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Single Idea 21612
[filed under theme 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
]
Full Idea
Argument by Cases (or or-elimination) is the standard way of using disjunctive premises. If one can argue from A and some premises to C, and from B and some premises to C, one can argue from 'A or B' and the combined premises to C.
Gist of Idea
Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
Source
Timothy Williamson (Vagueness [1994], 5.3)
Book Ref
Williamson,Timothy: 'Vagueness' [Routledge 1996], p.152
The
41 ideas
from 'Vagueness'
21592
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Supervaluation keeps classical logic, but changes the truth in classical semantics
[Williamson]
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21589
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When bivalence is rejected because of vagueness, we lose classical logic
[Williamson]
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21591
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Vagueness is epistemic. Statements are true or false, but we often don't know which
[Williamson]
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21590
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Asking when someone is 'clearly' old is higher-order vagueness
[Williamson]
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21596
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Vagueness undermines the stable references needed by logic
[Williamson]
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21599
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A sorites stops when it collides with an opposite sorites
[Williamson]
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21600
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'Blue' is not a family resemblance, because all the blues resemble in some respect
[Williamson]
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21601
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A vague term can refer to very precise elements
[Williamson]
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21602
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Many-valued logics don't solve vagueness; its presence at the meta-level is ignored
[Williamson]
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21603
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You can't give a precise description of a language which is intrinsically vague
[Williamson]
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21604
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Supervaluation assigns truth when all the facts are respected
[Williamson]
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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
[Williamson]
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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
[Williamson]
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21605
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Excluded Middle is 'A or not A' in the object language
[Williamson]
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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'
[Williamson]
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21611
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Formal semantics defines validity as truth preserved in every model
[Williamson]
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21608
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Truth-functionality for compound statements fails in supervaluation
[Williamson]
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21609
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Supervaluationism defines 'supertruth', but neglects it when defining 'valid'
[Williamson]
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21610
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Supervaluation adds a 'definitely' operator to classical logic
[Williamson]
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21613
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Supervaluationism cannot eliminate higher-order vagueness
[Williamson]
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21614
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The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept
[Williamson]
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21615
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References to the 'greatest prime number' have no reference, but are meaningful
[Williamson]
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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
[Williamson]
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21617
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We can say propositions are bivalent, but vague utterances don't express a proposition
[Williamson]
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21616
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Truth and falsity apply to suppositions as well as to assertions
[Williamson]
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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?
[Williamson]
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21619
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If a heap has a real boundary, omniscient speakers would agree where it is
[Williamson]
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21620
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The epistemic view says that the essence of vagueness is ignorance
[Williamson]
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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
[Williamson]
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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
[Williamson]
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21623
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True and false are not symmetrical; false is more complex, involving negation
[Williamson]
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21624
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It is known that there is a cognitive loss in identifying propositions with possible worlds
[Williamson]
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21625
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The vagueness of 'heap' can remain even when the context is fixed
[Williamson]
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9120
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Vagueness in a concept is its indiscriminability from other possible concepts
[Williamson]
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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
[Williamson]
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21627
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We have inexact knowledge when we include margins of error
[Williamson]
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21630
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If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries?
[Williamson]
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21629
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Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness
[Williamson]
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21632
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A river is not just event; it needs actual and counterfactual boundaries
[Williamson]
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21633
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Nominalists suspect that properties etc are our projections, and could have been different
[Williamson]
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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
[Williamson]
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