more on this theme
|
more from this text
Single Idea 10547
[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
]
Full Idea
An abstract object can be referred to only by means of a verbal phrase, ...and no confrontation with an abstract object is possible.
Gist of Idea
Abstract objects can never be confronted, and need verbal phrases for reference
Source
Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.494
A Reaction
So does this mean that animals are incapable of entertaining abstract concepts? Some research suggests otherwise. Does a dog understand what a 'walk' is, without use of the word? Dummett disgracefully neglects animals in his theories.
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]
|