Combining Philosophers

All the ideas for William James, Jan-Erik Jones and A.George / D.J.Velleman

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89 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
It is wisdom to believe what you desire, because belief is needed to achieve it [James]
     Full Idea: Clearly it is often the part of wisdom to believe what one desires; for the belief is one of indispensable preliminary conditions of the realisation of its object.
     From: William James (The Sentiment of Rationality [1882], p.43)
     A reaction: Roughly, action is impossible without optimism about possible success. This may count as instinct, rather than 'wisdom'.
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
All good philosophers start from a dumb conviction about which truths can be revealed [James]
     Full Idea: Every philosopher whose initiative counts for anything in the evolution of thought has taken his stand on a sort of dumb conviction that the truth must lie in one direction rather than another, and a preliminary assurance that this can be made to work.
     From: William James (The Sentiment of Rationality [1882], p.40)
     A reaction: I would refer to this as 'intuition', which I think of as reasons (probably good reasons) which cannot yet be articulated. Hence I like this idea very much, except for the word 'dumb'. It is more like a rational vision, yet to be filled in.
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
A complete system is just a classification of the whole world's ingredients [James]
     Full Idea: A completed theoretic philosophy can never be anything more than a completed classification of the world's ingredients.
     From: William James (The Sentiment of Rationality [1882], p.23)
     A reaction: I assume this is not just the physical ingredients, but must also include our conceptual scheme - but then we must first decide which is the best conceptual scheme to classify, and that's where the real action is. [He scorns such classifation later].
2. Reason / A. Nature of Reason / 5. Objectivity
A single explanation must have a single point of view [James]
     Full Idea: A single explanation of a fact only explains it from a single point of view.
     From: William James (The Sentiment of Rationality [1882], p.23)
     A reaction: I take this to imply that multiple viewpoints lead us towards objectivity. The single viewpoint of an expert is of much greater value than that of a novice, on the whole.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Man has an intense natural interest in the consistency of his own thinking [James]
     Full Idea: After man's interest in breathing freely, the greatest of all his interests (because it never fluctuates or remits….) is his interest in consistency, in feeling that what he now thinks goes with what he thinks on other occasions.
     From: William James (The Pragmatist Account of Truth [1908], 'Seventh')
     A reaction: People notoriously contradict themselves all the time, but I suspect that it is when they get out of their depth in complexities such as politics. They probably achieve great consistency within their own expertise, and in common knowledge.
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James]
     Full Idea: Our pleasure at finding that a chaos of facts is the expression of single underlying fact is like a musician's relief at discovering harmony. …The passion for economy of means in thought is the philosophic passion par excellence.
     From: William James (The Sentiment of Rationality [1882], p.21)
     A reaction: We do, though, possess an inner klaxon warning against stupid simplistic reductions. Reducing all the miseries of life to the workings of the Devil is not satisfactory, even it it is economical. Simplicities are dangerously tempting.
2. Reason / D. Definition / 4. Real Definition
'Nominal' definitions identify things, but fail to give their essence [Jones,J-E]
     Full Idea: In the Aristotelian tradition, a 'nominal' definition is a pseudo-definition that identifies the members of the species or genus, but fails to capture the essence, e.g. 'man is the featherless biped'.
     From: Jan-Erik Jones (Real Essence [2012], §2)
     A reaction: You can 'individuate' an object as 'the only object in that drawer', while revealing nothing about it. So what must a definition do, in addition to picking something out uniquely?
2. Reason / D. Definition / 7. Contextual Definition
Contextual definitions replace a complete sentence containing the expression [George/Velleman]
     Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
     A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step.
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative definitions quantify over the thing being defined [George/Velleman]
     Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
     A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known.
3. Truth / A. Truth Problems / 2. Defining Truth
You can only define a statement that something is 'true' by referring to its functional possibilities [James]
     Full Idea: Pragmatism insists that statements and beliefs are inertly and statically true only by courtesy: they practically pass for true; but you cannot define what you mean by calling them true without referring to their functional possibilities.
     From: William James (The Meaning of the Word "Truth" [1907], p.2)
     A reaction: I think this clarifies an objection to pragmatism, because all functional definitions (e.g. of the mind, or of moral behaviour) are preceded by the question of WHY this thing is able to function in this way. What special quality makes this possible?
3. Truth / A. Truth Problems / 9. Rejecting Truth
Truth is just a name for verification-processes [James]
     Full Idea: Truth for us is simply a collective name for verification-processes, just as 'health' is a name for other processes in life.
