Combining Texts

Ideas for 'fragments/reports', 'Paradoxes: Form and Predication' and 'Prior Analytics'

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6 ideas

5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-

11148	Deduction is when we suppose one thing, and another necessarily follows [Aristotle]
	Full Idea: A deduction is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so.
	From: Aristotle (Prior Analytics [c.328 BCE], 24b18)
	A reaction: Notice that it is modal ('suppose', rather than 'know'), that necessity is involved, which is presumably metaphysical necessity, and that there are assumptions about what would be true, and not just what follows from what.

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

18896	Aristotle places terms at opposite ends, joined by a quantified copula [Aristotle, by Sommers]
	Full Idea: Aristotle often preferred to formulate predications by placing the terms at opposite ends of the sentence and joining them by predicating expressions like 'belongs-to-some' or 'belongs-to-every'.
	From: report of Aristotle (Prior Analytics [c.328 BCE]) by Fred Sommers - Intellectual Autobiography 'Conceptions'
	A reaction: This is Sommers's picture of Aristotle, which led Sommers to develop his modern Term Logic.

5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic

3300	Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA]
	Full Idea: Basic to Aristotle's logic is the grammatical distinction between subject and predicate, which he glosses in terms of the contrast between a substance and its properties.
	From: report of Aristotle (Prior Analytics [c.328 BCE]) by José A. Benardete - Metaphysics: the logical approach Intro
	A reaction: The introduction of quantifiers and 'logical form' can't disguise the fact that we still talk about (and with) objects and predicates, because no one can think of any other way to talk.

5. Theory of Logic / G. Quantification / 1. Quantification

11149	Affirming/denying sentences are universal, particular, or indeterminate [Aristotle]
	Full Idea: Affirming/denying sentences are universal, particular, or indeterminate. Belonging 'to every/to none' is universal; belonging 'to some/not to some/not to every' is particular; belonging or not belonging (without universal/particular) is indeterminate.
	From: Aristotle (Prior Analytics [c.328 BCE], 24a16)

5. Theory of Logic / G. Quantification / 3. Objectual Quantification

8079	Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin]
	Full Idea: Aristotelian logic has two quantifiers of the subject ('all' and 'some'), and two ways to combine the subject with the predicate ('have', and 'have not'), giving four propositions: all-s-have-p, all-s-have-not-p, some-s-have-p, and some-s-have-not-p.
	From: report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: Frege seems to have switched from 'some' to 'at-least-one'. Since then other quantifiers have been proposed. See, for example, Ideas 7806 and 6068.

5. Theory of Logic / G. Quantification / 6. Plural Quantification

14235	Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
	Full Idea: If the rule is asserted 'Given any well-determined objects, they can be collected into a set by an application of the 'set of' operation', then on the usual account of 'they' this is a tautology. Collection comes automatically with this form of reference.
	From: James Cargile (Paradoxes: Form and Predication [1979], p.115), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? Intro
	A reaction: Is this a problem? Given they are well-determined (presumably implying countable) there just is a set of them. That's what set theory is, I thought. Of course, the iterative view talks of 'constructing' the sets, but the construction looks unstoppable.