display all the ideas for this combination of texts
32 ideas
| 23502 | Logic fills the world, to its limits [Wittgenstein] |
| Full Idea: Logic pervades the world: the limits of the world are also its limits. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.61) | |
| A reaction: This is a gospel belief for hardcore analytic philosophy. Hence Williamson writes a book on modal logic as metaphysics. |
| 23504 | Logic concerns everything that is subject to law; the rest is accident [Wittgenstein] |
| Full Idea: The exploration of logic means the exploration of everything that is subject to law. And outside logic everything is accidental. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.3) | |
| A reaction: Why should laws be logical? Legislatures can pass whimsical laws. Does he mean that the laws of nature are logically necessary? He can't just mean logical laws. |
| 6428 | Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell] |
| Full Idea: I think Wittgenstein is right when he says (in the 'Tractatus') that logic consists wholly of tautologies. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Bertrand Russell - My Philosophical Development Ch.10 | |
| A reaction: Despite Russell's support, I find this hard to accept. While a 'pure' or 'Platonist' logic may be hard to demonstrate or believe, I have a strong gut feeling that logic is more of a natural phenomenon than a human convention. |
| 11062 | Logic is a priori because it is impossible to think illogically [Wittgenstein] |
| Full Idea: What makes logic a priori is the impossibility of illogical thought. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.4731) | |
| A reaction: That places the a priori aspect of it in us (in the epistemology), rather than in the necessity of the logic (the ontology), which is as Kripke says it should be. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| Full Idea: If p follows from q, I can make an inference from q to p, deduce p from q. The nature of the inference can be gathered only from the two propositions. They are the only possible justification of the inference. 'Laws of Inference' would be superfluous. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.132) | |
| A reaction: That seems to imply that each inference is judged on its particulars. But logic aims to be general. There seem to be 'laws' at a more complex level in the logic. |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 18162 | The propositions of logic are analytic tautologies [Wittgenstein] |
| Full Idea: The propositions of logic are tautologies. Therefore the propositions of logic say nothing. (They are the analytic propositions). | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.1) |
| 7537 | Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk] |
| Full Idea: Russell took a Platonist view of logic, but reading the 'Tractatus' convinced him that logic was purely linguistic, so-called 'logical truths' being nothing more than tautologies. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.1 | |
| A reaction: If p-and-q and p-or-q are both tautologies, how do you explain the difference between them? The first is an indicative proposition about the actual world, but the second is modal. They are asserting very different things. |
| 23496 | Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein] |
| Full Idea: The simultaneous presence of two colours in the same place in the visual field is impossible, in fact logically impossible, since it is ruled out by the logical structure of colour. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.3751) | |
| A reaction: This sounds the wrong way around. We derive our concept of the logic of colour from experiencing the total incompatibility of two colours in the same location. What if each of our eyes saw a different colour? |
| 18154 | The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock] |
| Full Idea: The 'Tractatus' does not allow the introduction of a sign for identity. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 13429 | The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey] |
| Full Idea: Wittgenstein discovered that the sign of identity is not a necessary constituent of logical notation, but can be replaced by the convention that different signs must have different meanings. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Frank P. Ramsey - The Foundations of Mathematics p.139 | |
| A reaction: [Ramsey cites p.139 - need to track down the modern reference] Hence in modern logic it is usually necessary to say that we are using 'classical logic with identity', since the use of identity is very convenient, and reasonably harmless (I think). |
| 18268 | Apparent logical form may not be real logical form [Wittgenstein] |
| Full Idea: The apparent logical form of the proposition need not be its real logical form. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.0031), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 6 'The incom' | |
| A reaction: This is one of the key doctrines of modern analytic philosophy. |
| 10905 | My fundamental idea is that the 'logical constants' do not represent [Wittgenstein] |
| Full Idea: My fundamental idea is that the 'logical constants' do not represent; that the logic of facts does not allow of representation. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.0312) | |
| A reaction: This seems to a firm rebuttal of any sort of platonism about logic, and implies a purely formal account. |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| Full Idea: If there were an object called 'not', it would follow that 'not-not-p' would say something different from what 'p' said, just because the one proposition would then be about 'not', and the other would not. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.44) | |
| A reaction: That is, the first proposition would be about not-p, and the second would be about p. Assuming we can say what such things are 'about'. A rather good argument that the connectives are not entities. P and double-negated P should be indistinguishable. |
| 7784 | 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein] |
| Full Idea: The variable name ‘x’ is the proper sign of the pseudo-concept object. Wherever the word ‘object’ (‘thing’, ‘entity’, etc.) is rightly used, it is expressed in logical symbolism by the variable name. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.1272) | |
| A reaction: This seems to be the germ of Quine's famous dictum (Idea 1610). I am not persuaded that because logic must handle an object as a variable, that it follows that we are dealing with a pseudo-concept. Let logic limp behind life. |
| 23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
| Full Idea: A name cannot be dissected any further by means of a definition: it is a primitive sign. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.26) | |
| A reaction: All logicians and analytic philosophers seem to agree on this. He means terms which pick out specific objects. |
| 7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
| Full Idea: A name means an object; an object is its meaning. ...A name cannot be dissected further by means of a definition: it is a primitive sign. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.203/3.26) | |
| A reaction: This is the optimistic view of names, that they are the point at which language plugs into the world (Russell preferred demonstratives for that job). Kripke's baptismal view of names has the same aspiration. |
| 9467 | Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette] |
| Full Idea: Wittgenstein reduces the universal quantifier to conjunctions of singular predications, and the existential quantifier to disjunctions of singular predications. ..This is nowadays understood as a failed effort. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Dale Jacquette - Intro to III: Quantifiers p.143 | |
| A reaction: The problem this meets has something to do with infinite objects. In a domain of three objects it looks like a perfectly plausible strategy. 'All' is all three, and 'Some' is at least one of the three. |
| 15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
| Full Idea: Proof in logic is merely a mechanical expedient to facilitate recognition of tautologies in complicated cases. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.1262) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 13830 | Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking] |
| Full Idea: Wittgenstein's by-product theory is that the meanings of the logical constants are conveyed by their introduction rules, and these rules have as a by-product the class of logical truths. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ian Hacking - What is Logic? §03 | |
| A reaction: I find this approach highly plausible. All the truths about chess openings are just a by-product of the original rules. |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
| Full Idea: All the propositions of logic are of equal status: it is not the case that some of them are essentially primitive propositions and others essentially derived propositions. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.127) | |
| A reaction: So axioms are conventional. This specifically contradicts the claims of Frege and the earlier Russell. Their view is that logic has an explanatory essence, found in some core axioms or rules or concepts. I agree with them. |