     From: William James (Pragmatism - eight lectures [1907], Lec 6)
     A reaction: So the slogan is 'truth is success in belief'? Suicide and racist genocide can be 'successful'. I would have thought that truth was the end of a process, rather than the process itself.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
In many cases there is no obvious way in which ideas can agree with their object [James]
     Full Idea: When you speak of the 'time-keeping function' of a clock, it is hard to see exactly what your ideas can copy. ...Where our ideas cannot copy definitely their object, what does agreement with that object mean?
     From: William James (Pragmatism - eight lectures [1907], Lec 6)
     A reaction: This is a very good criticism of the correspondence theory of truth. It looks a lovely theory when you can map components of a sentence (like 'the pen is in the drawer') onto components of reality - but it has to cover the hard cases.
3. Truth / D. Coherence Truth / 1. Coherence Truth
Ideas are true in so far as they co-ordinate our experiences [James]
     Full Idea: Pragmatists say that ideas (which themselves are but parts of our experience) become true just in so far as they help us to get into satisfactory relation with other parts of our experience.
     From: William James (Pragmatism - eight lectures [1907], Lec 2)
     A reaction: I'm struck by the close similarity (at least in James) of the pragmatic view of truth and the coherence theory of truth (associated later with Blanshard). Perhaps the coherence theory is one version of the pragmatic account
New opinions count as 'true' if they are assimilated to an individual's current beliefs [James]
     Full Idea: A new opinion counts as 'true' just in proportion as it gratifies the individual's desire to assimilate the novel in his experience to his beliefs in stock.
     From: William James (Pragmatism - eight lectures [1907], Lec 2)
     A reaction: Note the tell-tale locution 'counts as' true, rather than 'is' true. The obvious problem is that someone with a big stock of foolish beliefs will 'count as' true some bad interpretation which is gratifyingly assimilated to their current confusions.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
If the hypothesis of God is widely successful, it is true [James]
     Full Idea: On pragmatistic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, it is true.
     From: William James (The Meaning of the Word "Truth" [1907], p.299), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 35 'Prag'
     A reaction: How you get from 'widely satisfactory' to 'true' is beyond my comprehension. This is dangerous nonsense. This view of truth seems to be a commonplace in American culture. Peirce hurray! James boo! James accepted verification, where possible.
True ideas are those we can assimilate, validate, corroborate and verify (and false otherwise) [James]
     Full Idea: True ideas are those that we can assimilate, validate, corroborate and verify. False ideas are those that we cannot.
     From: William James (Pragmatism - eight lectures [1907], Lec 6)
     A reaction: The immediate question is why you should label something as 'false' simply on the grounds that you can't corroborate it. Proving the falsity is a stronger position than the ignorance James seems happy with. 'Assimilate' implies coherence.
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'power set' of A is all the subsets of A [George/Velleman]
     Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman]
     Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: See Idea 10100 for the Axiom of Pairing.
Cartesian Product A x B: the set of all ordered pairs in which a∈A and b∈B [George/Velleman]
     Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
Grouping by property is common in mathematics, usually using equivalence [George/Velleman]
     Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman]
     Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: This is a key concept in the Fregean strategy for defining numbers.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman]
     Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman]
     Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman]
     Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)).
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: See Idea 10099 for an application of this axiom.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
The Axiom of Reducibility made impredicative definitions possible [George/Velleman]
     Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman]
     Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)
     A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets.
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman]
     Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)
     A reaction: Note that ZFC has not been proved consistent.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman]
     Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)
     A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism?
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
     Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)
     A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true.
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
Differences between isomorphic structures seem unimportant [George/Velleman]
     Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters?
5. Theory of Logic / K. Features of Logics / 2. Consistency
Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]
     Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]
     Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]
     Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
5. Theory of Logic / K. Features of Logics / 4. Completeness
A 'complete' theory contains either any sentence or its negation [George/Velleman]
     Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)
     A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences....
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Rational numbers give answers to division problems with integers [George/Velleman]
     Full Idea: We can think of rational numbers as providing answers to division problems involving integers.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: Cf. Idea 10102.
The integers are answers to subtraction problems involving natural numbers [George/Velleman]
     Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers provide answers to square root problems [George/Velleman]
     Full Idea: One reason for introducing the real numbers is to provide answers to square root problems.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Logicists say mathematics is applicable because it is totally general [George/Velleman]
     Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
     A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
The classical mathematician believes the real numbers form an actual set [George/Velleman]
     Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman]
     Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman]
     Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)
     A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
A successor is the union of a set with its singleton [George/Velleman]
     Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman]
     Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs).
