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All the ideas for 'Remarks on the definition and nature of mathematics', 'Pragmatism - eight lectures' and 'Ontology'

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45 ideas

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
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 / D. Modal Logic ML / 4. Alethic Modal Logic
The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette]
     Full Idea: The modal syntax and axiom systems of C.I.Lewis (1918) were formally interpreted by Kripke and Hintikka (c.1965) who, using Z-F set theory, worked out model set-theoretical semantics for modal logics and quantified modal logics.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: A historical note. The big question is always 'who cares?' - to which the answer seems to be 'lots of people', if they are interested in precision in discourse, in artificial intelligence, and maybe even in metaphysics. Possible worlds started here.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic describes inferences between sentences expressing possible properties of objects [Jacquette]
     Full Idea: It is fundamental that logic depends on logical possibilities, in which logically possible properties are predicated of logically possible objects. Logic describes inferential structures among sentences expressing the predication of properties to objects.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: If our imagination is the only tool we have for assessing possibilities, this leaves the domain of logic as being a bit subjective. There is an underlying Platonism to the idea, since inferences would exist even if nothing else did.
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette]
     Full Idea: At one level logic can be regarded as a theory of signs and formal rules, but we cannot neglect the meaning of propositions as they relate to states of affairs, and hence to possible properties and objects... there must be the possibility of truth-values.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: Thus if you define logical connectives by truth tables, you need the concept of T and F. You could, though, regard those too as purely formal (like 1 and 0 in electronics). But how do you decide which propositions are 1, and which are 0?
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
     Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
     A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette]
     Full Idea: It is infamous that on Russell's analysis the sentences "The winged horse has wings" and "The winged horse is a horse" are false, because in the extant domain of actual existent entities there contingently exist no winged horses
     From: Dale Jacquette (Ontology [2002], Ch. 6)
     A reaction: This is the best objection I have heard to Russell's account of definite descriptions. The connected question is whether 'quantifies over' is really a commitment to existence. See Idea 6067.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Can a Barber shave all and only those persons who do not shave themselves? [Jacquette]
     Full Idea: The Barber Paradox refers to the non-existent property of being a barber who shaves all and only those persons who do not shave themselves.
     From: Dale Jacquette (Ontology [2002], Ch. 9)
     A reaction: [Russell spotted this paradox, and it led to his Theory of Types]. This paradox may throw light on the logic of indexicals. What does "you" mean when I say to myself "you idiot!"? If I can behave as two persons, so can the barber.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
     Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
     A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Saying mathematics is logic is merely replacing one undefined term by another [Curry]
     Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
To grasp being, we must say why something exists, and why there is one world [Jacquette]
     Full Idea: We grasp the concept of being only when we have satisfactorily answered the question why there is something rather than nothing and why there is only one logically contingent actual world.
     From: Dale Jacquette (Ontology [2002], Conclusion)
     A reaction: See Ideas 7688 and 7692 for a glimpse of Jacquette's answer. Personally I don't yet have a full grasp of the concept of being, but I'm sure I'll get there if I only work a bit harder.
7. Existence / A. Nature of Existence / 5. Reason for Existence
Being is maximal consistency [Jacquette]
     Full Idea: Being is maximal consistency.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: You'll have to read Ch.2 of Jacquette to see what this is all about, but as it stands it is a lovely slogan, and a wonderful googly/curve ball to propel at Parmenides or Heidegger.
Existence is completeness and consistency [Jacquette]
     Full Idea: A combinatorial ontology holds that existence is nothing more or less than completeness and consistency, or what is also called 'maximal consistency'.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: You'll have to read Jacquette to understand this one! The claim is that existence is to be defined in terms of logic (and whatever is required for logic). I take this to be a bit Platonist (rather than conventionalist) about logic.
7. Existence / D. Theories of Reality / 1. Ontologies
Ontology is the same as the conceptual foundations of logic [Jacquette]
     Full Idea: The principles of pure philosophical ontology are indistinguishable ... from the conceptual foundations of logic.
     From: Dale Jacquette (Ontology [2002], Pref)
     A reaction: I would take Russell to be an originator of this view. If the young Wittgenstein showed that the foundations of logic are simply conventional (truth tables), this seems to make ontology conventional too, which sounds very odd indeed (to me).
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Ontology must include the minimum requirements for our semantics [Jacquette]
     Full Idea: The entities included in a theoretical ontology are those minimally required for an adequate philosophical semantics. ...These are the objects that we say exist, to which we are ontologically committed.
     From: Dale Jacquette (Ontology [2002], Pref)
     A reaction: Worded with exquisite care! He does not say that ontology is reducible to semantics (which is a silly idea). We could still be committed, as in a ghost story, to existence of some 'nameless thing'. Things utterly beyond our ken might exist.
