Ideas of Timothy Williamson, by Theme

[British, fl. 2000, Wykeham Professor of Logic at the Oxford University. Fellow of New College.]

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1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Progress in philosophy is incremental, not an immature seeking after drama
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
We can't presume that all interesting concepts can be analysed
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Analytic philosophy has much higher standards of thinking than continental philosophy
3. Truth / A. Truth Problems / 5. Truth Bearers
Truth and falsity apply to suppositions as well as to assertions
3. Truth / A. Truth Problems / 7. Falsehood
True and false are not symmetrical; false is more complex, involving negation
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
The truthmaker principle requires some specific named thing to make the difference
3. Truth / B. Truthmakers / 7. Making Modal Truths
The converse Barcan formula will not allow contingent truths to have truthmakers
Truthmaker is incompatible with modal semantics of varying domains
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Correspondence to the facts is a bad account of analytic truth
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
If metaphysical possibility is not a contingent matter, then S5 seems to suit it best
In S5 matters of possibility and necessity are non-contingent
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
If the domain of propositional quantification is constant, the Barcan formulas hold
Converse Barcan: could something fail to meet a condition, if everything meets that condition?
If a property is possible, there is something which can have it
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
Many-valued logics don't solve vagueness; its presence at the meta-level is ignored
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic uses a continuum of truth, but it implies contradictions
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Formal logic struck me as exactly the language I wanted to think in
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Formal semantics defines validity as truth preserved in every model
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded Middle is 'A or not A' in the object language
5. Theory of Logic / G. Quantification / 1. Quantification
Not all quantification is either objectual or substitutional
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
Not all quantification is objectual or substitutional
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
A sorites stops when it collides with an opposite sorites
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist
7. Existence / D. Theories of Reality / 3. Anti-realism
The realist/anti-realist debate is notoriously obscure and fruitless
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
If 'fact' is a noun, can we name the fact that dogs bark 'Mary'?
7. Existence / D. Theories of Reality / 9. Vagueness / a. Problem of vagueness
When bivalence is rejected because of vagueness, we lose classical logic
Vagueness undermines the stable references needed by logic
A vague term can refer to very precise elements
7. Existence / D. Theories of Reality / 9. Vagueness / b. Vagueness of reality
Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness
There cannot be vague objects, so there may be no such thing as a mountain
7. Existence / D. Theories of Reality / 9. Vagueness / c. Vagueness as epistemic
Vagueness is epistemic. Statements are true or false, but we often don't know which
If a heap has a real boundary, omniscient speakers would agree where it is
The epistemic view says that the essence of vagueness is ignorance
If there is a true borderline of which we are ignorant, this drives a wedge between meaning and use
Vagueness in a concept is its indiscriminability from other possible concepts
Close to conceptual boundaries judgement is too unreliable to give knowledge
7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as semantic
The vagueness of 'heap' can remain even when the context is fixed
The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept
We can say propositions are bivalent, but vague utterances don't express a proposition
If the vague 'TW is thin' says nothing, what does 'TW is thin if his perfect twin is thin' say?
7. Existence / D. Theories of Reality / 9. Vagueness / e. Higher-order vagueness
Asking when someone is 'clearly' old is higher-order vagueness
7. Existence / D. Theories of Reality / 9. Vagueness / f. Supervaluation for vagueness
Supervaluation keeps classical logic, but changes the truth in classical semantics
Truth-functionality for compound statements fails in supervaluation
You can't give a precise description of a language which is intrinsically vague
Supervaluation assigns truth when all the facts are respected
Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided
Supervaluationism defines 'supertruth', but neglects it when defining 'valid'
Supervaluation adds a 'definitely' operator to classical logic
Supervaluationism cannot eliminate higher-order vagueness
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalists suspect that properties etc are our projections, and could have been different
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
'Blue' is not a family resemblance, because all the blues resemble in some respect
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries?
What sort of logic is needed for vague concepts, and what sort of concept of truth?
Common sense and classical logic are often simultaneously abandoned in debates on vagueness
9. Objects / E. Objects over Time / 8. Continuity of Rivers
A river is not just event; it needs actual and counterfactual boundaries
10. Modality / A. Necessity / 1. Types of Modality
Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B)
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B)
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Hale/Hoffmann,A]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way
Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe]
We scorn imagination as a test of possibility, forgetting its role in counterfactuals
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Our ability to count objects across possibilities favours the Barcan formulas
If talking donkeys are possible, something exists which could be a talking donkey [Cameron]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
We have inexact knowledge when we include margins of error
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Belief aims at knowledge (rather than truth), and mere believing is a kind of botched knowing
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
Don't analyse knowledge; use knowledge to analyse other concepts in epistemology [DeRose]
We don't acquire evidence and then derive some knowledge, because evidence IS knowledge
Knowledge is prior to believing, just as doing is prior to trying to do
Belief explains justification, and knowledge explains belief, so knowledge explains justification
A neutral state of experience, between error and knowledge, is not basic; the successful state is basic
Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism
Knowledge-first says your total evidence IS your knowledge
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
Surely I am acquainted with physical objects, not with appearances?
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
There are 'armchair' truths which are not a priori, because experience was involved
12. Knowledge Sources / B. Perception / 1. Perception
How can one discriminate yellow from red, but not the colours in between?
12. Knowledge Sources / E. Direct Knowledge / 1. Intuition
Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence
When analytic philosophers run out of arguments, they present intuitions as their evidence
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
Imagination is important, in evaluating possibility and necessity, via counterfactuals
18. Thought / A. Modes of Thought / 2. Propositional Attitudes
To know, believe, hope or fear, one must grasp the thought, but not when you fail to do them
19. Language / A. Nature of Meaning / 6. Meaning as Use
You might know that the word 'gob' meant 'mouth', but not be competent to use it
19. Language / B. Reference / 1. Reference theories
References to the 'greatest prime number' have no reference, but are meaningful
19. Language / C. Assigning Meanings / 2. Semantics
The 't' and 'f' of formal semantics has no philosophical interest, and may not refer to true and false
Inferentialist semantics relies on internal inference relations, not on external references
How does inferentialism distinguish the patterns of inference that are essential to meaning?
Internalist inferentialism has trouble explaining how meaning and reference relate
19. Language / C. Assigning Meanings / 7. Extensional Semantics
Truth-conditional referential semantics is externalist, referring to worldly items
19. Language / D. Propositions / 2. Abstract Propositions / b. Propositions as possible worlds
It is known that there is a cognitive loss in identifying propositions with possible worlds
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist
25. Society / B. The State / 8. Culture
If languages are intertranslatable, and cognition is innate, then cultures are all similar
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
A thing can't be the only necessary existent, because its singleton set would be as well