49 ideas
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
| Full Idea: As Kreisel has remarked, what is important is not the existence of mathematical objects, but the objectivity of mathematical statements. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: [see Maddy 2011:115 for the history of this idea] It seems rather unclear where Frege stands on objectivity. Maddy embraces it, following up this idea, and Tyler Burge's fat book on objectivity. |
| 23247 | The need to act produces consciousness, and practical reason is the root of all reason [Fichte] |
| Full Idea: Consciousness of the real world proceeds from the need to act, not the other way around. …Practical reason is the root of all reason. | |
| From: Johann Fichte (The Vocation of Man [1800], 3.I) | |
| A reaction: Strongly agree with the last part. In my conceptual scheme 'sensible' behaviour (e.g. of animals) precedes, in every way, rational behaviour. Sensible attitudes to quantity and magnitude precede mathematical logic. Minds exist for navigation. |
| 23232 | Sufficient reason makes the transition from the particular to the general [Fichte] |
| Full Idea: The principle of sufficient reason is the point of transition from the particular, which is itself, to the general, which is outside it. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: Not sure I understand this, but it seems worth passing on. Personally I would say that we have a knack of generalising, triggered when we spot patterns. |
| 10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
| Full Idea: A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
| Full Idea: We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| Full Idea: In the intuitionist view, the notion of an intuitive proof cannot be expected to coincide with that of a proof in a formal system, and Gödel's incompleteness theorem is thus unsurprising from an intuitionist point of view. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
| Full Idea: From the intuitionist point of view natural numbers are mental constructions, so their totality is only potential, but it is neverthless a fully determinate totality. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This could only be if the means of constructing the numbers was fully determinate, so how does that situation come about? |
| 10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
| Full Idea: Dummett distinguishes, roughly, between those concrete objects which can be possible objects of ostension, and abstract objects which can only be referred to by functional expressions whose argument is some other object. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: At least someone has proposed a theory! Hale gives a nice critical discussion of the proposal. It is a moot point whether in the second case, when you pick out the 'other object', you are thereby able to refer to some new abstract object. |
| 10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
| Full Idea: The dichotomy between concrete and abstract objects comes to seem far too crude: to which of the two categories should we assign the Mistral, for instance? | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He has previously given colours and points as difficult borderline cases. We can generalise this particular problem case as the question of whether a potentiality or possibility is abstract or concrete. |
| 10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
| Full Idea: There is no reason for wanting a sharp distinction between concrete and abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This rather depends on your ontology. If you are happy for reality to be full of weird non-physical entities, then the blurring won't bother you. If the boundary is blurred but still real, it is a very interesting one. |
| 10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
| Full Idea: If abstractions were defined by whether they could affect human sense-organs, light-waves would be concrete but radio waves abstract. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is a pretty good baseline example. No account should draw an abstract/concrete line through the electromagnetic spectrum. |
| 10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
| Full Idea: The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims. |
| 10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
| Full Idea: What objects we recognise the world as containing depends upon the structure of our language. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: The background to this claim is the Fregean idea that there are no objects for us if there are no concepts. Dummett is adding that there are no concepts if there is no language. I say animals have concepts and recognise objects. |
| 23227 | Each object has a precise number of properties, each to a precise degree [Fichte] |
| Full Idea: Each object has a definite number of properties, no more, no less. …Each of these objects possesses each of these properties to a definite degree. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: Quine flatly disagrees with this. Fichte offers no grounds for his claim. On the whole I think of properties as psychologically abstracted by us from holistic objects, so there is plenty of room for error. The underlying powers are real. |
| 23228 | The principle of activity and generation is found in a self-moving basic force [Fichte] |
| Full Idea: The principle of activity, of generation and becoming in and for itself, is purely in that force itself and not in anything outside it…; the force is not driven or set in motion, it sets itself in motion. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: A good account of primitive powers, as self-motivating forces. I can't think what else could be fundamental to nature. This whole passage of Fichte expounds a powers ontology. |
