Ideas of Michael Dummett, by Theme
[British, b.1925, Professor at Oxford University. Fellow of New College and All Souls'.]
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1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
19066

Philosophy aims to understand the world, through ordinary experience and science

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
10838

To explain a concept, we need its purpose, not just its rules of usage

2. Reason / A. Nature of Reason / 5. Objectivity
17621

What matters in mathematics is its objectivity, not the existence of the objects

2. Reason / D. Definition / 7. Contextual Definition
9847

A contextual definition permits the elimination of the expression by a substitution

2. Reason / E. Argument / 6. Conclusive Proof
19067

A successful proof requires recognition of truth at every step

3. Truth / A. Truth Problems / 1. Truth
10837

It is part of the concept of truth that we aim at making true statements

3. Truth / A. Truth Problems / 2. Defining Truth
10840

We must be able to specify truths in a precise language, like winning moves in a game

3. Truth / F. Semantic Truth / 2. Semantic Truth
19171

Tarski's truth is like rules for winning games, without saying what 'winning' means [Davidson]

8166

Truth is part of semantics, since valid inference preserves truth

4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
19053

Logic would be more natural if negation only referred to predicates

4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
19060

Truthtables are dubious in some cases, and may be a bad way to explain connective meaning

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16951

It was realised that possible worlds covered all modal logics, if they had a structure

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
16952

If something is only possible relative to another possibility, the possibility relation is not transitive

16953

Relative possibility one way may be impossible coming back, so it isn't symmetrical

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
16960

If possibilitiy is relative, that might make accessibility nontransitive, and T the correct system

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
16958

In S4 the actual world has a special place

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18073

Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Kitcher]

18832

Mathematical statements and entities that result from an infinite process must lack a truthvalue

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
10537

The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}}

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193

ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality

9194

The main alternative to ZF is one which includes looser classes as well as sets

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10542

To associate a cardinal with each set, we need the Axiom of Choice to find a representative

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11066

Deduction is justified by the semantics of its metalanguage [Hanna]

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9820

In classical logic, logical truths are valid formulas; in higherorder logics they are purely logical

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
19058

Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
8173

Language can violate bivalence because of nonreferring terms or illdefined predicates

8195

Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
7334

Antirealism needs an intuitionist logic with no law of excluded middle [Miller,A]

8179

The law of excluded middle is the logical reflection of the principle of bivalence

9195

Intuitionists reject excluded middle, not for a third value, but for possibility of proof

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
19052

Natural language 'not' doesn't apply to sentences

18801

Classical negation is circular, if it relies on knowing negationconditions from truthconditions

5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
9182

Ancient names like 'Obadiah' depend on tradition, not on where the name originated

5. Theory of Logic / G. Quantification / 1. Quantification
19057

Classical quantification is an infinite conjunction or disjunction  but you may not know all the instances

5. Theory of Logic / G. Quantification / 5. SecondOrder Quantification
9186

Firstorder logic concerns objects; secondorder adds properties, kinds, relations and functions

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
19063

Beth trees show semantics for intuitionistic logic, in terms of how truth has been established

19059

In standard views you could replace 'true' and 'false' with mere 0 and 1

19062

Classical twovalued semantics implies that meaning is grasped through truthconditions

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187

Logical truths and inference are characterized either syntactically or semantically

5. Theory of Logic / K. Features of Logics / 4. Completeness
19065

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

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
8194

Surely there is no exact single grain that brings a heap into existence

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9896

A prime number is one which is measured by a unit alone

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18255

Addition of quantities is prior to ordering, as shown in cyclic domains like angles

9191

Ordinals seem more basic than cardinals, since we count objects in sequence

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
9895

A number is a multitude composed of units

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
9852

We understand 'there are as many nuts as apples' as easily by pairing them as by counting them

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
15938

Platonists ruin infinity, which is precisely a growing structure which is never completed

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10554

Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9829

The identity of a number may be fixed by something outside structure  by counting

9828

Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1

9192

The number 4 has different positions in the naturals and the wholes, with the same structure

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9876

Set theory isn't part of logic, and why reduce to something more complex?

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
15939

For intuitionists it is constructed proofs (which take time) which make statements true

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
10552

Intuitionism says that totality of numbers is only potential, but is still determinate

8190

Intuitionists rely on the proof of mathematical statements, not their truth

7. Existence / B. Change in Existence / 1. Nature of Change
8198

A 'Cambridge Change' is like saying 'the landscape changes as you travel east'

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
10540

We can't say that light is concrete but radio waves abstract

10515

Ostension is possible for concreta; abstracta can only be referred to via other objects [Hale]

10544

The concrete/abstract distinction seems crude: in which category is the Mistral?

