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Single Idea 19065

[filed under theme 5. Theory of Logic / K. Features of Logics / 4. Completeness ]

Full Idea

A proof of soundess or completeness is a test, not so much of the logical theory to which it applies, but of the theory of meaning which underlies the semantics.

Gist of Idea

Soundness and completeness proofs test the theory of meaning, rather than the logic theory

Source

Michael Dummett (The Justification of Deduction [1973], p.310)

Book Ref

Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.310

A Reaction

These two types of proof concern how the syntax and the semantics match up, so this claim sounds plausible, though I tend to think of them as more like roadworthiness tests for logic, checking how well they function.

The 132 ideas from Michael Dummett

16951 It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
16952 If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
16953 Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
16954 Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett]
16956 To explain generosity in a person, you must understand a generous action [Dummett]
16957 Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett]
16959 If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett]
16960 If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
16958 In S4 the actual world has a special place [Dummett]
15939 For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
18832 Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]
15938 Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
9181 The causal theory of reference can't distinguish just hearing a name from knowing its use [Dummett]
9182 Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett]
10320 If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale]
19168 Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson]
10549 Since abstract objects cannot be picked out, we must rely on identity statements [Dummett]
10547 Abstract objects can never be confronted, and need verbal phrases for reference [Dummett]
10531 There is a modern philosophical notion of 'object', first introduced by Frege [Dummett]
10548 The context principle for names rules out a special philosophical sense for 'existence' [Dummett]
10545 Abstract objects may not cause changes, but they can be the subject of change [Dummett]
10541 Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett]
10555 If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett]
10543 Abstract objects must have names that fall within the range of some functional expression [Dummett]
10516 A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale]
10542 To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]
10537 The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
17621 What matters in mathematics is its objectivity, not the existence of the objects [Dummett]
10554 Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett]
10540 We can't say that light is concrete but radio waves abstract [Dummett]
10552 Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett]
10515 Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale]
10544 The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett]
10546 We don't need a sharp concrete/abstract distinction [Dummett]
10281 The objects we recognise the world as containing depends on the structure of our language [Dummett]
10532 We can understand universals by studying predication [Dummett]
10534 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett]
9848 Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
9993 There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
18257 Why should the limit of measurement be points, not intervals? [Dummett]
18255 Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
9896 A prime number is one which is measured by a unit alone [Dummett]
9895 A number is a multitude composed of units [Dummett]
9820 In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
9829 The identity of a number may be fixed by something outside structure - by counting [Dummett]
9828 Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
9836 Fregean semantics assumes a domain articulated into individual objects [Dummett]
9833 To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
9842 Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
9847 A contextual definition permits the elimination of the expression by a substitution [Dummett]
9852 We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
9849 Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
9850 An argument for conceptual priority is greater simplicity in explanation [Dummett]
9857 We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
9859 It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
9860 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9858 Abstract objects nowadays are those which are objective but not actual [Dummett]
9869 Realism is just the application of two-valued semantics to sentences [Dummett]
9872 Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9873 Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
9885 The existence of abstract objects is a pseudo-problem [Dummett]
9884 The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
9876 Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
9880 Nominalism assumes unmediated mental contact with objects [Dummett]
11066 Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
19058 Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
19060 Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett]
19059 In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
19061 An explanation is often a deduction, but that may well beg the question [Dummett]
19062 Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
19063 Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
19064 Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett]
19065 Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
19066 Philosophy aims to understand the world, through ordinary experience and science [Dummett]
19067 A successful proof requires recognition of truth at every step [Dummett]
18801 Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett]
18073 Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
19054 Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
19055 Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
19056 If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
19057 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
9186 First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
9195 Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
19052 Natural language 'not' doesn't apply to sentences [Dummett]
19053 Logic would be more natural if negation only referred to predicates [Dummett]
22297 Dummett saw realism as acceptance of bivalence, rather than of mind-independent entities [Dummett, by Potter]
15049 Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett]
8163 Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett]
8161 We know we can state facts, with true statements [Dummett]
8165 To 'abstract from' is a logical process, as opposed to the old mental view [Dummett]
8167 If Presentism is correct, we cannot even say that the present changes [Dummett]
8166 Truth is part of semantics, since valid inference preserves truth [Dummett]
8170 Sentences are the primary semantic units, because they can say something [Dummett]
8169 We can't distinguish a proposition from its content [Dummett]
8168 To know the truth-conditions of a sentence, you must already know the meaning [Dummett]
8175 A theory of thought will include propositional attitudes as well as propositions [Dummett]
8174 The theories of meaning and understanding are the only routes to an account of thought [Dummett]
8176 We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett]
8173 Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett]
8179 The law of excluded middle is the logical reflection of the principle of bivalence [Dummett]
8181 A justificationist theory of meaning leads to the rejection of classical logic [Dummett]
8182 Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett]
8178 Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett]
8180 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett]
8183 If truths about the past depend on memories and current evidence, the past will change [Dummett]
8184 Philosophers should not presume reality, but only invoke it when language requires it [Dummett]
8185 We can't make sense of a world not apprehended by a mind [Dummett]
8186 Time is the measure of change, so we can't speak of time before all change [Dummett]
19171 Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
10838 To explain a concept, we need its purpose, not just its rules of usage [Dummett]
10837 It is part of the concept of truth that we aim at making true statements [Dummett]
10839 You can't infer a dog's abstract concepts from its behaviour [Dummett]
10840 We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
8189 Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett]
8191 The truth-conditions theory must get agreement on a conception of truth [Dummett]
8190 Intuitionists rely on the proof of mathematical statements, not their truth [Dummett]
8192 I no longer think what a statement about the past says is just what can justify it [Dummett]
8193 Verification is not an individual but a collective activity [Dummett]
8194 Surely there is no exact single grain that brings a heap into existence [Dummett]
8195 Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
8198 A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett]
8199 The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett]
8197 Maybe past (which affects us) and future (which we can affect) are both real [Dummett]
8196 The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett]
21628 To say reality itself is vague is not properly intelligible [Dummett]
3303 For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA]
7334 Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]