Ideas of Michael Dummett, by Theme

[British, 1925 - 2011, 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
Philosophy aims to understand the world, through ordinary experience and science
     Full Idea: Philosophy is an attempt to understand the world, as it is revealed to us both in our ordinary experience and by the discoveries and theories of science.
     From: Michael Dummett (The Justification of Deduction [1973], p.311)
     A reaction: I don't see a sharp division between 'ordinary' and 'scientific'. I really like this idea, first because it makes 'understanding' central, and second because it wants both revelations. In discussing matter and time, there is too much emphasis on science.
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
To explain a concept, we need its purpose, not just its rules of usage
     Full Idea: We cannot in general suppose that we give a proper account of a concept by describing those circumstance in which we do, and those in which we do not, make use of the relevant word. We explain the point of the concept, what we use the word for.
     From: Michael Dummett (Truth [1959], p.231)
     A reaction: Well said. I am beginning to develop a campaign to make sure that analytical philosophy focuses on understanding concepts (in a full 'logos' sort of way), and doesn't just settle for logical form or definition or rules of usage.
2. Reason / A. Nature of Reason / 5. Objectivity
What matters in mathematics is its objectivity, not the existence of the objects
     Full Idea: As Kreisel has remarked, what is important is not the existence of mathematical objects, but the objectivity of mathematical statements.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: [see Maddy 2011:115 for the history of this idea] It seems rather unclear where Frege stands on objectivity. Maddy embraces it, following up this idea, and Tyler Burge's fat book on objectivity.
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution
     Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11)
     A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems
2. Reason / E. Argument / 6. Conclusive Proof
A successful proof requires recognition of truth at every step
     Full Idea: For a demonstration to be cogent it is necessary that the passage from step to step involve a recognition of truth at each line.
     From: Michael Dummett (The Justification of Deduction [1973], p.313)
     A reaction: Dummett cited Quine (esp. 1970) as having an almost entirely syntactic view of logic. Rumfitt points out that logic can move validly from one falsehood to another. Even a 'proof' might detour into falsehood, but it would not be a 'canonical' proof!
3. Truth / A. Truth Problems / 1. Truth
It is part of the concept of truth that we aim at making true statements
     Full Idea: It is part of the concept of truth that we aim at making true statements.
     From: Michael Dummett (Truth [1959], p.231)
     A reaction: This strikes me as a rather contentious but very interesting claim. An even stronger claim might be that its value (its normative force) is ALL that the concept of truth contributes to speech, other aspects being analysed into something else.
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
     Full Idea: For a particular bounded language, if it is free of ambiguity and inconsistency, it must be possible to characterize the true sentences of the language; somewhat as, for a given game, we can say which moves are winning moves.
     From: Michael Dummett (Truth [1959], p.237)
     A reaction: The background of this sounds rather like Tarski, with truth just being a baton passed from one part of the language to another, though Dummett adds the very un-Tarskian notion that truth has a value.
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarski's truth is like rules for winning games, without saying what 'winning' means
     Full Idea: Tarski's definition of truth is like giving a definition of what it is to win in various games, without giving a hint as to what winning is (e.g. that it is what one tries to do when playing).
     From: report of Michael Dummett (Truth [1959]) by Donald Davidson - Truth and Predication 7
     A reaction: This led Dummett to his 'normative' account of truth. Formally, the fact that speakers usually aim at truth seems irrelevant, but in life you certainly wouldn't have grasped truth if you thought falsehood was just as satisfactory. The world is involved.
Truth is part of semantics, since valid inference preserves truth
     Full Idea: The concept of truth belongs to semantics, since after all truth is what must be preserved by a valid deductive inference.
     From: Michael Dummett (Thought and Reality [1997], 2)
     A reaction: Does this conclusion follow? Compare 'nice taste belongs to cooking, since that is what cooking must preserve'. I don't like this. I take 'truth' to be a relevant concept to a discussion of a dog's belief that it is going to be taken for a walk.
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Logic would be more natural if negation only referred to predicates
     Full Idea: A better proposal for a formal logic closer to natural language would be one that had a negation-operator only for (simple) predicates.
     From: Michael Dummett (Presupposition [1960], p.27)
     A reaction: Dummett observes that classical formal logic was never intended to be close to natural language. Term logic does have that aim, but the meta-question is whether that end is desirable, and why.
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
     Full Idea: It is arguable whether two-valued truth tables give correct meanings for certain sentential operators, and even whether they constitute legitimate explanations of any possible sentential operators.
     From: Michael Dummett (The Justification of Deduction [1973], p.294)
     A reaction: See 'Many-valued logic' for examples of non-binary truth tables. Presumably logicians should aspire to make their semantics precise, as well as their syntax.
