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All the ideas for '(Nonsolipsistic) Conceptual Role Semantics', 'Identity over Time' and 'Infinity: Quest to Think the Unthinkable'

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39 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Reasoning aims at increasing explanatory coherence [Harman]
     Full Idea: In reasoning you try among other things to increase the explanatory coherence of your view.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2)
     A reaction: Harman is a champion of inference to the best explanation (abduction), and I agree with him. I think this idea extends to give us a view of justification as coherence, and that extends from inner individual coherence to socially extended coherence.
Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman]
     Full Idea: Conservatism is important; you should continue to believe as you do in the absence of any special reason to doubt your view, and in reasoning you should try to minimize change in your initial opinions in attaining other goals of reasoning.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.6)
     A reaction: One of those principles like Ockham's Razor, which feels right but hard to justify. It seems the wrong principle for someone who can reason well, but has been brainwashed into a large collection of daft beliefs. Japanese soldiers still fighting WWII.
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
A set is 'well-ordered' if every subset has a first element [Clegg]
     Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Set theory made a closer study of infinity possible [Clegg]
     Full Idea: Set theory made a closer study of infinity possible.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
Any set can always generate a larger set - its powerset, of subsets [Clegg]
     Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
     Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: For any two sets there exists a set to which they both belong [Clegg]
     Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
     Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There exists a set of the empty set and the successor of each element [Clegg]
     Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Powers: All the subsets of a given set form their own new powerset [Clegg]
     Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
     Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Axiom of Existence: there exists at least one set [Clegg]
     Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
Specification: a condition applied to a set will always produce a new set [Clegg]
     Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman]
     Full Idea: There is as yet no substantial theory of inference or reasoning. To be sure, logic is well developed; but logic is not a theory of inference or reasoning. Logic is a theory of implication and inconsistency.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2)
     A reaction: One problem is that animals can draw inferences without the use of language, and I presume we do so all the time, so it is hard to see how to formalise such an activity.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman]
     Full Idea: Principles of implication imply there is not a purely probabilistic rule of acceptance for belief. Otherwise one might accept P and Q, without accepting their conjunction, if the conjuncts have a high probability, but the conjunction doesn't.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2)
     A reaction: [Idea from Scott Soames] I am told that my friend A has just won a very big lottery prize, and am then told that my friend B has also won a very big lottery prize. The conjunction seems less believable; I begin to suspect a conspiracy.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
     Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17)
     A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Beyond infinity cardinals and ordinals can come apart [Clegg]
     Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
An ordinal number is defined by the set that comes before it [Clegg]
     Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Transcendental numbers can't be fitted to finite equations [Clegg]
     Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
     Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
     Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
     Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
     Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
     Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14)
7. Existence / D. Theories of Reality / 3. Reality
Reality is the overlap of true complete theories [Harman]
     Full Idea: Reality is what is invariant among true complete theories.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.4)
     A reaction: The sort of slogan that gets coined in the age of Quine. The whole manner of starting from your theories and working out to what we think reality is seems to be putting the cart before the horse.
9. Objects / E. Objects over Time / 1. Objects over Time
If things change they become different - but then no one thing undergoes the change! [Gallois]
     Full Idea: If things really change, there can't literally be one thing before and after the change. However, if there isn't one thing before and after the change, then no thing has really undergone any change.
     From: André Gallois (Identity over Time [2011], Intro)
     A reaction: [He cites Copi for this way of expressing the problem of identity through change] There is an obvious simple ambiguity about 'change' in ordinary English. A change of property isn't a change of object. Painting a red ball blue isn't swapping it.
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois]
     Full Idea: We have four versions of Four-Dimensionalism: the relativistic view that time is space-like; a persisting thing is identical with its history (so objects are events); past and future are equally real; or (Lewis) things extend in time, with temporal parts.
     From: André Gallois (Identity over Time [2011], §2.5)
     A reaction: Broad proposed the second one. I prefer 3-D: at any given time a thing is wholly present. At another time it is wholly present despite having changed. It is ridiculous to think that small changes destroy identity. We acquire identity by dying??
9. Objects / F. Identity among Objects / 6. Identity between Objects
If two things are equal, each side involves a necessity, so the equality is necessary [Gallois]
     Full Idea: The necessity of identity: a=b; □(a=a); so something necessarily = a; so something necessarily must equal b; so □(a=b). [A summary of the argument of Marcus and Kripke]
     From: André Gallois (Identity over Time [2011], §3)
     A reaction: [Lowe 1982 offered a response] The conclusion seems reasonable. If two things are mistakenly thought to be different, but turn out to be one thing, that one thing could not possibly be two things. In no world is one thing two things!
