I have never studied logic, but a few months ago, simply for my own entertainment, I purchased some of Aristotle’s works and studied them. Among them were the Prior and Posterior Analytics. In the former Aristotle establishes his theory of logic and the syllogism; in the latter, he establishes his approach to scientific method. After reading them, I could not say enough good things about them. In fact, I still can’t say enough good things about the Posterior Analytics, but that’s for a different thread.
The thing that impressed me about the Prior Analytics and Aristotle’s theory of the syllogism is not so much that it formulates logical processes and can predict their outcomes – we already have our brains for that purpose – but that it provides insight into the way the brain works. The syllogism seems, to me, to be a pretty exact representation of what goes on in our minds when we reason; when I outline the syllogistic inferences made in an argument, I am quite convinced that it represents exactly how we think. The psychological insight of Aristotle’s discourse so impressed me that I, though usually not known for credulity, accepted every word of it as fact.
I was therefore much surprised when I discovered this article on Wikipedia, which calls the Aristotelian system “term logic,” says it’s just one system among several, and discusses how it was “used” (whatever that means) until the twentieth century, when suddenly someone figured out that it is flawed and came up with an alternative system that is elaborate and complicated, and that term logic is now obsolete.
I would like to know what term logic’s flaw is. Wikipedia offers no explanation of it, save one example:
but this cannot be right. Let A be owner of a car, B be car, and C be vehicle. Every A is an owner of a B; every B is a C; therefore every A is an owner of a C. Or, every owner of a car is an owner of a car; every car is a vehicle; therefore, every owner of a car is an owner of a vehicle.
This might seem like a clumsy way of doing it, since we have to begin with a redundant and self-evident statement. But I think this is exactly the process we unconsciously go through when we form the above statement: we duplicate “owner of a car,” and replace “car” with “vehicle” in the second instance.
It is possible, I suppose, that my syllogism is invalid because it violates some established rule of term logic – perhaps I am not allowed to use “is an owner of” as I do. But since it is clearly a valid logical process, why shouldn’t we change the rules of term logic to allow for it, instead of concocting an entirely new system?
So I would like to know from those of you who have studied both term logic and this fancy new predicate logic what the former’s flaws are, and what it can’t handle that the latter can. Examples would be appreciated.
Also, if any of you have studied the philosophy of this Fred Sommers guy that the Wikipedia article mentions, I would be interested to know what you think of it.