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1)
     A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory can prove the Peano Postulates [George/Velleman]
     Full Idea: The Peano Postulates can be proven in ZFC.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman]
     Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro)
     A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless!
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman]
     Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002])
     A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman]
     Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman]
     Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: The objects are Type 0, the basic sets Type 1, etc.
The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman]
     Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness.
Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman]
     Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
     A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them?
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Much infinite mathematics can still be justified finitely [George/Velleman]
     Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8)
     A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification.
Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman]
     Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
     A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
The intuitionists are the idealists of mathematics [George/Velleman]
     Full Idea: The intuitionists are the idealists of mathematics.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman]
     Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem.
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8)
     A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths.
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
Realities just are, and beliefs are true of them [James]
     Full Idea: Realities are not true, they are; and beliefs are true of them.
     From: William James (The Pragmatist Account of Truth [1908], 'Fourth')
     A reaction: At last, a remark by James about truth which I really like. For 'realities' I would use the word 'facts'.
7. Existence / E. Categories / 2. Categorisation
Classification can only ever be for a particular purpose [James]
     Full Idea: Every way of classifying a thing is but a way of handling it for some particular purpose. Conceptions, 'kinds', are teleological instruments.
     From: William James (The Sentiment of Rationality [1882], p.24)
     A reaction: Could there not be ways of classifying which suit all of our purposes? If there were a naturally correct way to classifying things, then any pragmatist would probably welcome that. (I don't say there is such a way).
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
A 'thing' is simply carved out of reality for human purposes [James]
     Full Idea: What shall we call a 'thing' anyhow? It seems quite arbitrary, for we carve out everything, just as we carve out constellations, to suit our human purposes.
     From: William James (Pragmatism - eight lectures [1907], Lec 7)
     A reaction: James wrote just before the discovery of galaxies, which are much more obviously 'things' than constellations like the Plough are! This idea suggests a connection between pragmatism and the nihilist view of objects of Van Inwagen and co.
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
'Substance' is just a word for groupings and structures in experience [James]
     Full Idea: 'Substance' appears now only as another name for the fact that phenomena as they come are actually grouped and given in coherent forms.
     From: William James (Pragmatism - eight lectures [1907], Lec 4)
     A reaction: This is the strongly empirical strain in James's empiricism. This sounds like a David Lewis comment on the Humean mosaic of experience. We Aristotelians at least believe that the groups run much deeper than the surface of experience.
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
Truth is a species of good, being whatever proves itself good in the way of belief [James]
     Full Idea: Truth is one species of good, and not, as is usually supposed, a category distinct from good, and co-ordinate with it. The true is whatever proves itself to be good in the way of belief, and good, too, for definite, assignable reasons.
     From: William James (Pragmatism - eight lectures [1907], Lec 2)
     A reaction: The trouble is that false optimism can often often be what is 'good in the way of belief'. That said, I think quite a good way to specify 'truth' is 'success in belief', but I mean intrinsically successful, not pragmatically successful.
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism accepts any hypothesis which has useful consequences [James]
     Full Idea: On pragmatic principles we cannot reject any hypothesis if consequences useful to life flow from it.
     From: William James (Pragmatism - eight lectures [1907], Lec 8)
     A reaction: Most governments seem to find lies more useful than the truth. Maybe most children are better off not knowing the truth about their parents. It might be disastrous to know the truth about what other people are thinking. Is 'useful but false' meaningful?
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James]
     Full Idea: We find satisfaction in consistency between the present idea and the entire rest of our mental equipment, including the whole order of our sensations, and that of our intuitions of likeness and difference, and our whole stock previously acquired truths.
     From: William James (The Pragmatist Account of Truth [1908], 'Fourth')
     A reaction: I like this, apart from the idea that the criterion of good coherence seems to be subjective 'satisfaction'. We should ask why some large set of beliefs is coherent. I assume nature is coherent, and truth is the best explanation of our coherence about it.
14. Science / A. Basis of Science / 1. Observation
Scientific genius extracts more than other people from the same evidence [James]
     Full Idea: What is the use of being a genius, unless with the same scientific evidence as other men, one can reach more truth than they?