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
     Full Idea: The new discovery was that with a suitable structure imposed on the space of possible worlds, the Leibnizian idea would work for all modal logics.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Relative possibility one way may be impossible coming back, so it isn't symmetrical
     Full Idea: If T is only possible if S obtains, T and S hold in the actual world, and S does not obtain in world v possible relative to the actual world, then the actual is not possible relative to v, since T holds in the actual. Accessibility can't be symmetrical.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
If something is only possible relative to another possibility, the possibility relation is not transitive
     Full Idea: If T is only possible if S obtains, and S is possible but doesn't obtain, then T is only possible in the world where S obtains, but T is not possible in the actual world. It follows that the relation of relative possibility is not transitive.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
     A reaction: [compressed]
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
     Full Idea: If some world is 'a way the world might be considered to be if things were different in a certain respect', that might show that the accessibility relation should not be taken to be transitive, and we should have to adopt modal logic T.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: He has already rejected symmetry from the relation, for reasons concerning relative identity. He is torn between T and S4, but rejects S5, and opts not to discuss it.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
In S4 the actual world has a special place
     Full Idea: In S4 logic the actual world is, in itself, special, not just from our point of view.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: S4 lacks symmetricality, so 'you can get there, but you can't get back', which makes the starting point special. So if you think the actual world has a special place in modal metaphysics, you must reject S5?
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability
     Full Idea: Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position.
     From: report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5
     A reaction: Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'?
Mathematical statements and entities that result from an infinite process must lack a truth-value
     Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result.
     From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3
     A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent.
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}}
     Full Idea: A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality
     Full Idea: ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 7)
     A reaction: If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them.
The main alternative to ZF is one which includes looser classes as well as sets
     Full Idea: The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1)
     A reaction: My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff.
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
     Full Idea: We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Deduction is justified by the semantics of its metalanguage
     Full Idea: For Dummett the semantics of the metalanguage is the external and objective source of the justification of deduction.
     From: report of Michael Dummett (The Justification of Deduction [1973]) by Robert Hanna - Rationality and Logic 3.4
     A reaction: This is offered as an answer to the Lewis Carroll problem that justifying deduction seems to need deduction, thus leading to a regress. [There is a reply to Dummett by Susan Haack]
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
     Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3)
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples
     Full Idea: A plausible account is that the syntactic notion of consequence is for positive results, that some form of argument is valid; the semantic notion is required for negative results, that some argument is invalid, because a counterexample can be found.
     From: Michael Dummett (The Justification of Deduction [1973], p.292)
     A reaction: This rings true for the two strategies of demonstration, the first by following the rules in steps, the second by using your imagination (or a tableau) to think up problems.
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Language can violate bivalence because of non-referring terms or ill-defined predicates
     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.
     From: Michael Dummett (Thought and Reality [1997], 4)
     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.
Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense
     Full Idea: I once wrote that there are three linguistic devices that make it possible for us to frame undecidable statements: quantification over infinity totalities, as expressed by word such as 'never'; the subjunctive conditional form; and the past tense.
     From: Michael Dummett (Truth and the Past [2001], 4)
     A reaction: Dummett now repudiates the third one. Statements containing vague concepts also appear to be undecidable. Personally I have no problems with deciding (to a fair extent) about 'never x', and 'if x were true', and 'it was x'.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Anti-realism needs an intuitionist logic with no law of excluded middle
     Full Idea: Dummett argues that antirealism implies that classical logic must be given up in favour of some form of intuitionistic logic that does not have the law of excluded middle as a theorem.
     From: report of Michael Dummett (works [1970]) by Alexander Miller - Philosophy of Language 9.4
     A reaction: Only realists can think every proposition is either true or false, even if it is beyond the bounds of our possible knowledge (e.g. tiny details from remote history). Personally I think "Plato had brown eyes" is either true or false.
The law of excluded middle is the logical reflection of the principle of bivalence
     Full Idea: The law of excluded middle is the reflection, within logic, of the principle of bivalence. It states that 'For any statement A, the statement 'A or not-A' is true'.
     From: Michael Dummett (Thought and Reality [1997], 5)
     A reaction: True-or-not-true is an easier condition to fulfil than true-or-false. The second says that 'false' is the only alternative, but the first allows other alternatives to 'true' (such as 'undecidable'). It is hard to challenge excluded middle. Somewhat true?
Intuitionists reject excluded middle, not for a third value, but for possibility of proof
     Full Idea: It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 8.1)
     A reaction: This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Natural language 'not' doesn't apply to sentences
     Full Idea: Natural language does not possess a sentential negation-operator.
     From: Michael Dummett (Presupposition [1960], p.27)
     A reaction: This is a criticism of Strawson, who criticises logic for not following natural language, but does it himself with negation. In the question of how language and logic connect, this idea seems important. Term Logic aims to get closer to natural language.
Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions
     Full Idea: Explanations of classical negation assume that knowing what it is for the truth-condition of some statement to obtain, independently of recognising it to obtain, we thereby know what it is for it NOT to obtain; but this presupposes classical negation.
     From: Michael Dummett (The Logical Basis of Metaphysics [1991], p.299), quoted by Ian Rumfitt - The Boundary Stones of Thought 1.1
     A reaction: [compressed wording] This is Dummett explaining why he prefers intuitionistic logic, with its doubts about double negation.
