (1) and (2) are not true, using them to get (3) is no good.  Now some day we might find, against all perceptions to the contrary, that the internet has color and is pink, but it’s not pink because of (1) and (2).

Validity is somewhat more tricky to understand. Validity is what applies to what I’ve been calling the “structure” of argument. Validity doesn’t have to do with the truth of the premises, but the structure or form of the argument. An argument is said to be valid only if the premises are true and the conclusion must also be true. Notice of our absurd Colored Internet reasoning that if it were the case that Bertrand Russel’s being alive really did affect whatever the color of the Internet is, and also if Bertrand Russel really was alive, that we’d be forced to accept that (3), the “Internet is pink.”  If premises (1) and (2) are true, then (3), i.e. the conclusion, must also be true.

To really reinforce this notion, go back to the symbols of p and m. Construct an “if-then” statement you believe is true with p and m, and notice that when the “if-then” is true and the “if clause” is true, you feel compelled to accept m.

Now back to our imaginary person who wants to reject the Creator argument above and accept the Presidential argument. With this distinction they can now say of both arguments that they are valid but only the Presidential argument is sound. We can see two things in the Creator argument. Of (1), they could say that irreducible complexity can arise in other ways than by a Creator or Designer. Or of (2) they might say that there is nothing which is irreducibly complex. Either of these empirical or theoretical observations would show the argument isn’t sound. And because the Creator argument isn’t sound, our reasoner does not accept it, even in the face of its validity.

An Open Question

What I find very interesting question about this distinction is where does validity “come from?” What I mean is, it is very obvious to me and everyone I’ve encountered that modus ponens (the name given to the structure of the arguments in this piece) is a “good” way of reasoning, but where does this goodness come from? Is the source of its goodness some deep truth about the nature of the universe which we all have access to? Or is the source its repeated success in our repeated use? In other words, is it just that it works?

Another way philosophers pose this question is, is valid reasoningnormative? Do we form norms about ways of reasoning and impose them on ourselves and others? Or have we accessed the truth about reasoning? One  fact relevant to this question is that you can construct a “truth table” with this form of reasoning and show that in every case of soundness you get a true conclusion. It is objectively demonstrable, then you can investigate it yourself.

But objectivity and “deep truths” aren’t the same. For instance, it’s objectively demonstrable that Rutgers University educates many people, but this isn’t a “deep truth about the Universe”.

What do you think? Is valid reasoning fundamentally true in some way? Or do we construct for ourselves norms which are “just reliable” or something akin? Is this question even sensible to ask?