7. Existence / E. Categories / 3. Proposed Categories
Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette]
     Full Idea: Logic involves the possibilities of predicating properties of objects in a conceptual scheme wherein either objects and properties are included in altogether separate categories, or objects are reducible to combinations of properties.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: In the first view, he says that objects are just 'logical pegs' for properties. Objects can't be individuated without properties. But combinations of properties would seem to need essences, or else they are too unstable to count as objects.
Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette]
     Full Idea: We can reduce references to states-of-affairs to object-property combinations, and we can reduce logically possible worlds to logically possible states-of-affairs combinations.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: If we further reduce object-property combinations to mere combinations of properties (Idea 7683), then we have reduced our ontology to nothing but properties. Wow. We had better be very clear, then, about what a property is. I'm not.
8. Modes of Existence / B. Properties / 11. Properties as Sets
If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette]
     Full Idea: If classes alone cannot be eliminated from ontology on Quine's terms, and if classes are defined as property combinations, then neither are all properties, universals in the tradition sense, entirely eliminable.
     From: Dale Jacquette (Ontology [2002], Ch. 9)
     A reaction: If classes were totally conventional (and there was no such things as a 'natural' class) then you might admit something to a class without knowing its properties (as 'the thing in the box').
9. Objects / A. Existence of Objects / 1. Physical Objects
An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette]
     Full Idea: To be an object is to be a predication subject, and to be this as opposed to that particular object, whether existent or not, is to have a distinctive combination of properties.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: The last part depends on Leibniz's Law. The difficulty is that two objects may only be distinguishable by being in different places, and location doesn't look like a property. Cf. Idea 5055.
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette]
     Full Idea: Roughly, numbers, sets and propositions are assumed to be abstract particulars, while properties, including qualities and relations, are usually thought to be universals.
     From: Dale Jacquette (Ontology [2002], Ch. 9)
     A reaction: There is an interesting nominalist project of reducing all of these to particulars. Numbers to patterns, sets to their members, propositions to sentences, properties to causal powers, relations to, er, something else.
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.
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The actual world is a consistent combination of states, made of consistent property combinations [Jacquette]
     Full Idea: The actual world is a maximally consistent state-of-affairs combination involving all and only the existent objects, which in turn exist because they are maximally consistent property combinations.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: [This extends Idea 7688]. This seems to invite the standard objections to the coherence theory of truth, such as Ideas 5422 and 4745. Is 'maximal consistency' merely a test for actuality, rather than an account of what actuality is?
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
The actual world is a maximally consistent combination of actual states of affairs [Jacquette]
     Full Idea: The actual world can be defined as a maximally consistent combination of actual states of affairs, or maximally consistent states-of-affairs combination.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: A key part of Jacquette's program of deriving ontological results from the foundations of logic. Is the counterfactual situation of my pen being three centimetres to the left of its current position a "less consistent" situation than the actual one?
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette]
     Full Idea: Many modal logicians in their philosophical moments have raised doubts about whether structures of propositions not associated with the actual world deserved to be called worlds at all.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: A good question. Consistency is obviously required, but we also need a lot of propositions before we would consider it a 'world'. Very remote but consistent worlds quickly become unimaginable. Does that matter?
We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette]
     Full Idea: Conventional modal semantics, in which all logically possible worlds are defined in terms of maximally consistent proposition sets, has no choice except to allow that the actual world is the world we experience in sensation, or that we inhabit.
     From: Dale Jacquette (Ontology [2002], Ch. 9)
     A reaction: Jacquette dislikes this because he is seeking an account of ontology that doesn't, as so often, merely reduce to epistemology (e.g. Berkeley). See Idea 7691 for his preferred account.
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?
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.
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette]
     Full Idea: If qualia supervene on intentional states, then intentionality is also more explanatorily fundamental than qualia.
     From: Dale Jacquette (Ontology [2002], Ch.10)
     A reaction: See Idea 7272 for opposite view. Maybe intentional states are large mental objects of which we are introspectively aware, but which are actually composed of innumerable fine-grained qualia. Intentional states would only explain qualia if they caused them.
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette]
     Full Idea: If intentionality sometimes involves a relation to nonexistent objects, like my dreamed-of visit to a Greek island, then such thoughts cannot be explained physically or causally, because only actual physical entities and events can be mentioned.
     From: Dale Jacquette (Ontology [2002], Ch.10)
     A reaction: Unimpressive. Thoughts of a Greek island will obviously reduce to memories of islands and Greece and travel brochures. Memory clearly retains past events in the present, and hence past events can be part of the material used in reductive accounts.
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.
19. Language / D. Propositions / 1. Propositions
The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette]
     Full Idea: The extreme ontological alternatives with respect to the metaphysics of propositions are a Fregean Platonism (his "gedanken", 'thoughts'), and a radical nominalism or inscriptionalism, as in Quine, where they are just marks related to stimuli.
     From: Dale Jacquette (Ontology [2002], Ch. 9)
     A reaction: Personally I would want something between the two - that propositions are brain events of a highly abstract kind. I say that introspection reveals pre-linguistic thoughts, which are propositions. A proposition is an intentional state.
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 / 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.