Ideas from 'Vagueness' by Timothy Williamson [1994], by Theme Structure

[found in 'Vagueness' by Williamson,Timothy [Routledge 1996,0-415-13980-5]].

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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
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
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 / 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
7. Existence / D. Theories of Reality / 9. Vagueness / a. Problem of vagueness
A vague term can refer to very precise elements
Vagueness undermines the stable references needed by logic
When bivalence is rejected because of vagueness, we lose classical logic
7. Existence / D. Theories of Reality / 9. Vagueness / b. Vagueness of reality
Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness
7. Existence / D. Theories of Reality / 9. Vagueness / c. Vagueness as ignorance
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
7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as linguistic
The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept
The vagueness of 'heap' can remain even when the context is fixed
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
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
Truth-functionality for compound statements fails in supervaluation
Supervaluationism defines 'supertruth', but neglects it when defining 'valid'
Supervaluation adds a 'definitely' operator to classical logic
Supervaluationism cannot eliminate higher-order vagueness
Supervaluation keeps classical logic, but changes the truth in classical semantics
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalists suspect that properties etc are our projections, and could have been different
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?
9. Objects / E. Objects over Time / 8. Continuity of Rivers
A river is not just event; it needs actual and counterfactual boundaries
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
11. Knowledge Aims / A. Knowledge / 1. Knowledge
We have inexact knowledge when we include margins of error
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
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
18. Thought / D. Concepts / 4. Structure of Concepts / h. Family resemblance
'Blue' is not a family resemblance, because all the blues resemble in some respect
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
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