10546

We don't need a sharp concrete/abstract distinction

9884

The distinction of concrete/abstract, or actual/nonactual, is a scale, not a dichotomy

7. Existence / D. Theories of Reality / 1. Realism
9869

Realism is just the application of twovalued semantics to sentences

15049

Metaphysical realists are committed to all unambiguous statements being true or not true

8184

Philosophers should not presume reality, but only invoke it when language requires it

7. Existence / D. Theories of Reality / 3. Antirealism
3303

For antirealists there are no natural distinctions between objects [Benardete,JA]

8185

We can't make sense of a world not apprehended by a mind

8192

I no longer think what a statement about the past says is just what can justify it

7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
8163

Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts

7. Existence / D. Theories of Reality / 7. Facts / c. Facts and truths
8161

We know we can state facts, with true statements

7. Existence / D. Theories of Reality / 9. Vagueness / b. Vagueness of reality
21628

To say reality itself is vague is not properly intelligible

7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as semantic
8180

'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not

7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
10548

The context principle for names rules out a special philosophical sense for 'existence'

10281

The objects we recognise the world as containing depends on the structure of our language

8. Modes of Existence / D. Universals / 1. Universals
10532

We can understand universals by studying predication

8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
10534

'Nominalism' used to mean denial of universals, but now means denial of abstract objects

9880

Nominalism assumes unmediated mental contact with objects

9. Objects / A. Existence of Objects / 1. Physical Objects
10541

Concrete objects such as sounds and smells may not be possible objects of ostension

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10545

Abstract objects may not cause changes, but they can be the subject of change

9885

The existence of abstract objects is a pseudoproblem

9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
10555

If we can intuitively apprehend abstract objects, this makes them observable and causally active

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10543

Abstract objects must have names that fall within the range of some functional expression

9859

It is absurd to deny the Equator, on the grounds that it lacks causal powers

9860

'We've crossed the Equator' has truthconditions, so accept the Equator  and it's an object

9858

Abstract objects nowadays are those which are objective but not actual

9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
10320

If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Hale]

10547

Abstract objects can never be confronted, and need verbal phrases for reference

9872

Abstract objects need the context principle, since they can't be encountered directly

9. Objects / A. Existence of Objects / 3. Objects in Thought
10531

There is a modern philosophical notion of 'object', first introduced by Frege

9. Objects / F. Identity among Objects / 2. Defining Identity
9848

Content is replaceable if identical, so replaceability can't define identity [Dummett]

9842

Frege introduced criteria for identity, but thought defining identity was circular

10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
16957

Possible worlds aren't how the world might be, but how a world might be, given some possibility

10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
16959

If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality

11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
8199

The existence of a universe without sentience or intelligence is an unintelligible fantasy

12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
8178

Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale

14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
19061

An explanation is often a deduction, but that may well beg the question

18. Thought / A. Modes of Thought / 1. Thought
8175

A theory of thought will include propositional attitudes as well as propositions

8174

The theories of meaning and understanding are the only routes to an account of thought

18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
19168

Concepts only have a 'functional character', because they map to truth values, not objects [Davidson]

18. Thought / D. Concepts / 4. Structure of Concepts / h. Conceptual priority
9850

An argument for conceptual priority is greater simplicity in explanation

9849

Maybe a concept is 'prior' to another if it can be defined without the second concept

18. Thought / E. Abstraction / 1. Abstract Thought
10839

You can't infer a dog's abstract concepts from its behaviour

9873

Abstract terms are acceptable as long as we know how they function linguistically

18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10549

Since abstract objects cannot be picked out, we must rely on identity statements

9993

There is no reason why abstraction by equivalence classes should be called 'logical' [Tait]

9857

We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus'

18. Thought / E. Abstraction / 8. Abstractionism Critique
9833

To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too

8165

To 'abstract from' is a logical process, as opposed to the old mental view

19. Language / A. Nature of Meaning / 4. Meaning as TruthConditions
19055

Stating a sentence's truthconditions is just paraphrasing the sentence

19056

If a sentence is effectively undecidable, we can never know its truth conditions

8168

To know the truthconditions of a sentence, you must already know the meaning

19. Language / A. Nature of Meaning / 5. Meaning as Verification
8183

If truths about the past depend on memories and current evidence, the past will change

8181

A justificationist theory of meaning leads to the rejection of classical logic

8182

Verificationism could be realist, if we imagined the verification by a superhuman power

8193

Verification is not an individual but a collective activity

19. Language / A. Nature of Meaning / 6. Meaning as Use
19054

Meaning as use puts use beyond criticism, and needs a holistic view of language

8176

We could only guess the meanings of 'true' and 'false' when sentences were used

19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
8170

Sentences are the primary semantic units, because they can say something

19. Language / A. Nature of Meaning / 10. Denial of Meanings
19064

Holism is not a theory of meaning; it is the denial that a theory of meaning is possible

19. Language / B. Reference / 3. Direct Reference / b. Causal reference
10516

A realistic view of reference is possible for concrete objects, but not for abstract objects [Hale]

9181

The causal theory of reference can't distinguish just hearing a name from knowing its use

19. Language / C. Assigning Meanings / 5. Fregean Semantics
9836

Fregean semantics assumes a domain articulated into individual objects

19. Language / C. Assigning Meanings / 6. TruthConditions Semantics
8189

Truthcondition theorists must argue use can only be described by appeal to conditions of truth

8191

The truthconditions theory must get agreement on a conception of truth

19. Language / D. Propositions / 1. Propositions
8169

We can't distinguish a proposition from its content

23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
16956

To explain generosity in a person, you must understand a generous action

26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
16954

Generalised talk of 'natural kinds' is unfortunate, as they vary too much

27. Natural Reality / C. SpaceTime / 1. Space / c. Points in space
18257

Why should the limit of measurement be points, not intervals?

27. Natural Reality / C. SpaceTime / 2. Time / f. Presentism
8167

If Presentism is correct, we cannot even say that the present changes

8196

The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless

27. Natural Reality / C. SpaceTime / 2. Time / g. Eternalism
8197

Maybe past (which affects us) and future (which we can affect) are both real

27. Natural Reality / C. SpaceTime / 2. Time / i. Time and change
8186

Time is the measure of change, so we can't speak of time before all change
