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Single Idea 19059
[filed under theme 5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
]
Full Idea
Nothing is lost, on this view, if in the standard semantic treatment of classical sentential logic, we replace the standard truth-values 'true' and 'false' by the numbers 0 and 1.
Gist of Idea
In standard views you could replace 'true' and 'false' with mere 0 and 1
Source
Michael Dummett (The Justification of Deduction [1973], p.294)
Book Ref
Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.294
A Reaction
[A long context will explain 'on this view'] He is discussing the relationship of syntactic and semantic consequence, and goes on to criticise simple binary truth-table accounts of connectives. Semantics on a computer would just be 0 and 1.
Related Ideas
Idea 19058
Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
Idea 3192
Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
The
23 ideas
with the same theme
[logic when interpreted, rather than mere formal systems]:
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13335
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Semantics is the concepts of connections of language to reality, such as denotation, definition and truth
[Tarski]
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13336
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A language containing its own semantics is inconsistent - but we can use a second language
[Tarski]
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18756
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Tarski built a compositional semantics for predicate logic, from dependent satisfactions
[Tarski, by McGee]
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19313
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Tarksi invented the first semantics for predicate logic, using this conception of truth
[Tarski, by Kirkham]
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19059
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In standard views you could replace 'true' and 'false' with mere 0 and 1
[Dummett]
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19062
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Classical two-valued semantics implies that meaning is grasped through truth-conditions
[Dummett]
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19063
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Beth trees show semantics for intuitionistic logic, in terms of how truth has been established
[Dummett]
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3810
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In real reasoning semantics gives validity, not syntax
[Searle]
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13364
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Interpretation by assigning objects to names, or assigning them to variables first
[Bostock, by PG]
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10283
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A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables
[Hodges,W]
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10284
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There are three different standard presentations of semantics
[Hodges,W]
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10285
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I |= φ means that the formula φ is true in the interpretation I
[Hodges,W]
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10016
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When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense'
[Hodes]
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10570
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Assigning an entity to each predicate in semantics is largely a technical convenience
[Fine,K]
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23539
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Classical semantics has referents for names, extensions for predicates, and T or F for sentences
[Fine,K]
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6653
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Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth
[Lowe]
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10898
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The semantics shows how truth values depend on instantiations of properties and relations
[Zalabardo]
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10902
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We can do semantics by looking at given propositions, or by building new ones
[Zalabardo]
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13697
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Valuations in PC assign truth values to formulas relative to variable assignments
[Sider]
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18792
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Situation semantics for logics: not possible worlds, but information in situations
[Mares]
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18753
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An ontologically secure semantics for predicate calculus relies on sets
[McGee]
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23447
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In classical semantics singular terms refer, and quantifiers range over domains
[Linnebo]
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15349
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It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F)
[Horsten]
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