48. The Bayesian Belief: 9. The Syllogism of Aristotle

[I certainly enjoyed writing my top ten things not to get Dad for Fathers Day [38] [39] [40] [41] [42] [43] [44] [45] [46] [47].  And I had a great summer break.  Thanks for asking.  But, all things end, and we must return to the business at hand.

To continue:   I have been discussing whether Bayes’ 1763 essay was devised as a challenge to the work of David Hume and I have been tracing the history of induction as a method of acquiring scientific knowledge. Induction begins with Aristotle and is introduced in Aristotle’s Posterior Analytics.   The Posterior Analytics is part of Aristotle’s Organon — his collection of essays on logic.  Aristotle’s Prior Analytics and Posterior Analytics are often considered together. The Prior Analytics focuses on syllogistic logic and deduction. The Posterior Analytics’ focus, on the other hand, is on induction and demonstration.]

Given that the syllogism is central to Aristotle’s logic and that Aristotle’s logic is important to the provenance of Western thought, it might be helpful to have a basic grasp of what Aristotle intended. (In fact, it is so important, that I have been avoiding it. There is a large and daunting volume of arguments and discussion regarding Aristotle’s Prior Analytics both currently and historically. No matter what I say, someone else has already said it and someone else has already argued against it. Stephen Hawking may have deemed philosophy dead but that corpse seems to keep rattling on. With fear, I proceed.)

As you search for different explanations of what exactly a syllogism is, you will find that those explanations range from the simple to the seemingly incomprehensible. For example, here is a description from the Stanford Encyclopedia of Philosophy:


All Aristotle’s logic revolves around one notion: the deduction (sullogismos). A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory. What, then, is a deduction? Aristotle says:

  • A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so.  (Prior Analytics I.2, 24b18-20)

Each of the “things supposed” is a premise (protasis) of the argument, and what “results of necessity” is the conclusion (sumperasma).

The core of this definition is the notion of “resulting of necessity” (ex anankês sumbainein). This corresponds to a modern notion of logical consequence: X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true. We could therefore take this to be a general definition of “valid argument”.


 

If the above definition represented your first foray into syllogisms, it is likely that your understanding would not be greatly increased. Now, the author(s) of this explanation are not trying to be difficult. They are trying to be precise. That is because the craft of philosophy is focused on words and their definitions. Words about ideas, words about what things are or may be, words about words.

It is not just academic twaddle. It is about how we use words — to persuade, to reason, to gain knowledge. To define what is and what is not.

Words matter.

When codified in law, words define whether or not you remain free or imprisoned. When placed in a social contract, words define your relationship as either matrimonial or non-committal — “Do you take this man (woman) as your lawfully wedded husband (wife)?”  Words are not just noise, they are ideas and thoughts made concrete.

To illustrate how words and their definitions are important, particularly in the context of syllogisms, let’s review an example of a syllogism. As do all syllogisms, it contains two premises and a conclusion.

  • All men are mortal,
    Socrates is a man, therefore,
    Socrates is mortal.

48. Socrates

Or, alternatively (because this is the 21st century):

  • All women are mortal,
    Hypatia is a woman, therefore
    Hypatia is mortal.

48. Hypatia

This form of syllogism is labelled ‘Barbara’ (not by Aristotle but by later scholars who studied Aristotle). Barbara is a mnemonic for AAA, where A reflects the Latin phrase Affirmo, or I Affirm. Like so:

  • B
    A (I affirm): All women are mortal,
    R B
    A (I affirm): Hypatia is a woman, therefore
    R
    A (I affirm): Hypatia is mortal.

So, a little bit of Greek, a little bit of Latin. Consider yourself erudite.

The mortality of Socrates is a common example of a syllogism (again, not by Aristotle but by those who studied Aristotle). In his wonderful Problems of Philosophy, Bertrand Russell observed that Socratic mortality represented the “stock instance of deduction that is always given in books on logic.”

Socrates, as protagonist, has a long history. Writing in the 3rd century, Sextus Empiricus described an example of those categorical syllogisms favored by Peripatetics (followers of Aristotle) as:

  • Socrates is a human being,
    Every human being is an animal, therefore,
    Socrates is an animal.

However, despite their use throughout antiquity and contemporary texts, Socratic syllogisms may not be the best example of what Aristotle intended. This point was raised by Lukasiewicz (whom we briefly discussed in 37) in his review of Aristotelian thought through the perspective of 20th century logic.

Now Socrates was many things. But the one thing he was not, was a category. And that, according to Lukasiewicz, was exactly the problem.

Socrates, like you and I, is singular. There are only one of us. To Lukasiewicz, singular items or terms have no place in Aristotle’s’ syllogism and, when used, they should be deemed false.

It would be easy to reject Lukasiewicz’s argument as trivial.  And certainly some critics did so. Yet, underneath this small point lies an important observation about the intent and purpose of Aristotle’s logic.

But to understand why this is so, we need to first understand how Aristotle defined the building blocks of the syllogism or its terms and premises.

And that is the focus of my next post.

[But first I am going to go off on a side trip and take a brief look at men, semen, and evolution.  Not to worry, I will come back to Aristotle.  I know that you are really really very excited but you will just have to calm down.]

  • Aristotle’s Logic.  Stanford Encyclopedia of Philosophy
  • Lukasiewicz, J.  (1957). Aristotle’s syllogistic from the standpoint of modern formal logic (2nd ed.). London: Oxford University Press. [First two chapters].

 

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