53 ideas
| 17275 | Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K] |
| Full Idea: We may broadly distinguish between two main branches of metaphysics: the 'realist' or 'critical' branch is concerned with what is real (tense, values, numbers); the 'naive' or 'pre-critical' branch concerns natures of things irrespective of reality. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: [compressed] The 'natures' of things are presumably the essences. He cites 3D v 4D objects, and the status of fictional characters, as examples of the second type. Fine says ground is central to realist metaphysics. |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11) | |
| A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems |
| 17282 | Truths need not always have their source in what exists [Fine,K] |
| Full Idea: There is no reason in principle why the ultimate source of what is true should always lie in what exists. | |
| From: Kit Fine (Guide to Ground [2012], 1.03) | |
| A reaction: This seems to be the weak point of the truthmaker theory, since truths about non-existence are immediately in trouble. Saying reality makes things true is one thing, but picking out a specific bit of it for each truth is not so easy. |
| 17283 | If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K] |
| Full Idea: The truth-making relation is usually explicated in modal terms, ...but this lets in far too much. Any necessary truth will be grounded by anything. ...The fact that singleton Socrates exists will be a truth-maker for the proposition that Socrates exists. | |
| From: Kit Fine (Guide to Ground [2012], 1.03) | |
| A reaction: If truth-makers are what has to 'exist' for something to be true, then maybe nothing must exist for a necessity to be true - in which case it has no truth maker. Or maybe 2 and 4 must 'exist' for 2+2=4? |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 17286 | Logical consequence is verification by a possible world within a truth-set [Fine,K] |
| Full Idea: Under the possible worlds semantics for logical consequence, each sentence of a language is associated with a truth-set of possible worlds in which it is true, and then something is a consequence if one of these worlds verifies it. | |
| From: Kit Fine (Guide to Ground [2012], 1.10) | |
| A reaction: [compressed, and translated into English; see Fine for more symbolic version; I'm more at home in English] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| Full Idea: A prime number is one which is measured by a unit alone. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11) | |
| A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes. |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 9895 | A number is a multitude composed of units [Dummett] |
| Full Idea: A number is a multitude composed of units. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2) | |
| A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction. |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'? |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that. |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory. |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental. |
| 17272 | 2+2=4 is necessary if it is snowing, but not true in virtue of the fact that it is snowing [Fine,K] |
| Full Idea: It is necessary that if it is snowing then 2+2=4, but the fact that 2+2=4 does not obtain in virtue of the fact that it is snowing. | |
| From: Kit Fine (Guide to Ground [2012], 1.01) | |
| A reaction: Critics dislike 'in virtue of' (as vacuous), but I can't see how you can disagree with this obvervation of Fine's. You can hardly eliminate the word 'because' from English, or say p is because of some object. We demand the right to keep asking 'why?'! |
| 17276 | If you say one thing causes another, that leaves open that the 'other' has its own distinct reality [Fine,K] |
| Full Idea: It will not do to say that the physical is causally determinative of the mental, since that leaves open the possibility that the mental has a distinct reality over and above that of the physical. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: The context is a defence of grounding, so that if we say the mind is 'grounded' in the brain, we are saying rather more than merely that it is caused by the brain. A ghost might be 'caused' by a bar of soap. Nice. |
| 17284 | An immediate ground is the next lower level, which gives the concept of a hierarchy [Fine,K] |
| Full Idea: It is the notion of 'immediate' ground that provides us with our sense of a ground-theoretic hierarchy. For any truth, we can take its immediate grounds to be at the next lower level. | |
| From: Kit Fine (Guide to Ground [2012], 1.05 'Mediate') | |
| A reaction: Are the levels in the reality, the structure or the descriptions? I vote for the structure. I'm defending the idea that 'essence' picks out the bottom of a descriptive level. |
| 17285 | 'Strict' ground moves down the explanations, but 'weak' ground can move sideways [Fine,K] |
| Full Idea: We might think of strict ground as moving us down in the explanatory hierarchy. ...Weak ground, on the other hand, may also move us sideways in the explanatory hierarchy. | |
| From: Kit Fine (Guide to Ground [2012], 1.05 'Weak') | |
| A reaction: This seems to me rather illuminating. For example, is the covering law account of explanation a 'sideways' move in explanation. Are inductive generalities mere 'sideways' accounts. Both fail to dig deeper. |
| 17288 | We learn grounding from what is grounded, not what does the grounding [Fine,K] |
| Full Idea: It is the fact to be grounded that 'points' to its ground and not the grounds that point to what they ground. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) | |
| A reaction: What does the grounding may ground all sorts of other things, but what is grounded only has one 'full' (as opposed to 'partial', in Fine's terminology) ground. He says this leads to a 'top-down' approach to the study of grounds. |