| 10532 | We can understand universals by studying predication [Dummett] |
| Full Idea: It is by the study of the character of predication that we shall come to understand the essential nature of universals. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I haven't founded a clearer manifesto for linguistic philosophy than that! Personally I find it highly dubious, given the shifting nature of linguistic forms, and the enormous variation between remote languages. |
| 10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
| Full Idea: The original sense of 'nominalism' is the denial of universals, that is the denial of reference to either predicates or to abstract nouns. The modern sense (of Nelson Goodman) is the denial of the existence of abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is why you find loads of modern philosophers vigorous attacking nominalism, only to gradually realise that they don't actually believe in universals, as traditionally understood. It's hard to keep up, when words shift their meaning. |
| 10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
| Full Idea: We cannot simply distinguish concrete objects as objects of ostension, if it literally involves a pointing gesture, as this would exclude a colourless gas, a sound or a smell. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He shifts to verbal ostension as a result, since we can talk of 'this smell'. On p.491 he suggests that affecting our senses is a sufficient condition to be concrete, but not a necessary one. |
| 10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
| Full Idea: To say that an abstract object cannot be the cause of change seems plausible enough, but the thesis that it cannot be the subject of change is problematic. The shape of an object can change, or the number of sheep on a hill. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This seems a pretty crucial difficulty for the standard notion of abstracta as non-causal. I would say that it is an acid which could eat away the whole edifice if you thought about it for long enough. He shifts shape-change to the physical object. |
| 10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
| Full Idea: For intuitionists, it ceases to be true that abstract objects are not observable and cannot be involved in causal interaction, since such intuitive apprehension of them may be regarded as just such an interaction. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I would say that since abstract objects can be involved in causal interactions, in the mind, and since the mind is entirely physical (oh yes), this makes abstract objects entirely physical, which may come as a shock to some people. |
| 10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
| Full Idea: For an object to be abstract, we require only that an understanding of any name of that object involves a recognition that the object is in the range of some functional expression. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I'm not sure I understand this, but a function must involve a relation between some objects, such that a unique object is consequently picked out. |
| 10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
| Full Idea: Dummett's best argument for excluding abstract nouns relies upon the entirely Fregean requirement that with any genuine singular term there must be associated a criterion of identity. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Bob Hale - Abstract Objects Ch.2.II | |
| A reaction: This sounds a rather rigid test. Must the criteria be logically precise, or must you just have some vague idea of what you are talking about? |
| 10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
| Full Idea: An abstract object can be referred to only by means of a verbal phrase, ...and no confrontation with an abstract object is possible. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: So does this mean that animals are incapable of entertaining abstract concepts? Some research suggests otherwise. Does a dog understand what a 'walk' is, without use of the word? Dummett disgracefully neglects animals in his theories. |
| 10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
| Full Idea: The notion of 'object', as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: If we say 'objects exist', I think it is crucial that if we are going to introduce 'object' as a term of art, then 'exist' had better stick to normal usage. If that drifts into a term of art as well (incorporating 'subsist', or some such) we have no hope! |
| 23241 | I am myself, but not the external object; so I only sense myself, and not the object [Fichte] |
| Full Idea: I sense in myself, not in the object, for I am myself and not the object; therefore I sense only myself and my condition, and not the condition of the object. | |
| From: Johann Fichte (The Vocation of Man [1800], 2) | |
| A reaction: I'm not clear why anyone would have total confidence in internal experience and almost no confidence in experience of externals. In daily life I am equally confident about both. In philosophical mode I make equally cautious judgements about both. |
| 21966 | Self-consciousness is the basis of knowledge, and knowing something is knowing myself [Fichte] |
| Full Idea: The immediate consciousness of myself is the condition of all other consciousness; and I know a thing only in so far as I know that I know it; no element can enter into the latter cognition which is not contained in the former. | |
