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All the ideas for 'What is Logic?st1=Ian Hacking', 'works' and 'Introduction to Mathematical Logic'

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58 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Derrida focuses on other philosophers, rather than on science [Derrida]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is just a linguistic display [Derrida]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophy aims to build foundations for thought [Derrida, by May]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophy is necessarily metaphorical, and its writing is aesthetic [Derrida]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Interpretations can be interpreted, so there is no original 'meaning' available [Derrida]
Hermeneutics blunts truth, by conforming it to the interpreter [Derrida, by Zimmermann,J]
Hermeneutics is hostile, trying to overcome the other person's difference [Derrida, by Zimmermann,J]
1. Philosophy / H. Continental Philosophy / 4. Linguistic Structuralism
Structuralism destroys awareness of dynamic meaning [Derrida]
1. Philosophy / H. Continental Philosophy / 6. Deconstruction
The idea of being as persistent presence, and meaning as conscious intelligibility, are self-destructive [Derrida, by Glendinning]
Sincerity can't be verified, so fiction infuses speech, and hence reality also [Derrida]
Sentences are contradictory, as they have opposite meanings in some contexts [Derrida]
We aim to explore the limits of expression (as in Mallarmé's poetry) [Derrida]
2. Reason / D. Definition / 3. Types of Definition
A decent modern definition should always imply a semantics [Hacking]
3. Truth / A. Truth Problems / 9. Rejecting Truth
Derrida says that all truth-talk is merely metaphor [Derrida, by Engel]
True thoughts are inaccessible, in the subconscious, prior to speech or writing [Derrida]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Post proved the consistency of propositional logic in 1921 [Walicki]
Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Names have a subjective aspect, especially the role of our own name [Derrida]
'I' is the perfect name, because it denotes without description [Derrida]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
Two infinite ordinals can represent a single infinite cardinal [Walicki]
Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Inductive proof depends on the choice of the ordering [Walicki]
10. Modality / A. Necessity / 2. Nature of Necessity
Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Heidegger showed that passing time is the key to consciousness [Derrida]
18. Thought / A. Modes of Thought / 1. Thought
'Tacit theory' controls our thinking (which is why Freud is important) [Derrida]
19. Language / A. Nature of Meaning / 1. Meaning
Meanings depend on differences and contrasts [Derrida]
For Aristotle all proper nouns must have a single sense, which is the purpose of language [Derrida]
Capacity for repetitions is the hallmark of language [Derrida]
The sign is only conceivable as a movement between elusive presences [Derrida]
Writing functions even if the sender or the receiver are absent [Derrida, by Glendinning]
Madness and instability ('the demonic hyperbole') lurks in all language [Derrida]
19. Language / A. Nature of Meaning / 9. Ambiguity
'Dissemination' is opposed to polysemia, since that is irreducible, because of multiple understandings [Derrida, by Glendinning]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Words exist in 'spacing', so meanings are never synchronic except in writing [Derrida]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
The good is implicitly violent (against evil), so there is no pure good [Derrida]