A short post about Aristotle and syllogisms

Aristotle is not the first person you would expect to be making regular appearances in a discussion of science-fiction awards but he keeps appearing primarily due to the chief Rabid Puppy’s frequent mentioning of him. A recent post from that quarter has come out battling in defense of Aristotle’s logic:

Now the SJWs are openly coming out against Aristotle’s logic at File 770:

Stevie on June 4, 2015 at 6:21 pm said:
Incidentally, had not Athens been Lords of the Sea then we not have their Golden Age. We would not have the works of Aristotle. For one brief moment I thought wistfully of what an improvement this would be, but came down on the side of sanity….

Chris Hensley on June 4, 2015 at 6:26 pm said:
The works of Aristotle are important. Much of it has been replaced by better knowledge, but we wouldn’t have that knowledge was still built upon Aristotle. It is time that his logic be put upon the shelf next to his physics.

One thing that is readily apparent is that they very much resent how we have correctly identified them as rhetoricals incapable of rational dialectic and ruled by their feelbads rather than reason. Consider exactly what it is that they are rejecting. They are rejecting logic for fantasy because they cannot be instructed by information, they are only guided by emotion.

I don’t know if my experience cosplaying two-syllogisms makes me much of an authority but I promised that this blog would talk about logic and so far it has been more probability than logic (sure probability and logic are best-buds but still I have standards to maintain)

So Chris Hensley is right. It isn’t that the system of syllogistic reasoning that Aristotle proposed was wrong but it genuinely has been superseded. The fact that we are using computers to discuss this is partly as a consequence of that. In the 19th and 20th century logic went through a revolution that took it far beyond the simple syllogism. Liebniz, Boole, Frege, Whitehead, Russell, Tarski, Godel made giant leaps and these leaps were not just freaky abstract navel gazing.

Consider this chain: Russel and Whitehead’s Principia inspired Kurt Godel’s incompleteness theorem. Alonzo Church and Alan Turing developed a related theorem that examined incompleteness from the position of an abstract mechanical device. John Von Neumann at around the same time was also looking at logical foundations of mathematics. The jump from freaky-abstract-navel gazing to birth-of-the-modern-electronic computer is almost a direct one.

So what is wrong with syllogisms? Well nothing as far as they go. They adequately describe one form of logical reasoning but it is essentially self limiting. Later Stoic philosophers made significant headway in developing Propositional Logic. Propositional Logic itself has limitations but it allows for more complex arguments to be modeled and to deal with the notion of implication. The basic difference between the syllogistic logic and propositional was the kinds of units that were being used. In syllogisms terms are important. For example take this Syllogism:

  • All SJW’s lie
  • Camestros is a SJW
  • Camestros lies

SJW and Camestros are terms and the syllogism shows logical connections between these terms. A syllogism can be re-cast in terms of different objects being members of specific sets.

Propositional logic gives less detail as it treats as a unit whole propositions. “All SJW’s lie” can be a proposition but because it is at an atomic level, propositional logic can’t tease apart the structure inside as easily. This makes the syllogism an easier logical system to use in verbal argument. Propositional logic though allows for us to tease out distinct propositions, show the logical connection (via implication) and then consider the truth value of each. The advantage here is it allows for us to connect a formal logical process with an empirical one.

In the post-Roman Europe the stoic work on propositional logic was lost but various attempts were made to revive it. What brought it back into prominence was it’s capacity to be dealt with symbolically. Symbolic propositional logic allows for more formal mathematical-like proofs of complex arguments.

First-order logic advanced beyond propositional-logic by adding quantification (e.g. all, every, there exists, etc) which allows highly complex logical structures to be examined. This comes with a downside. As downsides go I’m of the personal opinion it is possibly the greatest achievement of humanity (at least so far). The downside is this:

  • Propositional logic is decidable: in other words given a statement in propositional logic in which propositions are connected in a well-formed way (i.e. following the rules) then given the truth values of the propositions it can always be determined what the truth value of the more complex statement is.
  • First-order logic isn’t: the full implications of this are too substantial to discuss here. However it was this discovery by Godel (and Turing and Church) that marks a dividing line in the history of thought.

So yes – Aristotle a big thanks for the syllogism. It is the handy screwdriver of logic but yes, it has its limitations.

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9 comments

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  3. Steven French

    Thanks for this. I’ve been face-palming for weeks now over Vox Days espousal of Aristotle! He likes to portray himself as the Boice of Reason but he knows about as much logic as he does science.

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