Combining Philosophers

Ideas for Melvin Fitting, Theodore Sider and Ludwig Wittgenstein

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61 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
23502 Logic fills the world, to its limits [Wittgenstein]
18724 In logic nothing is hidden [Wittgenstein]
16908 We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein]
23504 Logic concerns everything that is subject to law; the rest is accident [Wittgenstein]
14980 There is a real issue over what is the 'correct' logic [Sider]
15000 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6428 Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
11062 Logic is a priori because it is impossible to think illogically [Wittgenstein]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15020 Classical logic is good for mathematics and science, but less good for natural language [Sider]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
11026 Classical logic is deliberately extensional, in order to model mathematics [Fitting]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13678 The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
13679 Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
13682 Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
13680 Maybe logical consequence is a primitive notion [Sider]
15029 Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
13722 A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
18277 If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
18162 The propositions of logic are analytic tautologies [Wittgenstein]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
7537 Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
18709 Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
23496 Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein]
18736 Contradiction is between two rules, not between rule and reality [Wittgenstein]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18154 The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock]
13429 The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18276 A statement's logical form derives entirely from its constituents [Wittgenstein]
18743 Wittgenstein says we want the grammar of problems, not their first-order logical structure [Wittgenstein, by Horsten/Pettigrew]
18268 Apparent logical form may not be real logical form [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
10905 My fundamental idea is that the 'logical constants' do not represent [Wittgenstein]
6563 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin]
15019 Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
23493 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein]
18723 We may correctly use 'not' without making the rule explicit [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
18718 Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
7784 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein]
13696 When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
13700 A 'total' function must always produce an output for a given domain [Sider]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
23506 Names are primitive, and cannot be analysed [Wittgenstein]
18727 A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein]
4139 Naming is a preparation for description [Wittgenstein]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
4946 A name is not determined by a description, but by a cluster or family [Wittgenstein, by Kripke]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
7089 A name is primitive, and its meaning is the object [Wittgenstein]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11028 λ-abstraction disambiguates the scope of modal operators [Fitting]
13703 λ can treat 'is cold and hungry' as a single predicate [Sider]
5. Theory of Logic / G. Quantification / 1. Quantification
9467 Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
15089 Logical proof just explicates complicated tautologies [Wittgenstein]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13688 Good axioms should be indisputable logical truths [Sider]
13687 No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
13690 Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
13691 Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13685 Natural deduction helpfully allows reasoning with assumptions [Sider]
15001 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
13686 We can build proofs just from conclusions, rather than from plain formulae [Sider]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
13697 Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
13830 Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking]
13684 The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
13704 It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13724 In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
19292 Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein]
5. Theory of Logic / K. Features of Logics / 4. Completeness
13698 In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13699 Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6569 'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin]