Combining Texts

All the ideas for 'fragments/reports', 'Logical Necessity' and 'Philosophy of Logic'

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26 ideas

3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
18951 For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18953 Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18949 The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
18952 '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
12204 The logic of metaphysical necessity is S5 [Rumfitt]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
18958 In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
18954 Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
18956 Asserting first-order validity implicitly involves second-order reference to classes [Putnam]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
18962 Unfashionably, I think logic has an empirical foundation [Putnam]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194 Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
18961 We can identify functions with certain sets - or identify sets with certain functions [Putnam]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198 Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18955 Having a valid form doesn't ensure truth, as it may be meaningless [Putnam]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
18959 Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
18957 Nominalism only makes sense if it is materialist [Putnam]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
18950 Physics is full of non-physical entities, such as space-vectors [Putnam]
10. Modality / A. Necessity / 3. Types of Necessity
14532 A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A]
10. Modality / A. Necessity / 6. Logical Necessity
12193 Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt]
12200 A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt]
12202 Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
12203 If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt]
14. Science / A. Basis of Science / 4. Prediction
18960 Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]