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
There is no natural border between inner and outer [Harman]
     Full Idea: There is no natural border between inner and outer.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.4)
     A reaction: Perhaps this is the key idea for the anti-individualist view of mind. Subjectively I would have to accept this idea, but looking objectively at another person it seems self-evident nonsense.
We can only describe mental attitudes in relation to the external world [Harman]
     Full Idea: No one has ever described a way of explaining what beliefs, desires, and other mental states are except in terms of actual or possible relations to things in the external world.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.4)
     A reaction: If I pursue my current favourite idea, that how we explain things is the driving force in what ontology we adopt, then this way of seeing the mind, and taking an externalist anti-individualist view of it seems quite attractive.
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
The way things look is a relational matter, not an intrinsic matter [Harman]
     Full Idea: According to functionalism, the way things look to you is a relational characteristic of your experience, not part of its intrinsic character.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.3)
     A reaction: No, can't make sense of that. How would being in a relation determine what something is? Similar problems with the structuralist account of mathematics. If the whole family love some one cat or one dog, the only difference is intrinsic to the animal.
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
Concepts in thought have content, but not meaning, which requires communication [Harman]
     Full Idea: Concepts and other aspects of mental representation have content but not (normally) meaning (unless they are also expressions in a language used in communication).
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.2)
     A reaction: Given his account of meaning as involving some complex 'role', he has to say this, though it seems a dubious distinction, going against the grain of a normal request to ask what some concept 'means'. What is 'democracy'?
19. Language / A. Nature of Meaning / 6. Meaning as Use
Take meaning to be use in calculation with concepts, rather than in communication [Harman]
     Full Idea: (Nonsolipsistic) conceptual role semantics is a version of the theory that meaning is use, where the basic use is taken to be in calculation, not in communication, and where concepts are treated as symbols in a 'language of thought'.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.1)
     A reaction: The idea seems to be to connect the highly social Wittgensteinian view of language with the reductive physicalist account of how brains generate concepts. Interesting, thought I never like meaning-as-use.
The use theory attaches meanings to words, not to sentences [Harman]
     Full Idea: A use theory of meaning has to suppose it is words and ways of putting words together that have meaning because of their uses, not sentences.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.3)
     A reaction: He says that most sentences are unique, so cannot have a standard use. Words do a particular job over and over again. How do you distinguish the quirky use of a word from its standard use?
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman]
     Full Idea: Conceptual role semantics involves meanings of expressions determined by used contents of concepts and thoughts, contents constructed from concepts, concepts determined by functional role, which involves relations to things in the world.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1)
     A reaction: This essay is the locus classicus for conceptual-role semantics. Any attempt to say what something IS by giving an account of its function always feels wrong to me.
Some regard conceptual role semantics as an entirely internal matter [Harman]
     Full Idea: I call my conceptual role semantics 'non-solipsistic' to contrast it with that of authors (Field, Fodor, Loar) who think of conceptual role solipsistically as a completely internal matter.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1)
     A reaction: Evidently Harman is influenced by Putnam's Twin Earth, and that meanings ain't in the head, so that the conceptual role has to be extended out into the world to get a good account. I prefer extending into the language community, rather into reality.
The content of thought is relations, between mental states, things in the world, and contexts [Harman]
     Full Idea: In (nonsolipsistic) conceptual role semantics the content of thought is not in an 'intrinsic nature', but is rather a matter of how mental states are related to each other, to things in the external world, and to things in a context understood as normal.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.3)
     A reaction: This is part of Harman's functional view of consciousness, which I find rather dubious. If things only have identity because of some place in a flow diagram, we must ask why that thing has that place in that diagram.
19. Language / F. Communication / 3. Denial
If one proposition negates the other, which is the negative one? [Harman]
     Full Idea: A relation of negation might hold between two beliefs without there being anything that determines which belief is the negative one.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.4)
     A reaction: [He attributes this thought to Brian Loar] This seems to give us a reason why we need a semantics for a logic, and not just a structure of inferences and proofs.
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Mastery of a language requires thinking, and not just communication [Harman]
     Full Idea: If one cannot think in a language, one has not yet mastered it. A symbol system used only for communication, like Morse code, is not a language.
     From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.2)
     A reaction: This invites the question of someone who has mastered thinking, but has no idea how to communicate. No doubt we might construct a machine with something like that ability. I think it might support Harman's claim.