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
     Full Idea: In the case of 'Obadiah', associated only with one act of writing a prophecy, ..it is the tradition which connects our use of the name with the man; where the actual name itself first came from has little to do with it.
     From: Michael Dummett (Frege's Distinction of Sense and Reference [1975], p.256)
     A reaction: Excellent. This seems to me a much more accurate account of reference than the notion of a baptism. In the case of 'Homer', whether someone was ever baptised thus is of no importance to us. The tradition is everything. Also Shakespeare.
5. Theory of Logic / G. Quantification / 1. Quantification
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances
     Full Idea: Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246)
     A reaction: In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though.
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions
     Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1)
     A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy.
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
     Full Idea: Beth trees give a semantics for intuitionistic logic, by representing sentence meaning in terms of conditions under which it is recognised to have been established as true.
     From: Michael Dummett (The Justification of Deduction [1973], p.305)
In standard views you could replace 'true' and 'false' with mere 0 and 1
     Full Idea: Nothing is lost, on this view, if in the standard semantic treatment of classical sentential logic, we replace the standard truth-values 'true' and 'false' by the numbers 0 and 1.
     From: Michael Dummett (The Justification of Deduction [1973], p.294)
     A reaction: [A long context will explain 'on this view'] He is discussing the relationship of syntactic and semantic consequence, and goes on to criticise simple binary truth-table accounts of connectives. Semantics on a computer would just be 0 and 1.
Classical two-valued semantics implies that meaning is grasped through truth-conditions
     Full Idea: The standard two-valued semantics for classical logic involves a conception under which to grasp the meaning of a sentence is to apprehend the conditions under which it is, or is not, true.
     From: Michael Dummett (The Justification of Deduction [1973], p.305)
     A reaction: The idea is that you only have to grasp the truth tables for sentential logic, and that needs nothing more than knowing whether a sentence is true or false. I'm not sure where the 'conditions' creep in, though.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically
     Full Idea: There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1)
     A reaction: Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth?
5. Theory of Logic / K. Features of Logics / 4. Completeness
Soundness and completeness proofs test the theory of meaning, rather than the logic theory
     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.
     From: Michael Dummett (The Justification of Deduction [1973], 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.
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
     Full Idea: There is surely no number n such that "n grains of sand do not make a heap, although n+1 grains of sand do" is true.
     From: Michael Dummett (Truth and the Past [2001], 4)
     A reaction: It might be argued that there is such a number, but no human being is capable of determing it. Might God know the value of n? On the whole Dummett's view seems the most plausible.
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
     Full Idea: A prime number is one which is measured by a unit alone.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11)
     A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes.
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
     Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit')
Ordinals seem more basic than cardinals, since we count objects in sequence
     Full Idea: It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 5)
     A reaction: Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units
     Full Idea: A number is a multitude composed of units.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2)
     A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction.
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
     Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'?
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
     Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed.
     From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication
     A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians.
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
     Full Idea: In the intuitionist view, the notion of an intuitive proof cannot be expected to coincide with that of a proof in a formal system, and Gödel's incompleteness theorem is thus unsurprising from an intuitionist point of view.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting
     Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)
     A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that.
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1
     Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)
     A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory.
The number 4 has different positions in the naturals and the wholes, with the same structure
     Full Idea: The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure.
     From: Michael Dummett (The Philosophy of Mathematics [1998], 6.1)
     A reaction: Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done.
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?
     Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
For intuitionists it is constructed proofs (which take time) which make statements true
     Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time.
     From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2
     A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionism says that totality of numbers is only potential, but is still determinate
     Full Idea: From the intuitionist point of view natural numbers are mental constructions, so their totality is only potential, but it is neverthless a fully determinate totality.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: This could only be if the means of constructing the numbers was fully determinate, so how does that situation come about?
Intuitionists rely on the proof of mathematical statements, not their truth
     Full Idea: The intuitionist account of the meaning of mathematical statements does not employ the notion of a statement's being true, but only that of something's being a proof of the statement.
     From: Michael Dummett (Truth and the Past [2001], 2)
     A reaction: I remain unconvinced that anyone could give an account of proof that didn't discreetly employ the notion of truth. What are we to make of "we suspect this is true, but no one knows how to prove it?" (e.g. Goldbach's Conjecture).
7. Existence / B. Change in Existence / 1. Nature of Change
A 'Cambridge Change' is like saying 'the landscape changes as you travel east'
     Full Idea: The idea of 'Cambridge Change' is like saying 'the landscape changes as you travel east'.
     From: Michael Dummett (Truth and the Past [2001], 5)
     A reaction: The phrase was coined in Oxford. It is a useful label with which realists can insult solipsists, idealists and other riff-raff. Four Dimensionalists seem to see time in this way. Events sit there, and we travel past them. But there are indexical events.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
We can't say that light is concrete but radio waves abstract
     Full Idea: If abstractions were defined by whether they could affect human sense-organs, light-waves would be concrete but radio waves abstract.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: This is a pretty good baseline example. No account should draw an abstract/concrete line through the electromagnetic spectrum.
