The Prior Analytics theory of propositions An. Pr. A, ch. 1 (24a10ff) Premise: protasis (= haplé apophansis) Particular: en merei (= ou katholou) Singular: missing. Conclusion (sumperasma) has the same form.

Deduction: sullogismos It means valid inference. Sometimed inference in general, sometimes the special sort of inference investigated in An.Pr. Deduction comes about: genesthai ton sullogismon.

Maybe much simpler: „… by adding ‚is’ or ‚is not’”.

Definition of syllogism as valid inference in general. „Results”: sumbainei (follows) Complete syllogisms are the axioms of the system. They are evident by themselves, need no proof.

„To be in another as a whole” (en holói einai), „predicated” (katégoreiszthai): new paraphrases for the subject-predicate relation. huparkhei remains as central. This is a semantical definition of the truth of universal affirmative (type a) and universal negative/privative (e) propositions. No explicit mention of particular affirmative (i) and negative (o) propositions. Here we can suppose that the Hermeneutics theory about contradictory pairs remains in force.

A2: theory of conversion (antistrephein) The converse of a premise: change the role of subject and predicate Theorems first: e and i are convertible (i.e. the converse is true as well), a is weakly convertible (i. e. the i proposition with the converted terms follows), o is not convertible. Proof for e-conversion: Indirect proof: 1. Suppose that B belongs to some A (contradictory to the conclusion) 2. Let us take such an A, say C (exemplification [ekthesis]) 3. C is a B, and A belongs to it. [‚C is a B’ and ‚B belongs to C’ are apparently synonymous.] 4. Therefore, A belongs to some B – contradiction. First use of term variables for general proofs. Is C a singular or an universal term?

1. It refers to the previous result. 2. Tacitly refers to the De Int. thesis that contraries (‚A belongs to no B’, ‚A belongs to every B’) exclude each other – impossibility. i-conversion: reference to e-conversion again.

Refutation of o-conversion by counterexample. Makes it logic dependent from empirical facts? What was used? Contradictory and contrary pairs (De Int.) The rule of the indirect proof („proof by impossibility”): If a hypothesis leads to a contradiction (impossibility), the negation of it is proved. Existential import: from the thesis that contraries cannot be true together. Two interpretations: Empty terms are excluded altogether. (Łukasiewicz) a-propositions imply the nonemptiness of the subject term.

Extension to modal propositions: „It is necessary for A to belong to some B”, two traditional readings: De dicto: „A belongs to some B” is a necessary truth. De re: „For some B it is necessary to be an A”, i. e., A is a necessary property of some B-s. The i-conversion is at least plausible for the de dicto but not for the de re readings.