     From: William James (The Sentiment of Rationality [1882], p.40)
     A reaction: This is aimed at Clifford's famous principle. He isn't actually contraverting the principle, but it is a nice point about evidence. Simple empiricists think detectives only have to stare at the evidence and the solution creates itself.
14. Science / A. Basis of Science / 6. Falsification
Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James]
     Full Idea: Each tester of the truth of a theory …acts as if it were true, and expects the result to disappoint him if his assumption is false. The longer disappointment is delayed, the stronger grows his faith in his theory.
     From: William James (The Sentiment of Rationality [1882], p.42)
     A reaction: This is almost exactly Popper's falsificationist proposal for science, which interestingly shows the close relationship of his view to pragmatism. Believe it as long as it is still working.
14. Science / B. Scientific Theories / 2. Aim of Science
Theories are practical tools for progress, not answers to enigmas [James]
     Full Idea: Theories are instruments, not answers to enigmas, in which we can rest. We don't lie back upon them, we move forward, and, on occasion, make nature over again by their aid. Pragmatism unstiffens all our theories, limbers them up and sets each one to work.
     From: William James (Pragmatism - eight lectures [1907], Lec 2)
     A reaction: This follows his criticism of the quest for 'solving names' - big words that give bogus solutions to problems. James's view is not the same as 'instrumentalism', though he would probably sympathise with that view. The defines theories badly.
14. Science / B. Scientific Theories / 3. Instrumentalism
True thoughts are just valuable instruments of action [James]
     Full Idea: The possession of true thoughts means everywhere the possession of invaluable instruments of action.
     From: William James (Pragmatism - eight lectures [1907], Lec 6)
     A reaction: It looks to me like we should distinguish 'active' and 'passive' instrumentalism. The passive version says there is no more to theories and truth than what instruments record. James's active version says truth is an instrument for doing things well.
Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James]
     Full Idea: The pragmatist view is that all our theories are instrumental, are mental modes of adaptation to reality, rather than revelations or gnostic answers to some divinely instituted world enigma.
     From: William James (Pragmatism - eight lectures [1907], Lec 5)
     A reaction: This treats instrumentalism as the pragmatic idea of theories as what works (and nothing more), with, presumably, no interest in grasping something called 'reality'. Presumably instrumentalism might have other motivations - such as fun.
14. Science / C. Induction / 3. Limits of Induction
We can't know if the laws of nature are stable, but we must postulate it or assume it [James]
     Full Idea: That nature will follow tomorrow the same laws that she follows today is a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it.
     From: William James (The Sentiment of Rationality [1882], p.39)
     A reaction: The stability of nature is something to be assessed, not something taken for granted. If you arrive in a new city and it all seems quiet, you keep your fingers crossed and treat it as stable. But revolution or coup could be just round the corner.
14. Science / C. Induction / 6. Bayes's Theorem
Trying to assess probabilities by mere calculation is absurd and impossible [James]
     Full Idea: The absurd abstraction of an intellect verbally formulating all its evidence and carefully estimating the probability thereof solely by the size of a vulgar fraction, is as ideally inept as it is practically impossible.
     From: William James (The Sentiment of Rationality [1882], p.40)
     A reaction: James probably didn't know about Bayes, but this is directed at the Bayesian approach. My view is that full rational assessment of coherence is a much better bet than a Bayesian calculation. Factors must be weighted.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
We have a passion for knowing the parts of something, rather than the whole [James]
     Full Idea: Alongside the passion for simplification …is the passion for distinguishing; it is the passion to be acquainted with the parts rather than to comprehend the whole.
     From: William James (The Sentiment of Rationality [1882], p.22)
     A reaction: As I child I dismantled almost every toy I was given. This seems to be the motivation for a lot of analytic philosophy, but Aristotle also tended to think that way.
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
The mind has evolved entirely for practical interests, seen in our reflex actions [James]
     Full Idea: It is far too little recognised how entirely the intellect is built up of practical interests. The theory of evolution is beginning to do very good service by its reduction of all mentality to the type of reflex action.
     From: William James (The Sentiment of Rationality [1882], p.34)
     A reaction: Hands evolved for manipulating tools end up playing the piano. Minds evolved for action can be afflicted with boredom. He's not wrong, but he is risking the etymological fallacy (origin = purpose). I take navigation to be the original purpose of mind.
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Dogs' curiosity only concerns what will happen next [James]
     Full Idea: A dog's curiosity about the movements of his master or a strange object only extends as far as the point of what is going to happen next.
