Combining Texts

All the ideas for 'On the Philosophy of Logic', 'Knowledge, Possibility and Consciousness' and 'On Second-Order Logic'

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31 ideas

2. Reason / A. Nature of Reason / 1. On Reason
We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Many concepts can only be expressed by second-order logic [Boolos]
7. Existence / D. Theories of Reality / 10. Vagueness / g. Degrees of vagueness
We could make our intuitions about heaps precise with a million-valued logic [Fisher]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vagueness can involve components (like baldness), or not (like boredom) [Fisher]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry]
10. Modality / B. Possibility / 1. Possibility
We can't explain 'possibility' in terms of 'possible' worlds [Fisher]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry]
15. Nature of Minds / A. Nature of Mind / 3. Mental Causation
We try to cause other things to occur by causing mental events to occur [Perry]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Brain states must be in my head, and yet the pain seems to be in my hand [Perry]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
It seems plausible that many animals have experiences without knowing about them [Perry]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry]
18. Thought / C. Content / 1. Content
Although we may classify ideas by content, we individuate them differently, as their content can change [Perry]
18. Thought / C. Content / 8. Intension
The intension of an expression is a function from possible worlds to an appropriate extension [Perry]
19. Language / D. Propositions / 2. Abstract Propositions / b. Propositions as possible worlds
A proposition is a set of possible worlds for which its intension delivers truth [Perry]
19. Language / E. Analyticity / 3. Analytic and Synthetic
A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry]