Episode 30: Marko Malink discusses modal syllogistic
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What is the quick announcement about the Elucidations blog?
This is just a quick message to let you know that Elucidations now has a blog. Check it out at Lucian that's L U C I A N Lucian dot ushicago.edu slash blogs slash elucidations. Check it out. Let us know what you think.
Hello, welcome to Elucidations, a philosophy podcast recorded at the University of Chicago. I'm Matt Teichman.
And I am Jamie Edwards.
With us today is Marco Malink, Assistant Professor of Philosophy at the University of Chicago, and he's here to talk to us about modosylogistic. Marco Malink, welcome.
What is Aristotle's syllogistic and why is it considered the first formal logic system?
Hello Matt. Hi Jane. So I guess the first question that's going to be on everybody's minds is what is syllogistic?
Right. Aristotle's syllogistic basically is the first system of formal logic in the history of philosophy. And it is basically a theory where Aristotle gives an account of valid deductive inferences. As such, it is similar to logical systems which we find in the 20th century also. But there is a crucial difference between Aristotle's and logical systems which we find in the twentieth century. And this is um connected with the kinds of sentences which Aristotle considers in his syllogistic. So in a syllogistic Aristotle is mainly concerned with sentences such as every B is an A, so for example, every man is an animal. And um He studies inferences of the form like every C is a B, every B is an A, therefore every C is an A.
How does Aristotle distinguish valid from invalid syllogistic inferences?
That's one of the basic inferences which Aristotle considers in his syllogistic. And he gives an account of which of these inferences which we can construct out of such sentences. I mean he he also considers sentences of the type sum M B is an A or no B is an A and he um gives an account of which inferences which we can construct out of these sentences are valid and which of these inferences aren't valid.
Like what would be an example of a valid inference and an example of an invalid inference?
Right, so um an example of a valid inference is just the example which I just gave. Every C is a B, every B is an A, therefore every C is an A. And also a further example would be every C is a B, no B is an A, therefore no C is an A. And then Ertot also considers invalid or he also says which of these inferences are invalid. So for example, if no C is a B and every B is an A, then it does not follow that no C is an A.
Okay, right.
How does Aristotle's three‑part sentence structure differ from modern predicate logic?
So we're talking about sort of different these sort of like argument patterns and these are sort of templates for building arguments out of actual sentences. W you know without B's and C's, but where we sort of plug stuff in wherever we have a C or wherever we have a B or we have an A, so that every giraffe is a mammal, every mammal breathes, therefore every giraffe breathes or something. You know, we sort of abstract away from these argument patterns that have actual sentences in them to try to get to the more abstract form so that we can say anything that has this form will be a good argument.
This right, that's perfectly right. One of the big differences between Aristotle's logistics and systems of logic which we find in the twentieth century concerns, as I said, the syntax of his sentences. For Aristotle, uh the basic sentences consist of two terms in the third part which connects these two terms. For example, in the sentence every B is an A consists of two terms, namely B and B. And A, an example, would be man animal of these terms, and a third part which forms a sentence out of these two terms. And the third part would correspond to the words every and is. Aristotle himself actually doesn't say every B is an A, he rather says things like A belongs to all B. And in this way of saying things, this third element would be
Correspond to all, to the phrase belongs to all. And Aristotle considers these sentences which have this tripartite syntax consisting of two terms which are of the same syntactic type and the third element as basic sentences. Whereas in 20th century logic, I mean basically the Phugian logic, predicate logic, first-order logic, the basic sentence.
What does Frege's reconstruction imply about the extensional semantics of Aristotle's sentences?
Sentences consist just of two terms. They have a bipartite syntax consisting of a singular term and a general term.
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Chapters
8 chapters
1
What is the quick announcement about the Elucidations blog?
0:00–0:54
2
What is Aristotle's syllogistic and why is it considered the first formal logic system?
0:54–2:07
3
How does Aristotle distinguish valid from invalid syllogistic inferences?
2:07–3:15
4
How does Aristotle's three‑part sentence structure differ from modern predicate logic?
3:15–5:02
5
What does Frege's reconstruction imply about the extensional semantics of Aristotle's sentences?
5:02–6:41
6
Why does Aristotle limit subjects to substances and predicates to non‑substances?
6:41–8:49
7
What are the key features of Aristotle's modal syllogistic?
8:49–11:22
8
How does Theophrastus' counterexample challenge Aristotle's modal syllogistic?
11:22–30:17
Speakers
2 identifiedMore from Elucidations
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Episode 154: Greg Salmieri discusses free speech, "cancel culture," and "academic freedom"
Episode 153: Sam Enright discusses lifelong learning
Epsiode 152: Luca Gattoni-Celli discusses the housing crisis