     From: William James (The Sentiment of Rationality [1882], p.31)
     A reaction: Good. A nice corrective to people like myself who are tempted to inflate animal rationality, in order to emphasise human evolutionary continuity with them. It is hard to disagree with his observation. But dogs do make judgements! True/false!
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
Consciousness is not a stuff, but is explained by the relations between experiences [James]
     Full Idea: Consciousness connotes a kind of external relation, and not a special stuff or way of being. The peculiarity of our experiences, that they not only are, but are known, is best explained by their relations to one another, the relations being experiences.
     From: William James (Does Consciousness Exist? [1904], §3)
     A reaction: This view has suddenly caught people's interest. It might be better than the higher/lower relationship, which seems to leave the basic problem untouched. Does a whole network of relations between experiences gradually 'add up' to consciousness?
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
'Consciousness' is a nonentity, a mere echo of the disappearing 'soul' [James]
     Full Idea: 'Consciousness' is the name of a nonentity. ..Those who cling to it are clinging to a mere echo, the faint rumour left behind by the disappearing 'soul' upon the air of philosophy. ..I deny that it stands for an entity, but it does stand for a function.
     From: William James (Does Consciousness Exist? [1904], Intro)
     A reaction: This kind of view is often treated as being preposterous, but I think it is correct. No one is denying the phenomenology, but it is the ontology which is at stake. Either you are a substance dualist, or mind must be eliminated as an 'entity'.
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Rage is inconceivable without bodily responses; so there are no disembodied emotions [James]
     Full Idea: Can one fancy a state of rage and picture no flushing of the face, no dilation of the nostrils, no clenching of the teeth, no impulse to vigorous action? …A purely disembodied human emotion is a nonentity.
     From: William James (What is an Emotion? [1884], p.194), quoted by Peter Goldie - The Emotions 3 'Bodily'
     A reaction: Plausible for rage, but less so for irritation or admiration. Goldie thinks James is wrong. James says if intellectual feelings don't become bodily then they don't qualify as emotions. No True Scotsman!
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
How can the ground of rationality be itself rational? [James]
     Full Idea: Can that which is the ground of rationality in all else be itself properly called rational?
     From: William James (The Sentiment of Rationality [1882], p.25)
     A reaction: This is the perennial problem in deciding grounds, and in deciding what to treat as primitive. The stoics see the whole of nature as rational. Cf how can the ground of what is physical be itself physical?
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
It seems that we feel rational when we detect no irrationality [James]
     Full Idea: I think there are very good grounds for upholding the view that the feeling of rationality is constituted merely by the absence of any feelings of irrationality.
     From: William James (The Sentiment of Rationality [1882], p.20)
     A reaction: A very interesting proposal. Nothing is more basic to logic (well, plausible versions of logic) than the principle of non-contradiction - perhaps because it is the foundation of our natural intellectual equipment.
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Corresponding to every concept there is a class (some of them sets) [George/Velleman]
     Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes).
     From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
We return to experience with concepts, where they show us differences [James]
     Full Idea: Concepts for the pragmatist are things to come back into experience with, things to make us look for differences.
     From: William James (Pragmatism - eight lectures [1907], Lec 3)
     A reaction: That's good. I like both halves of this. Experience gives us the concepts, but then we 'come back' into experience equipped with them. Presumably animals can look for differences, but concepts enhance that hugely. Know the names of the flowers.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
Evolution suggests prevailing or survival as a new criterion of right and wrong [James]
     Full Idea: The philosophy of evolution offers us today a new criterion, which is objective and fixed, as an ethical test between right and wrong: That is to be called good which is destined to prevail or survive.
     From: William James (The Sentiment of Rationality [1882], p.44)
     A reaction: Perceptive for its time. Herbert Spencer may have suggested the idea. James dismisses it, because it implies a sort of fatalism, whereas genuine moral choices are involved in what survives.
23. Ethics / E. Utilitarianism / 4. Unfairness
Imagine millions made happy on condition that one person suffers endless lonely torture [James]
     Full Idea: Consider a case in which millions could be made permanently happy on the one simple condition that a certain lost soul on the far-off edge of things should lead a life of lonely torture.
     From: William James (The Will to Believe [1896], p.188), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.2
     A reaction: This seems to be one of the earliest pinpointings of a key problem with utilitiarianism, which is that other values than happiness (in this case, fairness) seem to be utterly overruled. If we ignore fairness, why shouldn't we ignore happiness?