| 17281 | If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K] |
| Full Idea: In so far as ground is regarded as a relation it should be between entities of the same type, and the entities should probably be taken as worldly entities, such as facts, rather than as representational entities, such as propositions. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: That's more like it (cf. Idea 17280). The consensus of this discussion seems to point to facts as the best relata, for all the vagueness of facts, and the big question of how fine-grained facts should be (and how dependent they are on descriptions). |
| 17280 | Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K] |
| Full Idea: Ground is perhaps best regarded as an operation (signified by an operator on sentences) rather than as a relation (signified by a predicate) | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: Someone in this book (Koslicki?) says this is to avoid metaphysical puzzles over properties. I don't like the idea, because it makes grounding about sentences when it should be about reality. Fine is so twentieth century. Audi rests ground on properties. |
| 17290 | Only metaphysical grounding must be explained by essence [Fine,K] |
| Full Idea: If the grounding relation is not metaphysical (such as normative or natural grounding), there is no need for there to be an explanation of its holding in terms of the essentialist nature of the items involved. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) | |
| A reaction: He accepts that some things have partial grounds in different areas of reality. |
| 17274 | Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K] |
| Full Idea: For philosophers interested in explanation - of what accounts for what - it is largely through the notion of ontological ground that such questions are to be pursued. Ground, if you like, stands to philosophy as cause stands to science. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: Why does the ground have to be 'ontological'? It isn't the existence of the snow that makes me cold, but the fact that I am lying in it. Better to talk of 'factual' ground (or 'determinative' ground), and then causal grounds are a subset of those? |
| 17278 | We can only explain how a reduction is possible if we accept the concept of ground [Fine,K] |
| Full Idea: It is only by embracing the concept of a ground as a metaphysical form of explanation in its own right that one can adequately explain how a reduction of the reality of one thing to another should be understood. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: I love that we are aiming to say 'how' a reduction should be understood, and not just 'that' it exists. I'm not sure about Fine's emphasis on explaining 'realities', when I think we are after more like structural relations or interconnected facts. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist. |
| 17287 | Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K] |
| Full Idea: Given any facts, there will be a fusion of those facts. Given the facts that the ball is red and that it is round, there is a fused fact that it is 'red and round'. | |
| From: Kit Fine (Guide to Ground [2012], 1.10) | |
| A reaction: This is how we make 'units' for counting. Any type of thing which can be counted can be fused, such as the first five prime numbers, forming the 'first' group for some discussion. Any objects can be fused to make a unit - but is it thereby a 'unity'? |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts. |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| Full Idea: The existence of abstract objects is a pseudo-problem. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
| 17279 | Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K] |
| Full Idea: Even the three-dimensionalist might be willing to admit that material things have temporal parts. For given any persisting object, he might suppose that 'in thought' we could mark out its temporal segments or parts. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: A big problem with temporal parts is how thin they are. Hawley says they are as fine-grained as time itself, but what if time has no grain? How thin can you 'think' a temporal part to be? Fine says imagined parts are grounded in things, not vice versa. |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
| A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |
| 17273 | Each basic modality has its 'own' explanatory relation [Fine,K] |
| Full Idea: I am inclined to the view that ....each basic modality should be associated with its 'own' explanatory relation. | |
| From: Kit Fine (Guide to Ground [2012], 1.01) | |
| A reaction: He suggests that 'grounding' connects the various explanatory relations of the different modalities. I like this a lot. Why assert any necessity without some concept of where the necessity arises, and hence where it is grounded? You've got to eat. |
| 17289 | Every necessary truth is grounded in the nature of something [Fine,K] |
| Full Idea: It might be held as a general thesis that every necessary truth is grounded in the nature of certain items. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) | |
| A reaction: [He cites his own 1994 for this] I'm not sure if I can embrace the 'every' in this. I would only say, more cautiously, that I can only make sense of necessity claims when I see their groundings - and I don't take a priori intuition as decent grounding. |
| 17291 | We explain by identity (what it is), or by truth (how things are) [Fine,K] |
| Full Idea: I think it should be recognised that there are two fundamentally different types of explanation; one is of identity, or of what something is; and the other is of truth, or of how things are. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) |
| 17271 | Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K] |
| