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
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21616
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Truth and falsity apply to suppositions as well as to assertions
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3. Truth / A. Truth Problems / 7. Falsehood
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21623
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True and false are not symmetrical; false is more complex, involving negation
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4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
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21602
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Many-valued logics don't solve vagueness; its presence at the meta-level is ignored
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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21611
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Formal semantics defines validity as truth preserved in every model
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5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
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21606
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'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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21605
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Excluded Middle is 'A or not A' in the object language
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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21612
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Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
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21599
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A sorites stops when it collides with an opposite sorites
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7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
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21596
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Vagueness undermines the stable references needed by logic
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21601
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A vague term can refer to very precise elements
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21589
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When bivalence is rejected because of vagueness, we lose classical logic
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7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
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21629
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Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness
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7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
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21591
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Vagueness is epistemic. Statements are true or false, but we often don't know which
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21619
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If a heap has a real boundary, omniscient speakers would agree where it is
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21620
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The epistemic view says that the essence of vagueness is ignorance
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21622
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If there is a true borderline of which we are ignorant, this drives a wedge between meaning and use
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9120
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Vagueness in a concept is its indiscriminability from other possible concepts
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7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
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21614
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The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept
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21625
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The vagueness of 'heap' can remain even when the context is fixed
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21617
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We can say propositions are bivalent, but vague utterances don't express a proposition
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21618
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If the vague 'TW is thin' says nothing, what does 'TW is thin if his perfect twin is thin' say?
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7. Existence / D. Theories of Reality / 10. Vagueness / e. Higher-order vagueness
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21590
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Asking when someone is 'clearly' old is higher-order vagueness
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7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
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21592
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Supervaluation keeps classical logic, but changes the truth in classical semantics
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21603
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You can't give a precise description of a language which is intrinsically vague
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21604
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Supervaluation assigns truth when all the facts are respected
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21607
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Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided
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21608
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Truth-functionality for compound statements fails in supervaluation
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21609
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Supervaluationism defines 'supertruth', but neglects it when defining 'valid'
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21610
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Supervaluation adds a 'definitely' operator to classical logic
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21613
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Supervaluationism cannot eliminate higher-order vagueness
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8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
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21633
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Nominalists suspect that properties etc are our projections, and could have been different
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9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
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21630
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If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries?
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9. Objects / E. Objects over Time / 8. Continuity of Rivers
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21632
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A river is not just event; it needs actual and counterfactual boundaries
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10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
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21621
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We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way
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11. Knowledge Aims / A. Knowledge / 1. Knowledge
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21627
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We have inexact knowledge when we include margins of error
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13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
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21626
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Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered
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18. Thought / A. Modes of Thought / 2. Propositional Attitudes
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21631
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To know, believe, hope or fear, one must grasp the thought, but not when you fail to do them
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18. Thought / D. Concepts / 4. Structure of Concepts / h. Family resemblance
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21600
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'Blue' is not a family resemblance, because all the blues resemble in some respect
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19. Language / B. Reference / 1. Reference theories
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21615
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References to the 'greatest prime number' have no reference, but are meaningful
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19. Language / C. Assigning Meanings / 2. Semantics
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18038
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The 't' and 'f' of formal semantics has no philosophical interest, and may not refer to true and false
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19. Language / D. Propositions / 2. Abstract Propositions / b. Propositions as possible worlds
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21624
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It is known that there is a cognitive loss in identifying propositions with possible worlds
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