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
Understanding by means of causes is useless if they are not reduced to a minimum number [James]
     Full Idea: The knowledge of things by their causes, which is often given as a definition of rational knowledge, is useless unless the causes converge to a minimum number, while still producing the maximum number of effects.
     From: William James (The Sentiment of Rationality [1882], p.21)
     A reaction: This is certainly the psychological motivation for trying to identify 'the' cause of something, but James always tries to sell such things as subjective. 'Useless' to one person is a subjective criterion; useless to anyone is much more objective.
28. God / A. Divine Nature / 3. Divine Perfections
If there is a 'greatest knower', it doesn't follow that they know absolutely everything [James]
     Full Idea: The greatest knower of them all may yet not know the whole of everything, or even know what he does know at one single stroke: - he may be liable to forget.
     From: William James (Pragmatism - eight lectures [1907], Lec 4)
     A reaction: And that's before you get to the problem of how the greatest knower could possibly know whether or not they knew absolutely everything, or whether there might be some fact which was irremediably hidden from them.
28. God / A. Divine Nature / 4. Divine Contradictions
It is hard to grasp a cosmic mind which produces such a mixture of goods and evils [James]
     Full Idea: We can with difficulty comprehend the character of a cosmic mind whose purposes are fully revealed by the strange mixture of good and evils that we find in this actual world's particulars.
     From: William James (Pragmatism - eight lectures [1907], Lec 3)
     A reaction: And, of course, what counts as 'goods' or 'evils' seems to have a highly relative aspect to it. To claim that really it is all good is massive hope based on flimsy evidence.
28. God / B. Proving God / 1. Proof of God
If the God hypothesis works well, then it is true [James]
     Full Idea: On pragmatistic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, it is true.
     From: William James (Pragmatism - eight lectures [1907], Lec 8)
     A reaction: The truth of God's existence certainly is a challenging test case for the pragmatic theory of truth, and James really bites the bullet here. Pragmatism may ultimately founder on the impossibility of specifying what 'works satisfactorily' means.
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
The wonderful design of a woodpecker looks diabolical to its victims [James]
     Full Idea: To the grub under the bark the exquisite fitness of the woodpecker's organism to extract him would certainly argue a diabolical designer.
     From: William James (Pragmatism - eight lectures [1907], Lec 3)
     A reaction: What an elegant sentence! The huge problem for religious people who accept (probably reluctantly) evolution by natural selection is the moral nature of the divine being who could use such a ruthless method of design.
Things with parts always have some structure, so they always appear to be designed [James]
     Full Idea: The parts of things must always make some definite resultant, be it chaotic or harmonious. When we look at what has actually come, the conditions must always appear perfectly designed to ensure it.
     From: William James (Pragmatism - eight lectures [1907], Lec 3)
     A reaction: In so far as the design argument is an analogy with human affairs, we can't deny that high levels of order suggest an organising mind, and mere chaos suggests a coincidence of unco-ordinated forces.
28. God / B. Proving God / 3. Proofs of Evidence / d. Religious Experience
Private experience is the main evidence for God [James]
     Full Idea: I myself believe that the evidence for God lies primarily in inner personal experience.
     From: William James (Pragmatism - eight lectures [1907], Lec 3)
     A reaction: There is not much you can say to someone who claims incontrovertible evidence which is utterly private to themselves. Does total absence of private religious experience count as evidence on the subject?
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Early Christianity says God recognises the neglected weak and tender impulses [James]
     Full Idea: In what did the emancipating message of primitive Christianity consist but in the announcement that God recognizes those weak and tender impulses which paganism had so rudely overlooked.
     From: William James (The Sentiment of Rationality [1882], p.36)
     A reaction: Nietzsche says these are the virtues of a good slave. Previous virtues were dominated by military needs, but the new virtues are those of large cities, where communal living with strangers is the challenge.
29. Religion / C. Spiritual Disciplines / 3. Buddhism
Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James]
     Full Idea: Nirvana means safety from the everlasting round of adventures of which the world of sense consists. The hindoo and the buddhist for this is essentially their attitude, are simply afraid, afraid of more experience, afraid of life.
     From: William James (Pragmatism - eight lectures [1907], Lec 8)
     A reaction: Wonderfully American! From what I have seen of eastern thought, including Taoism, I agree with James, in general. There is a rejection of knowledge and of human life which I find shocking. I suspect it is a defence mechanism for downtrodden people.