"True" and "false" syllogisms in Aristotle's ANALYTICS. In Aristotle's ANALYTICS, what does Aristotle mean by saying that a syllogism is true or that it is false? For example, see POSTERIOR ANALYTICS, Book I, Chapter 32. More generally, where in the corpus is 'true' or 'false' applied to syllogisms, or to anything other than a proposition, and in each case what is meant?
I suppose that "true" and "false" syllogisms means 1) if all of the premises are 'true", then conclusion (and syllogism in whole) is 'true'; 2) syllogism is "false" if one of the premises is "false". Certainly, it is very disputable that "syllogism" = "conclusion", but it looks as an optimum way of understanding.
The example model Aristotle presents is when A prop is true but B is false (by prior knowledge) but results in C which is true. One could reason pragmatically to achieve such a syllogism, which is false though its conclusion is correct.
All men have two legs. Socrates is a great dancer. Therefore Socrates has two legs.
Scholars are still scratching on the surface concerning this issue. There are at least two ways in which Aristotle uses those expressions: on the one hand, “false syllogism” is used for an argument that is not valid (but Aristotle does not use “true syllogism”, but only “syllogism”, for the contrast case of valid arguments… although this does not mean that he could never have used “true syllogism” in this way, maybe there is one occurrence in the corpus to which no one has paid attention so far); on the other hand, “true syllogism” is used for a valid argument in which all the propositions are (or at least the conclusion is) true. The question is a very good one, since it is also a disaster to assume from the start that Aristotle’s expressions do not change their meaning according to context. Topics VIII.12 is very helpful: the word there is not “syllogismos”, but “logos”; Aristotle says that a logos is called false in four different situations: when the conclusion does not follow; when the conclusion follows but is not what should have been proved; when the conclusion follows and prove what should have been proved but not according to the “proper method”; when the conclusion follows but the premises are false. There are still distinctions inside those four heading. For instance, Aristotle add “be the conclusion itself true or false” for both the third and the four heading. This shows how complex the subject is.
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