Ostension is possible for concreta; abstracta can only be referred to via other objects
     Full Idea: Dummett distinguishes, roughly, between those concrete objects which can be possible objects of ostension, and abstract objects which can only be referred to by functional expressions whose argument is some other object.
     From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II
     A reaction: At least someone has proposed a theory! Hale gives a nice critical discussion of the proposal. It is a moot point whether in the second case, when you pick out the 'other object', you are thereby able to refer to some new abstract object.
The concrete/abstract distinction seems crude: in which category is the Mistral?
     Full Idea: The dichotomy between concrete and abstract objects comes to seem far too crude: to which of the two categories should we assign the Mistral, for instance?
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: He has previously given colours and points as difficult borderline cases. We can generalise this particular problem case as the question of whether a potentiality or possibility is abstract or concrete.
We don't need a sharp concrete/abstract distinction
     Full Idea: There is no reason for wanting a sharp distinction between concrete and abstract objects.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: This rather depends on your ontology. If you are happy for reality to be full of weird non-physical entities, then the blurring won't bother you. If the boundary is blurred but still real, it is a very interesting one.
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy
     Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't.
7. Existence / D. Theories of Reality / 2. Realism
Dummett saw realism as acceptance of bivalence, rather than of mind-independent entities
     Full Idea: Dummett aimed to characterise realism in terms not of the mind-independence of the entities but of the validity of bivalence for sentences referring to them.
     From: report of Michael Dummett (Realism [1982]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 21 'Lang'
     A reaction: Hence he called himself a 'philosopher of language', rather than a 'philosopher of thought'. Philosophers of language are more likely to end up as anti-realists, I suspect.
Realism is just the application of two-valued semantics to sentences
     Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist.
Metaphysical realists are committed to all unambiguous statements being true or not true
     Full Idea: The anti-realist view undercuts the ground for accepting bivalence. ...Acceptance of bivalence should not be taken as a sufficient condition for realism. ..They accept the weaker principle that unambiguous statements are determinately true or not true.
     From: Michael Dummett (Realism and Anti-Realism [1992], p.467)
     A reaction: [cited by Kit Fine, when discussing anti-realism] I take it be quite an important component of realism that there might be facts which will never be expressed, or are even beyond our capacity to grasp or express them
Philosophers should not presume reality, but only invoke it when language requires it
     Full Idea: The philosopher's task is not to make a prior commitment for or against realism, but to discover how far realist considerations must be invoked in order to describe our understanding of our language: they may be invoked only if they must be invoked.
     From: Michael Dummett (Thought and Reality [1997], 6)
     A reaction: I don't see why the default position should be solipsism, or a commitment to Ockham's Razor. This is the Cartesian 'Enlightenment Project' approach to philosophy - that everything has to be proved. There is more to ontology than language.
7. Existence / D. Theories of Reality / 4. Anti-realism
For anti-realists there are no natural distinctions between objects
     Full Idea: Dummett says that anti-realism offers us a picture of reality as an amorphous lump not yet articulated into discrete objects.
     From: report of Michael Dummett (works [1970]) by José A. Benardete - Metaphysics: the logical approach Ch.2
     A reaction: This might be called 'weak' anti-realism, where 'strong' anti-realism is the view that reality is quite unknowable, and possibly non-existent.
We can't make sense of a world not apprehended by a mind
     Full Idea: We can make no clear sense of there being a world that is not apprehended by any mind.
     From: Michael Dummett (Thought and Reality [1997], 8)
     A reaction: I find Dummett's view quite baffling. It is no coincidence that Dummett is a theist, along (it seems) Berkeleian lines. I see no more problem with imagining such worlds than with imagining ships sunken long ago which will never be found.
I no longer think what a statement about the past says is just what can justify it
     Full Idea: In distinguishing between what can establish a statement about the past as true and what it is that that statement says, we are repudiating antirealism about the past.
     From: Michael Dummett (Truth and the Past [2001], 3)
     A reaction: This is a late shift of ground from the champion of antirealism. If Dummett's whole position is based on a 'justificationist' theory of meaning, he must surely have a different theory of meaning now for statements about the past?
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts
     Full Idea: What complex of objects constitutes the fact that there is no bird on the bough, and how is that distinct from no squirrel on the bough? This drives us to see the world as composed of 'atomic' facts, making complexes into compounds, not reality itself.
     From: Michael Dummett (Thought and Reality [1997], 1)
     A reaction: [He cites early Wittgenstein as an example] But 'no patch of red here' (or sense-datum) seems identical to 'no patch of green here'. I suppose you could catalogue all the atomic facts, and note that red wasn't among them. But you could do that for birds.
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
We know we can state facts, with true statements
     Full Idea: One thing we know about facts, namely that we can state them. Whenever we make some true statement, we state some fact.
