Combining Texts

All the ideas for 'Prior Analytics', 'Must We Believe in Set Theory?' and 'Truth and Probability'

expand these ideas     |    start again     |     specify just one area for these texts

27 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
22271 Aristotle was the first to use schematic letters in logic [Aristotle, by Potter]
11060 Aristotelian syllogisms are three-part, subject-predicate, existentially committed, with laws of thought [Aristotle, by Hanna]
18909 Aristotelian sentences are made up by one of four 'formative' connectors [Aristotle, by Engelbretsen]
8080 Aristotelian identified 256 possible syllogisms, saying that 19 are valid [Aristotle, by Devlin]
13912 Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae' [Aristotle, by Engelbretsen/Sayward]
8071 Aristotle listed nineteen valid syllogisms (though a few of them were wrong) [Aristotle, by Devlin]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
13819 Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9403 There are three different deductions for actual terms, necessary terms and possible terms [Aristotle]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
11148 Deduction is when we suppose one thing, and another necessarily follows [Aristotle]
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]
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]
5. Theory of Logic / G. Quantification / 1. Quantification
11149 Affirming/denying sentences are universal, particular, or indeterminate [Aristotle]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
8079 Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
10. Modality / A. Necessity / 4. De re / De dicto modality
14641 A deduction is necessary if the major (but not the minor) premise is also necessary [Aristotle]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
13766 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
14. Science / C. Induction / 6. Bayes's Theorem
19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
18911 Linguistic terms form a hierarchy, with higher terms predicable of increasing numbers of things [Aristotle, by Engelbretsen]