| From: Johann Fichte (The Vocation of Man [1800], p.37), quoted by A.W. Moore - The Evolution of Modern Metaphysics 06.2 | |
| A reaction: This strikes me as false, and a lot of intellectual contortion would be needed to believe it. Is knowing this pen is in front of me a case of knowing that I have knowledge of this pen, or is it just knowledge of this pen? [cf Kant 1781:A129] |
| 21967 | There is nothing to say about anything which is outside my consciousness [Fichte] |
| Full Idea: Of any connection beyond the limits of my consciousness I cannot speak. ...I cannot proceed a hair's breadth beyond this consciousness, any more than I can spring out of myself. | |
| From: Johann Fichte (The Vocation of Man [1800], p.74), quoted by A.W. Moore - The Evolution of Modern Metaphysics 06.3 | |
| A reaction: I can't see that this is any different from the idealism of Berkeley, although they get there from different starting points. Idealist seem unable to even begin explaining consciousness. |
| 21969 | Awareness of reality comes from the free activity of consciousness [Fichte] |
| Full Idea: It is the necessary faith in our freedom of power, in our own real activity, and in the definite laws of human action, which lies at the root of all our consciousness of a reality external to ourselves. | |
| From: Johann Fichte (The Vocation of Man [1800], p.98), quoted by A.W. Moore - The Evolution of Modern Metaphysics 06.4 | |
| A reaction: I'd love to know what the 'laws of human action' are. Is it what Hume was trying to do? Moore says there is an 'element of self-creation' in Fichte's account of the source of reality. This is Descartes' dream argument biting back. |
| 23231 | I immediately know myself, and anything beyond that is an inference [Fichte] |
| Full Idea: Immediately I know only of myself. What I am able to know beyond that I am only able to know through inference. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: A direct descendant of the Cartesian Cogito, I assume. Personally, if I bang my head on a beam I take the beam to be a full paid-up member of reality. Is it not possible that he also knows himself through inference? Do animals infer reality? |
| 23246 | Faith is not knowledge; it is a decision of the will [Fichte] |
| Full Idea: Faith is no knowledge, but a decision of the will to recognise the validity of knowledge. | |
| From: Johann Fichte (The Vocation of Man [1800], 3.I) | |
| A reaction: What matters is the grounds for the decision. Mad conspiracy theories are decisions of the will which are false. Legitimate faith is an intuition of coherence which cannot be fully articulated. |
| 23245 | Knowledge can't be its own foundation; there has to be regress of higher and higher authorities [Fichte] |
| Full Idea: No knowledge can be its own foundation and proof. Every knowledge presupposes something still higher as its foundation, and this ascent has no end. | |
| From: Johann Fichte (The Vocation of Man [1800], 3.I) | |
| A reaction: A metaphor that's hard to visualise! He must have in mind a priori as well as empirical knowledge. The 'higher' levels don't seem to be God, but some region of absolute rationality, to which free minds have access. I think. |
| 23242 | Consciousness has two parts, passively receiving sensation, and actively causing productions [Fichte] |
| Full Idea: My immediate consciousness is composed of two constituent parts, the consciousness of my passivity, the sensation; and the consciousness of my activity, in the production of an object according to the principle of causality. | |
| From: Johann Fichte (The Vocation of Man [1800], 2) | |
| A reaction: Kind of obvious, but unusual to make this sharp binary division. Modern neuroscience strongly militates against any and every simple binary division of brain activities. |
| 23240 | We can't know by sight or hearing without realising that we are doing so [Fichte] |
| Full Idea: Q. Could you not perhaps know an object through sight or hearing without knowing that you are seeing or hearing? A. Not at all. | |
| From: Johann Fichte (The Vocation of Man [1800], 2) | |
| A reaction: A nice statement of the traditional view which seemed to be demolished by the discovery of blindsight. In the light of modern brain research, the views of the mind found in past philosophers mostly seem very naïve. |
| 23243 | Consciousness of external things is always accompanied by an unnoticed consciousness of self [Fichte] |
| Full Idea: Q. So that constantly and under all circumstances my consciousness of things outside of me is accompanied by an unnoticed consciousness of myself? A. Quite so. | |
| From: Johann Fichte (The Vocation of Man [1800], 2) | |
| A reaction: He should be more cautious about asserting the existence of something 'unnoticed'. The Earth's core is unnoticed by me, but there is plenty of evidence for it. Not so sure about unnoticed self. Still, I think central control of the mind is indispensable. |
| 23244 | Forming purposes is absolutely free, and produces something from nothing [Fichte] |
| Full Idea: My thinking and originating of a purpose is in its nature absolutely free and brings forth something from nothing. | |
| From: Johann Fichte (The Vocation of Man [1800], 3.I) | |
| A reaction: Modern fans of free will are more equivocal in their assertions, and would be uncomfortable bluntly claiming to 'get something from nothing'. But that's what free will is! Embrace it, or run for your life. |
| 23237 | The capacity for freedom is above the laws of nature, with its own power of purpose and will [Fichte] |