     From: Michael Dummett (Thought and Reality [1997], 1)
     A reaction: Then facts become boring, and are subsumed within the problem of what 'true' means. Personally I have a concept of facts which includes unstatable facts. The physical basis of melancholy I take to be a complex fact which is beyond our powers.
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
To say reality itself is vague is not properly intelligible
     Full Idea: The notion that things might actually be vague, as well as being vaguely described, is not properly intelligible.
     From: Michael Dummett (Wang's Paradox [1970], p.260)
     A reaction: It seems hard to disagree with this. It seems crazy that a pile of grain, or the hair on someone's head, are vague, and even quantum indeterminacies are not very well described as 'vague'. Vagueness is a very human concept.
7. Existence / D. Theories of Reality / 10. 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
     Full Idea: A statement of the form 'that is red or orange', said of something on the borderline between the two colours, might rank as true, although neither 'that is red' nor 'that is orange' was true.
     From: Michael Dummett (Thought and Reality [1997], 5)
     A reaction: It seems to me that the problem here would be epistemological rather than ontological. One of the two is clearly true, but sometimes we can't decide which. How can anyone say 'It isn't red and it isn't orange, but it is either red or orange'?
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
The context principle for names rules out a special philosophical sense for 'existence'
     Full Idea: The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims.
The objects we recognise the world as containing depends on the structure of our language
     Full Idea: What objects we recognise the world as containing depends upon the structure of our language.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: The background to this claim is the Fregean idea that there are no objects for us if there are no concepts. Dummett is adding that there are no concepts if there is no language. I say animals have concepts and recognise objects.
8. Modes of Existence / D. Universals / 1. Universals
We can understand universals by studying predication
     Full Idea: It is by the study of the character of predication that we shall come to understand the essential nature of universals.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: I haven't founded a clearer manifesto for linguistic philosophy than that! Personally I find it highly dubious, given the shifting nature of linguistic forms, and the enormous variation between remote languages.
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
'Nominalism' used to mean denial of universals, but now means denial of abstract objects
     Full Idea: The original sense of 'nominalism' is the denial of universals, that is the denial of reference to either predicates or to abstract nouns. The modern sense (of Nelson Goodman) is the denial of the existence of abstract objects.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: This is why you find loads of modern philosophers vigorous attacking nominalism, only to gradually realise that they don't actually believe in universals, as traditionally understood. It's hard to keep up, when words shift their meaning.
Nominalism assumes unmediated mental contact with objects
     Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts.
9. Objects / A. Existence of Objects / 1. Physical Objects
Concrete objects such as sounds and smells may not be possible objects of ostension
     Full Idea: We cannot simply distinguish concrete objects as objects of ostension, if it literally involves a pointing gesture, as this would exclude a colourless gas, a sound or a smell.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: He shifts to verbal ostension as a result, since we can talk of 'this smell'. On p.491 he suggests that affecting our senses is a sufficient condition to be concrete, but not a necessary one.
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
     Full Idea: To say that an abstract object cannot be the cause of change seems plausible enough, but the thesis that it cannot be the subject of change is problematic. The shape of an object can change, or the number of sheep on a hill.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: This seems a pretty crucial difficulty for the standard notion of abstracta as non-causal. I would say that it is an acid which could eat away the whole edifice if you thought about it for long enough. He shifts shape-change to the physical object.
The existence of abstract objects is a pseudo-problem
     Full Idea: The existence of abstract objects is a pseudo-problem.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought.
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
     Full Idea: For intuitionists, it ceases to be true that abstract objects are not observable and cannot be involved in causal interaction, since such intuitive apprehension of them may be regarded as just such an interaction.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: I would say that since abstract objects can be involved in causal interactions, in the mind, and since the mind is entirely physical (oh yes), this makes abstract objects entirely physical, which may come as a shock to some people.
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects must have names that fall within the range of some functional expression
     Full Idea: For an object to be abstract, we require only that an understanding of any name of that object involves a recognition that the object is in the range of some functional expression.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: I'm not sure I understand this, but a function must involve a relation between some objects, such that a unique object is consequently picked out.
It is absurd to deny the Equator, on the grounds that it lacks causal powers
     Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object.
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object
     Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology.
Abstract objects nowadays are those which are objective but not actual
     Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'.
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
     Full Idea: Dummett's best argument for excluding abstract nouns relies upon the entirely Fregean requirement that with any genuine singular term there must be associated a criterion of identity.
     From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Bob Hale - Abstract Objects Ch.2.II
     A reaction: This sounds a rather rigid test. Must the criteria be logically precise, or must you just have some vague idea of what you are talking about?
Abstract objects can never be confronted, and need verbal phrases for reference
     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.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     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.
Abstract objects need the context principle, since they can't be encountered directly
     Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
     A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta?
9. Objects / A. Existence of Objects / 3. Objects in Thought
There is a modern philosophical notion of 'object', first introduced by Frege
     Full Idea: The notion of 'object', as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: If we say 'objects exist', I think it is crucial that if we are going to introduce 'object' as a term of art, then 'exist' had better stick to normal usage. If that drifts into a term of art as well (incorporating 'subsist', or some such) we have no hope!
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity
     Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability.
     From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12
     A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable.
Frege introduced criteria for identity, but thought defining identity was circular
     Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10)
     A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria.
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
     Full Idea: The equation of a possible world with the way that the (actual) world might be is wrong: the way a distant world might be is not a way the world might be, but a way we might allow it to be given how some intervening world might be.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: The point here is that a system of possible worlds must include relative possibilities as well as actual possibilities. Dummett argues against S5 modal logic, which makes them all equal. Things impossible here might become possible. Nice.
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
     Full Idea: If our space of possible worlds has no structure, as in the semantics for S5, then, from the standpoint of the semantics, all possible worlds are on the same footing; it then becomes difficult to resist the claim that all are equally real.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: This is a rather startling and interesting claim, given that modern philosophy seems full of thinkers who both espouse S5 for metaphysics, and also deny Lewisian realism about possible worlds. I'll ponder that one. Must read the new Williamson….
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
The existence of a universe without sentience or intelligence is an unintelligible fantasy
     Full Idea: The existence of a universe from which sentience was permanently absent is an unintelligible fantasy. What exists is what can be known to exist. What is true is what can be known to be true. Reality is what can be experienced and known.
     From: Michael Dummett (Truth and the Past [2001], 5)
     A reaction: This strikes me as nonsense. The fact that we cannot think about a universe without introducing a viewpoint does not mean that we cannot 'intellectually imagine' its existence devoid of viewpoints. Nothing could ever experience a star's interior.
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale
     Full Idea: Our sentences cannot be divided into two classes, empirical and a priori, the truth of one to be decided by observation, the other by ratiocination. They lie on a scale, with observational sentences at one end, and mathematical ones at the other.
     From: Michael Dummett (Thought and Reality [1997], 5)
     A reaction: The modern post-Kantian dissolution of the rationalist-empiricist debate. I would say that mathematical sentences require no empirical evidence (for their operation, rather than foundation), but a bit of reasoning is involved in observation.
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
     Full Idea: An explanation is often a deductive argument, with the fact needing explaining as its conclusion. ...But the conclusion is usually given in advance, and we may only believe the premisses because they plausibly explain the conclusion.
     From: Michael Dummett (The Justification of Deduction [1973], p.296)
     A reaction: [compressed (Dummett's wordy prose cries out for it!)] I suppose this works better in mathematics, which is central to Dummett's interests. In the real world the puzzle is not usually logically implied by its explanation.
18. Thought / A. Modes of Thought / 1. Thought
A theory of thought will include propositional attitudes as well as propositions
     Full Idea: A comprehensive theory of thought will include such things as judgement and belief, as well as the mere grasp of propositions.
     From: Michael Dummett (Thought and Reality [1997], 4)
     A reaction: This seems to make any theory of thought a neat two-stage operation. Beware of neatness. While propositions might be explained using concepts, syntax and truth, the second stage looks faintly daunting. See Idea 2209, for example.
The theories of meaning and understanding are the only routes to an account of thought
     Full Idea: For the linguistic philosopher, the theory of meaning, and the theory of understanding that is built upon it, form the only route to a philosophical account of thought.
     From: Michael Dummett (Thought and Reality [1997], 4)
     A reaction: I am of the party that thinks thought is prior to language (esp. because of animals), but Dummett's idea does not deny this. He may well be right that this is the 'only route'. We can only hope to give an account of human thought.
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
     Full Idea: Real functions map objects onto objects, but concepts map objects onto truth value, ...so Dummett says that concepts are not functions, but that they have a 'functional character'.
     From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Donald Davidson - Truth and Predication 6
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept
     Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help!
An argument for conceptual priority is greater simplicity in explanation
     Full Idea: An argument for conceptual priority is greater simplicity in explanation.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?).
18. Thought / E. Abstraction / 1. Abstract Thought
You can't infer a dog's abstract concepts from its behaviour
     Full Idea: One could train a dog to bark only when a bell rang and a light shone without presupposing that it possessed the concept of conjunction.
     From: Michael Dummett (Truth [1959], p.235)
Abstract terms are acceptable as long as we know how they function linguistically
     Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
     A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Since abstract objects cannot be picked out, we must rely on identity statements
     Full Idea: Since we cannot pick an abstract object out from its surrounding, all that we need to master is the use of statements of identity between objects of a certain kind.
     From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
     A reaction: This is the necessary Fregean preliminary to using a principle of abstraction to identify two objects which are abstract (when the two objects are in an equivalence relation). Presumably circular squares and square circles are identical?
There is no reason why abstraction by equivalence classes should be called 'logical'
     Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'.
     From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14
     A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981.
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus'
     Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14)
     A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction...
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
     Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)
     A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'.
To 'abstract from' is a logical process, as opposed to the old mental view
     Full Idea: The phrase 'abstracted from' does not refer to the mental process of abstraction by disregarding features of concrete objects, in which many nineteenth century thinkers believed; it is a logical (not mental) process of concept-formation.
     From: Michael Dummett (Thought and Reality [1997], 1)
     A reaction: I take Frege's attack on 'psychologism' to be what dismissed the old view (Idea 5816). Could one not achieve the same story by negating properties in quantified logical expressions, instead of in the mind?
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Stating a sentence's truth-conditions is just paraphrasing the sentence
     Full Idea: An ability to state the condition for the truth of a sentence is, in effect, no more than an ability to express the content of the sentence in other words.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.224)
     A reaction: Alternatively, if you give something other than a paraphrase of the sentence as its meaning (such as a proof of its truth), then you seem to have departed from your target sentence. Can we reduce and eliminate our sentences in this way?
If a sentence is effectively undecidable, we can never know its truth conditions
     Full Idea: If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225)
     A reaction: The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning?
To know the truth-conditions of a sentence, you must already know the meaning
     Full Idea: You can know the condition for a sentence to be true only when you know what the sentence means.
     From: Michael Dummett (Thought and Reality [1997], 3)
     A reaction: This makes the truth-conditions theory of meaning circular, and is Dummett's big objection to Davidson's view. The composition of a sentence creates a model of a world. Truth-conditions may only presuppose knowledge of concepts.
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A justificationist theory of meaning leads to the rejection of classical logic
     Full Idea: If we adopt a justificationist theory of meaning, we must reject the universal law of excluded middle, and with it classical logic (which rests on the two-valued semantics of bivalence). We admit only intuitionist logic, which preserves justifiability.
     From: Michael Dummett (Thought and Reality [1997], 5)
     A reaction: This is Dummett's philosophy in a very neat nutshell. He seems to have started by accepting Brouwer's intuitionism, and then working back to language. It all implies anti-realism. I don't buy it.
Verificationism could be realist, if we imagined the verification by a superhuman power
     Full Idea: There is a possible route to realism, which has been called 'ideal verificationism', if we base our grasping the understanding and truth of a range of sentences on the procedure that would be available to an imagined being with superhuman powers.
     From: Michael Dummett (Thought and Reality [1997], 5)
     A reaction: This is actually a slippery slope for verificationists, as soon as they allow that verification could be done by other people. A verifier might turn up who had telepathy, or x-ray vision, or could see quarks...
If truths about the past depend on memories and current evidence, the past will change
     Full Idea: If justificationists succumb to the temptation for statements in the past, we shall view their senses as given by present memories and present traces of past events; but this will force us into a view of the past as itself changing.
     From: Michael Dummett (Thought and Reality [1997], 6)
     A reaction: Obviously Dummett attempts to sidestep this problem, but it strikes me as powerful support for the realist view about the past. How can we not be committed to the view that there are facts about the past quite unconnected to our verifying abilities?
Verification is not an individual but a collective activity
     Full Idea: Verification is not an individual but a collective activity.
     From: Michael Dummett (Truth and the Past [2001], 3)
     A reaction: This generates problems. Are deceased members of the community included? (Yes, says Dummett). If someone speaks to angels (Blake!), do they get included? Is a majority necessary? What of weird loners? Etc.
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning as use puts use beyond criticism, and needs a holistic view of language
     Full Idea: If use constitutes meaning, it might seem that use is beyond criticism. ....But such an attitude can, ultimately, be supported onlly by the adoption of a holistic view of language.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.218)
     A reaction: Dummett goes on to say that the rejection of the holistic view of mathematical meaning leads to his preference for intuitionistic logic.
We could only guess the meanings of 'true' and 'false' when sentences were used
     Full Idea: Even if we guessed that the two words denoted the two truth-values, we should not know which stood for the value 'true' and which for the value 'false' until we knew how the sentences were in practice used.
     From: Michael Dummett (Thought and Reality [1997], 4)
     A reaction: These types of problem are always based on the idea that some one item must have logical priority in the process, but there is a lot of room for benign circularity in the development of mental and linguistic functions.
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Sentences are the primary semantic units, because they can say something
     Full Idea: While words are semantic atoms, sentences remain the primary semantic units, in the sense of the smallest bits of language by means of which it is possible to say anything.
     From: Michael Dummett (Thought and Reality [1997], 3)
     A reaction: Syncategorematic terms (look it up!) may need sentences, but most nouns and verbs can communicate quite a lot on their own. Whether words or sentences come first may not be a true/false issue.
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
     Full Idea: In the sense of giving a model for the content of a sentence, its representative power, holism is not a theory of meaning; it is the denial that a theory of meaning is possible.
     From: Michael Dummett (The Justification of Deduction [1973], p.309)
     A reaction: This will obviously be because sentences just don't have meaning in isolation, so their meaning can't be given in terms of the sentences.
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
     Full Idea: Dummett claims that a realistic conception of reference can be sustained for concrete objects (possible objects of ostension), but breaks down for (putative) names of (pure) abstract objects.
     From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II
     A reaction: An extremely hard claim to evaluate, because a case must first be made for abstract objects which are fundamentally different in kind. Realistic reference must certainly deal with these hard cases. Field rejects Dummett's abstract points.
The causal theory of reference can't distinguish just hearing a name from knowing its use
     Full Idea: The causal theory of reference, in a full-blown form, makes it impossible to distinguish between knowing the use of a proper name and simply having heard the name and recognising it as a name.
     From: Michael Dummett (Frege's Distinction of Sense and Reference [1975], p.254)
     A reaction: None of these things are all-or-nothing. I have an inkling of how to use it once I realise it is a name. Of course you could be causally connected to a name and not even realise that it was a name, so something more is needed.
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects
     Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)
     A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc.
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
     Full Idea: To demonstrate the necessity of a truth-conditional theory of meaning, a proponent of such a theory must argue that use cannot be described without appeal to the conditions for the truth of statements.
     From: Michael Dummett (Truth and the Past [2001], 1)
     A reaction: Unlike Dummett, I find that argument rather appealing. How do you decide the possible or appropriate use for a piece of language, if you don't already know what it means. Basing it all on social conventions means it could be meaningless ritual.
The truth-conditions theory must get agreement on a conception of truth
     Full Idea: It is not enough for the truth-condition theorist to argue that we need the concept of truth: he must show that we should have the same conception of truth that he has.
     From: Michael Dummett (Truth and the Past [2001], 2)
     A reaction: Davidson invites us to accept Tarski's account of truth. It invites the question of what the theory would be like with a very robust correspondence account of truth, or a flabby rather subjective coherence view, or the worst sort of pragmatic view.
19. Language / D. Propositions / 1. Propositions
We can't distinguish a proposition from its content
     Full Idea: No distinction can be drawn between a proposition and its content; no two distinct propositions can have the same content.
     From: Michael Dummett (Thought and Reality [1997], 3)
     A reaction: And one proposition cannot have two possible contents (ambiguity). Are we to say that a proposition supervenes on its content, or that proposition and content are identical? Ockham favours the latter.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
To explain generosity in a person, you must understand a generous action
     Full Idea: It cannot be explained what it is for a person to be generous without first explaining what it is for an action to be generous.
     From: Michael Dummett (Could There Be Unicorns? [1983], 4)
     A reaction: I presume a slot machine can't be 'generous', even if it favours the punter, so you can't specify a generous action without making reference to the person. A benign circle, as Aristotle says.
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Generalised talk of 'natural kinds' is unfortunate, as they vary too much
     Full Idea: In my view, Kripke's promotion of 'natural kinds', coverning chemical substances and animal and plant species, is unfortunate, since these are rather different types of things, and words used for them behave differently.
     From: Michael Dummett (Could There Be Unicorns? [1983], 2)
     A reaction: My view is that the only significant difference among natural kinds is their degree of stability in character. Presumably particles, elements and particular molecules are fairly invariant, but living things evolve.
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals?
     Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval?
     From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit')
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is the measure of change, so we can't speak of time before all change
     Full Idea: Time is the measure of change, and it makes no sense to speak of how things were before there was anything that changed.
     From: Michael Dummett (Thought and Reality [1997], 8)
     A reaction: Something creating its own measure sounds like me marking my own exam papers. If an object appears, then inverts five seconds later, how can the inversion create the five seconds? How does that differ from inverting ten seconds later?
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
Maybe past (which affects us) and future (which we can affect) are both real
     Full Idea: Maybe both the past and the future are real, determined by our current temporal perspective. Past is then events capable of having a causal influence upon events near us, and future is events we can affect, but from which we receive no information.
     From: Michael Dummett (Truth and the Past [2001], 5)
     A reaction: This is the Four-Dimensional view, which is opposed to Presentism. Might immediate unease is that it gives encouragement to fortune-tellers, whom I have always dismissed with 'You can't see the future, because it doesn't exist'.
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
If Presentism is correct, we cannot even say that the present changes
     Full Idea: If Presentism is correct - the doctrine that there is nothing at all, save what holds good at the present moment - then we cannot even say that the present changes, because that requires that things are not now as they were some time ago.
     From: Michael Dummett (Thought and Reality [1997], 2)
     A reaction: Presumably we can compare our present memory with our present experience. See Idea 6668. The logic (very ancient!) is that the present has not duration at all, and so no experiences can occur during it.
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless
     Full Idea: The idea that only the present is real cannot be sustained. St Augustine pointed out that the present has no duration; it is a mere boundary between past and future, and dependent on them. It also denies truth-value to statements about past or future.
     From: Michael Dummett (Truth and the Past [2001], 5)
     A reaction: To defend Presentism, I suspect that one must focus entirely on the activities of consciousness and short-term memory. All truths, of past or future, must refer totally to such mental events. But what could an event be if there is no enduring time?