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Single Idea 8173
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
]
Full Idea
Two features of natural languages cause them to violate bivalence: singular terms (or proper names) which have a sense but fail to denote an object ('the centre of the universe'); and predicates which are not well defined for every object.
Clarification
Bivalence says sentences can only be 'true' or 'false'
Gist of Idea
Language can violate bivalence because of non-referring terms or ill-defined predicates
Source
Michael Dummett (Thought and Reality [1997], 4)
Book Ref
Dummett,Michael: 'Thought and Reality (Gifford Lectures)' [OUP 2006], p.47
A Reaction
If we switch from sentences to propositions these problems might be avoided. If there is no reference, or a vague predicate, then there is (maybe) just no proposition being expressed which could be evaluated for truth.
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]
|
19168
|
Concepts only have a 'functional character', because they map to truth values, not objects
[Dummett, by Davidson]
|
10320
|
If a genuine singular term needs a criterion of identity, we must exclude abstract nouns
[Dummett, by Hale]
|
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]
|
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]
|
10549
|
Since abstract objects cannot be picked out, we must rely on identity statements
[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]
|
10552
|
Intuitionism says that totality of numbers is only potential, but is still determinate
[Dummett]
|
10540
|
We can't say that light is concrete but radio waves abstract
[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]
|
10548
|
The context principle for names rules out a special philosophical sense for 'existence'
[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]
|
10541
|
Concrete objects such as sounds and smells may not be possible objects of ostension
[Dummett]
|
10545
|
Abstract objects may not cause changes, but they can be the subject of change
[Dummett]
|
9993
|
There is no reason why abstraction by equivalence classes should be called 'logical'
[Dummett, by Tait]
|
9848
|
Content is replaceable if identical, so replaceability can't define identity
[Dummett, by Dummett]
|
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]
|
9876
|
Set theory isn't part of logic, and why reduce to something more complex?
[Dummett]
|
9885
|
The existence of abstract objects is a pseudo-problem
[Dummett]
|
9880
|
Nominalism assumes unmediated mental contact with objects
[Dummett]
|
9884
|
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy
[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]
|
19059
|
In standard views you could replace 'true' and 'false' with mere 0 and 1
[Dummett]
|
19060
|
Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning
[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]
|
8169
|
We can't distinguish a proposition from its content
[Dummett]
|
8170
|
Sentences are the primary semantic units, because they can say something
[Dummett]
|
8168
|
To know the truth-conditions of a sentence, you must already know the meaning
[Dummett]
|
8174
|
The theories of meaning and understanding are the only routes to an account of thought
[Dummett]
|
8175
|
A theory of thought will include propositional attitudes as well as propositions
[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]
|
8178
|
Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale
[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]
|
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]
|