Combining Texts

All the ideas for 'The philosophical basis of intuitionist logic', 'Maths as a Science of Patterns' and 'Formal and Material Consequence'

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20 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18073 Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
14187 If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
14188 Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
14182 If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
14183 Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
14184 In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
14186 Logical connectives contain no information, but just record combination relations between facts [Read]
5. Theory of Logic / G. Quantification / 1. Quantification
19057 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
14185 Conditionals are just a shorthand for some proof, leaving out the details [Read]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
19055 Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
19056 If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
19. Language / A. Nature of Meaning / 6. Meaning as Use
19054 Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]