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Single Idea 6653
[filed under theme 5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
]
Full Idea
Syntactical methods of proof (e.g.'natural deduction') have regard only to the formal structure of premises and conclusions, whereas semantic methods (e.g. truth-tables) consider their possible interpretations as expressing true or false propositions.
Gist of Idea
Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth
Source
E.J. Lowe (Introduction to the Philosophy of Mind [2000], Ch. 8)
Book Ref
Lowe,E.J.: 'Introduction to the Philosophy of Mind' [CUP 2000], p.203
A Reaction
This is highly significant, because the first method of reasoning could be mechanical, whereas the second requires truth, and hence meaning, and hence (presumably) consciousness. Is full rationality possible with 'natural deduction'?
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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