Combining Texts
Ideas for
'God and Human Attributes', 'Philosophy of Mathematics' and 'Tractatus Logico-Philosophicus'
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33 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
23502
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Logic fills the world, to its limits [Wittgenstein]
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23504
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Logic concerns everything that is subject to law; the rest is accident [Wittgenstein]
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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6428
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Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
11062
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Logic is a priori because it is impossible to think illogically [Wittgenstein]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10259
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The two standard explanations of consequence are semantic (in models) and deductive [Shapiro]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
18277
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If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
10257
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Intuitionism only sanctions modus ponens if all three components are proved [Shapiro]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10253
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Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
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18162
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The propositions of logic are analytic tautologies [Wittgenstein]
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5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
7537
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Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
10251
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The law of excluded middle might be seen as a principle of omniscience [Shapiro]
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5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
23496
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Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18154
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The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock]
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13429
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The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18268
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Apparent logical form may not be real logical form [Wittgenstein]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
10905
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My fundamental idea is that the 'logical constants' do not represent [Wittgenstein]
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10212
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Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
23493
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'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
7784
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'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein]
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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
10209
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A function is just an arbitrary correspondence between collections [Shapiro]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
23506
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Names are primitive, and cannot be analysed [Wittgenstein]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
7089
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A name is primitive, and its meaning is the object [Wittgenstein]
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5. Theory of Logic / G. Quantification / 1. Quantification
9467
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Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
10268
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Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro]
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5. Theory of Logic / H. Proof Systems / 1. Proof Systems
15089
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Logical proof just explicates complicated tautologies [Wittgenstein]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
13830
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Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10235
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A sentence is 'satisfiable' if it has a model [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10239
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The central notion of model theory is the relation of 'satisfaction' [Shapiro]
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10240
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Model theory deals with relations, reference and extensions [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10214
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Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro]
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10238
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The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10234
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Any theory with an infinite model has a model of every infinite cardinality [Shapiro]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
19292
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Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein]
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