Kreeft and Hume's Critique of the Syllogism

 

Peter Kreeft’s Socratic Logic (2004) is more than a textbook on classical, Aristotelian logic. It is also a philosophy of what is called “critical thinking,” in the parlance of our times. As a former teacher’s assistant instructor of introductory logic, I love the book. But I have some questions and perhaps some criticisms of the philosophy part, which has been valuable to stimulate further thinking on the issues raised there. Here I want to reflect on what he writes about Hume’s critique of the syllogism and its connection to the problem of induction. 

. . . 

A syllogism is to argument what an atom is to matter: a fundamental unit whose properties are indispensable for understanding the whole, but which by itself cannot explain the richness of the larger structures built from it. What is a syllogism and what does it have to do with ordinary reasoning? Consider the following argument: 

Many parents lie to their children because they tell them that Santa Claus brings the presents. 

Or you could express it like this: 

Many parents tell their children that Santa Claus brings the presents. Therefore, the parents are lying to their children. 

So like every argument, there is a premise and a conclusion. 

         Premise:

Many parents tell their children that Santa Claus brings the presents.

 

         Conclusion:

Therefore, the parents are lying to their children.

To think well about this argument, you would have to inquire as to whether the terms were clear (parents, children, Santa, lying, bringing presents) and, if so, whether the premise was true: that is, you can only think about whether the premise is true if its truth doesn’t depend on what different people may mean by the terms. Here, I am just focused on logic.

   And focusing on logic, you can perhaps see that, just like that, the conclusion can’t follow because the premise says nothing about lying at all, so you can make a deduction about lying from that premise alone. And the premise contains a term, Santa Claus, that is not in the conclusion. Thus there is an implicit premise containing lying, one that connects lying with Santa Claus. 

1)   Many parents tell their children that Santa Claus brings the presents. 

2)   Anyone who tells a child that Santa Claus brings the presents is lying to that child. [implicit premise] 

3)   Therefore, many parents lie to their children.

 

This is now a syllogism. I want to further analyze it before coming to Hume’s criticism so as it bring out the force of that criticism. There is often a tension between English grammar and logical grammar that need not confuse you. In English grammar the predicate is the entire verb phrase: 

          …tell their children that Santa Claus brings the presents 

Logical grammar only cares about what predicate is being attributed to the subject, what general set of things the subject belongs to. So we might rewrite the sentence as: 

{Many parents} are {people who tell their children that Santa Claus brings the presents}.

 Now the subject term is still parents, but the predicate term is people who tell their children that Santa Claus brings the presents. Logically, the statement asserts that parents and caregivers belong to the set (or class) of people who tell their children that Santa Claus brings the presents.

    So rewriting the entire argument, including the implicit premise, in logical form (classical), and adding the logical quantifier (only three: all, no or some) you get:

 

1)   Some {parents} are {people who tell their children that Santa Claus brings the presents}. 

2)   All {people who tell a child that Santa Claus brings the presents} are {people who lie to their children}. [implicit premise] 

3)   Some {parents} are {people who lie to their children}.

 

That is the logical grammar or the original argument, one possible way of describing the logical grammar, namely, according to Aristotelian logic. I will keep coming back to this example. 

. . . 

  Hume's criticism of the syllogism is that it cannot teach us anything new. Consider the classic example: 

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

 Hume's argument is that the conclusion is just contained in the premises. If "Socrates" is already included under "all men," then nothing genuinely new has been discovered. Deduction merely unfolds what was already there implicitly. So if the conclusion contains more than the premises, the argument is invalid. But if the conclusion contains no more than the premises, then the argument is useless because it tells us nothing we did not already know. The syllogism is either invalid or trivial.

    Applied to the example above, Hume would say the conclusion is already contained in the premises. If you already know that some parents belong to the class "Santa-tellers," and all Santa-tellers belong to the class "people who lie to their children," then you have not learned anything fundamentally new by concluding that some parents lie to their children. The syllogism merely rearranges what you already accepted. 

. . . 

   Kreeft argues that Hume equivocates on the phrase "already known." The conclusion is contained in the premises implicitly, but not explicitly. That difference is everything. He uses a number of analogies. A sculptor "contains" the statue in the marble, but the statue still has to be carved out. Likewise, a syllogism makes explicit what was previously only implicit. Another analogy is that of unpacking luggage. You already possess everything inside the suitcase, yet opening it genuinely increases your usable knowledge. Nothing has been added, but something has been revealed.

    His deeper point is that Hume assumes that knowledge is like collecting more and more isolated facts. The Aristotelian instead sees knowledge as primarily understanding relations. What does that mean?

    Compare Hume and Aristotle. Suppose someone accepts the premises: 

Some parents tell their children that Santa Claus brings the presents.

Everyone who tells a child that Santa Claus brings the presents lies to the child.

 For Hume, then you already know that some parents lie to their children. The conclusion is simply hidden inside the premises like a folded piece of paper. The syllogism merely unfolds it. Knowledge, on this picture, is essentially possession of information.

   The Aristotelian view is different. Suppose a parent says: "I never lie to my children." Then, after some discussion, he also admits: "Yes, I tell them Santa brings the presents." The syllogism forces him to ask about the relation between these two beliefs. He may never have seen that relation before. The syllogism shows that the following three judgments cannot all stand together: 

1. I tell my children Santa brings the presents.
2. Anyone who tells children Santa brings the presents lies to them.
3. I never lie to my children.

 The intellectual gain is not a new isolated fact. It is an understanding of how these judgments fit, or fail to fit, together.

    For Aristotle, science/knowledge/understanding (epistēmē) is not a collection of propositions expressing states of affairs. It is seeing why things belong together. The example syllogism does not merely state that "Some parents lie." It reveals a conceptual structure. If telling children that Santa brings the presents is true and belongs under lying, then some parents must also belong under people who lie to their children. The syllogism makes that relationship visible.

    Imagine someone who owns three pieces of a jigsaw puzzle but has never fitted them together. For Hume they already possessed the fourth piece because it was implicit in the pieces. For Aristotle, what they lacked was not another piece but seeing how the pieces fit together. That, in my opinion, is genuine understanding. 

. . .

    I think my example may point beyond Kreeft. Suppose someone rejects the second premise. The issue is what counts as a lie, or does this particular kind of case constitute lying. So the syllogism has performed a philosophical service by identifying the exact conceptual relation that is in dispute, allowing us to locate the fault line. The disagreement is about whether telling children fictional stories as true stands in the relation of species to genus with lying. That is also an increase in understanding.

    Kreeft wrote that knowledge consisted in understanding relations. If he means by that that knowing/understanding is a seeing of the conceptual and logical relations among terms and propositions, then that makes sense to me. Whether or not anyone changes their mind about the Santa question, the syllogism identifies exactly which relation must be examined: the relation between telling children that Santa brings the presents and lying. Once that relation is made explicit, the real philosophical discussion can begin. The syllogism has not settled the debate, but it has revealed its logical structure. It makes the architecture of a disagreement visible. That is more than saying it "unpacks" what was already implicit.

. . .

The problem raised by this argument is conceptual, not logical. The syllogism itself cannot settle the question. Everything depends on how we understand lie. If one person’s understanding of the concept is intentionally asserting what one believes false in order to create a false belief, then the premise is prima facie true. If another understands lying in a richer moral sense involving betrayal of trust, then prima facie the Santa stories are not lies. The syllogism remains valid either way as long as the same definition is used in both premises, but you get different statements depending on the meaning attributed to lying. We have to settle the question of whether the Santa stories are real lies.