| Full Idea: This capacity [for freedom], once it exists, is in the servitude of a power which is higher than nature and quite free of its laws, the power of purposes, and the will. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: You would think this could only refer to God, but he in fact is referring to the power of human free will. The clearest statement I have found of the weird human exceptionalism implied by a strong commitment to free will. |
| 23235 | I want independent control of the fundamental cause of my decisions [Fichte] |
| Full Idea: I want to be independent - not to be in and through another but to be something for myself: and as such I want myself to be the fundamental cause of all my determinations. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: I think this sums up the absurdity of the concept of free will. The only reason he gives for his passionate belief in free will is that he desperately wants some imagined 'fundamental cause' for his action, and he wants full control of that chimera. |
| 23230 | Nature contains a fundamental force of thought [Fichte] |
| Full Idea: There is an original force of thought in nature just as there is an original formative force. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: I think this idea is false, but it helps to understand Fichte. |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
| Full Idea: Real functions map objects onto objects, but concepts map objects onto truth value, ...so Dummett says that concepts are not functions, but that they have a 'functional character'. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Donald Davidson - Truth and Predication 6 |
| 10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
| Full Idea: Since we cannot pick an abstract object out from its surrounding, all that we need to master is the use of statements of identity between objects of a certain kind. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is the necessary Fregean preliminary to using a principle of abstraction to identify two objects which are abstract (when the two objects are in an equivalence relation). Presumably circular squares and square circles are identical? |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| Full Idea: Dummett claims that a realistic conception of reference can be sustained for concrete objects (possible objects of ostension), but breaks down for (putative) names of (pure) abstract objects. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: An extremely hard claim to evaluate, because a case must first be made for abstract objects which are fundamentally different in kind. Realistic reference must certainly deal with these hard cases. Field rejects Dummett's abstract points. |
| 23233 | The will is awareness of one of our inner natural forces [Fichte] |
| Full Idea: To will is to be immediately conscious of the activity of one of our inner natural forces. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: A more Nietzschean view would be that to will is to be conscious of the victor among our inner natural drives. It can't just be awareness of one force, because the will feels conflicts. |
| 23234 | I cannot change the nature which has been determined for me [Fichte] |
| Full Idea: I cannot will the intention of making myself something other than what I am determined to be by nature, for I don't make myself at all but nature makes me and whatever I become. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: I take this to be a lot more accurate than Sartre's claim that we can re-make ourselves, but Fichte doesn't seem quite right. Don't I get any credit at all if I give up smoking, or train myself to treat someone more sympathetically? |
| 23239 | The self is, apart from outward behaviour, a drive in your nature [Fichte] |
| Full Idea: This 'you' for which you show such a lively interest is, so far as it is not overt behaviour, at least a drive in your own peculiar nature. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: I assume this use of 'drive' is the origin of Nietzsche's picture of such things, focused on the basic will to power. I like Fichte's emphasis on active forces as the basis of nature. |
| 23238 | If life lacks love it becomes destruction [Fichte] |
| Full Idea: Only in love is there life; without it there is death and annihilation. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: He gives not context of justification for this sudden claim. Watching from a melancholy distance the current 2022 Russian invasion of Ukraine, I take this idea to be a profound truth. If you let go of love, you float away down a dark stream. |
| 23236 | Freedom means making yourself become true to your essential nature [Fichte] |
| Full Idea: I want to be free means: I myself want to make myself be whatever I will be. I would therefore …already have to be, in a certain sense, what I am to become, so that I could make myself be it. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: This is much closer to the existenial picture of the malleable self, which Fichte arrives out once he commits to his desperate desire to have free will. [Not sure if my gist captures what he says]. |
| 23229 | Nature is wholly interconnected, and the tiniest change affects everything [Fichte] |
| Full Idea: Nature is an interconnected whole; …you could shift no grain of sand from its spot without thereby, perhaps invisibly to your eyes, changing something in all parts of the immeasurable whole. | |
| From: Johann Fichte (The Vocation of Man [1800], 1) | |
| A reaction: Sounds like idealist daydreaming, but might it actually be true with respect to gravity? |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |