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All the ideas for 'Leibniz', 'Sophistical Refutations' and 'Principles of Theoretical Logic'

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9 ideas

2. Reason / A. Nature of Reason / 1. On Reason
2676 Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle]
     Full Idea: Didactic arguments are those which reason from the principles appropriate to each branch of learning and not from the opinions of the answerer (for he who is learning must take things on trust).
     From: Aristotle (Sophistical Refutations [c.331 BCE], 165b01)
2. Reason / A. Nature of Reason / 4. Aims of Reason
2675 Reasoning is a way of making statements which makes them lead on to other statements [Aristotle]
     Full Idea: Reasoning is based on certain statements made in such a way as necessarily to cause the assertion of things other than those statements and as a result of those statements.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 165a01)
2. Reason / C. Styles of Reason / 1. Dialectic
2677 Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle]
     Full Idea: Dialectical arguments are those which, starting from generally accepted opinions, reason to establish a contradiction.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 165b03)
2. Reason / C. Styles of Reason / 3. Eristic
2674 Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle]
     Full Idea: Those who compete and contend in argument aim at five objects: refutation, fallacy, paradox, solecism, and the reduction of one's opponent to a state of babbling, that is, making him say the same thing over and over again.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 165b15)
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
17750 The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki]
     Full Idea: The first clear proof of the consistency of the first order predicate logic is found in the 1928 book of Hilbert and Ackermann.
     From: report of Hilbert,D/Ackermann,W (Principles of Theoretical Logic [1928]) by Michal Walicki - Introduction to Mathematical Logic History E.2.1
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
16967 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle]
     Full Idea: If you ask 'Are Coriscus and Callias at home or not at home?', whether they are both at home or not there, the number of propositions is more than one. For if the answer is true, it does not follow that the question is a single one.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 176a08)
     A reaction: [compressed] Aristotle is saying that some questions should not receive a 'yes' or 'no' answer, because they are equivocal. Arthur Prior cites this passage, on 'and'. Ordinary use of 'and' need not be the logical use of 'and'.
9. Objects / D. Essence of Objects / 10. Essence as Species
16149 Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle]
     Full Idea: 'Man', and every generic term, denotes not an individual substance but a quality or relation or mode or something of the kind.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 179a01)
     A reaction: This is Aristotle's denial that species constitutes the essence of anything. I take 'man' to be a categorisation of individuals, and is ontologically nothing at all in its own right.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
7566 The Identity of Indiscernibles is really the same as the verification principle [Jolley]
     Full Idea: Various writers have noted that the Identity of Indiscernibles is really tantamount to the verification principle.
     From: Nicholas Jolley (Leibniz [2005], Ch.3)
     A reaction: Both principles are false, because they are the classic confusion of epistemology and ontology. The fact that you cannot 'discern' a difference between two things doesn't mean that there is no difference. Things beyond verification can still be discussed.
9. Objects / F. Identity among Objects / 8. Leibniz's Law
11840 Only if two things are identical do they have the same attributes [Aristotle]
     Full Idea: It is only to things which are indistinguishable and one in essence [ousia] that all the same attributes are generally held to belong.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 179a37)
     A reaction: This simply IS Leibniz's Law (to which I shall from now on quietly refer to as 'Aristotle's Law'). It seems that it just as plausible to translate 'ousia' as 'being' rather than 'essence'. 'Indistinguishable' and 'one in ousia' are not the same.