Combining Philosophers

All the ideas for Michael Burke, J.M.E. McTaggart and Michael Dummett

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147 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims to understand the world, through ordinary experience and science [Dummett]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
To explain a concept, we need its purpose, not just its rules of usage [Dummett]
2. Reason / A. Nature of Reason / 5. Objectivity
What matters in mathematics is its objectivity, not the existence of the objects [Dummett]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
2. Reason / E. Argument / 6. Conclusive Proof
A successful proof requires recognition of truth at every step [Dummett]
3. Truth / A. Truth Problems / 1. Truth
It is part of the concept of truth that we aim at making true statements [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
Truth is part of semantics, since valid inference preserves truth [Dummett]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Logic would be more natural if negation only referred to predicates [Dummett]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
In S4 the actual world has a special place [Dummett]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett]
Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]
The law of excluded middle is the logical reflection of the principle of bivalence [Dummett]
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Natural language 'not' doesn't apply to sentences [Dummett]
Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett]
5. Theory of Logic / G. Quantification / 1. Quantification
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Surely there is no exact single grain that brings a heap into existence [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
The identity of a number may be fixed by something outside structure - by counting [Dummett]
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett]
Intuitionists rely on the proof of mathematical statements, not their truth [Dummett]
7. Existence / B. Change in Existence / 1. Nature of Change
How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
Change is not just having two different qualities at different points in some series [McTaggart]
A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale]
The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett]
We don't need a sharp concrete/abstract distinction [Dummett]
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
We can't say that light is concrete but radio waves abstract [Dummett]
7. Existence / D. Theories of Reality / 1. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett]
Philosophers should not presume reality, but only invoke it when language requires it [Dummett]
7. Existence / D. Theories of Reality / 3. Anti-realism
For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA]
I no longer think what a statement about the past says is just what can justify it [Dummett]
We can't make sense of a world not apprehended by a mind [Dummett]
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett]
7. Existence / D. Theories of Reality / 7. Facts / c. Facts and truths
We know we can state facts, with true statements [Dummett]
7. Existence / D. Theories of Reality / 9. Vagueness / b. Vagueness of reality
To say reality itself is vague is not properly intelligible [Dummett]
7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as linguistic
'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett]
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
The objects we recognise the world as containing depends on the structure of our language [Dummett]
The context principle for names rules out a special philosophical sense for 'existence' [Dummett]
8. Modes of Existence / D. Universals / 1. Universals
We can understand universals by studying predication [Dummett]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett]
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 1. Physical Objects
Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Abstract objects may not cause changes, but they can be the subject of change [Dummett]
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
Abstract objects must have names that fall within the range of some functional expression [Dummett]
Abstract objects nowadays are those which are objective but not actual [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale]
Abstract objects can never be confronted, and need verbal phrases for reference [Dummett]
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9. Objects / A. Existence of Objects / 3. Objects in Thought
There is a modern philosophical notion of 'object', first introduced by Frege [Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
9. Objects / F. Identity among Objects / 2. Defining Identity
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
An explanation is often a deduction, but that may well beg the question [Dummett]
18. Thought / A. Modes of Thought / 1. Thought
The theories of meaning and understanding are the only routes to an account of thought [Dummett]
A theory of thought will include propositional attitudes as well as propositions [Dummett]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson]
18. Thought / D. Concepts / 4. Structure of Concepts / h. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
You can't infer a dog's abstract concepts from its behaviour [Dummett]
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Since abstract objects cannot be picked out, we must rely on identity statements [Dummett]
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
To 'abstract from' is a logical process, as opposed to the old mental view [Dummett]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
To know the truth-conditions of a sentence, you must already know the meaning [Dummett]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Verification is not an individual but a collective activity [Dummett]
A justificationist theory of meaning leads to the rejection of classical logic [Dummett]
Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett]
If truths about the past depend on memories and current evidence, the past will change [Dummett]
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Sentences are the primary semantic units, because they can say something [Dummett]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale]
The causal theory of reference can't distinguish just hearing a name from knowing its use [Dummett]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett]
The truth-conditions theory must get agreement on a conception of truth [Dummett]
19. Language / D. Propositions / 1. Propositions
We can't distinguish a proposition from its content [Dummett]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
To explain generosity in a person, you must understand a generous action [Dummett]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett]
27. Natural Reality / C. Space-Time / 1. Space / c. Points in space
Why should the limit of measurement be points, not intervals? [Dummett]
27. Natural Reality / C. Space-Time / 2. Time / a. Time
For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]
27. Natural Reality / C. Space-Time / 2. Time / e. Existence of time
There could be no time if nothing changed [McTaggart]
Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / C. Space-Time / 2. Time / f. Presentism
If Presentism is correct, we cannot even say that the present changes [Dummett]
The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett]
27. Natural Reality / C. Space-Time / 2. Time / g. Eternalism
Maybe past (which affects us) and future (which we can affect) are both real [Dummett]
27. Natural Reality / C. Space-Time / 2. Time / i. Time and change
Time is the measure of change, so we can't speak of time before all change [Dummett]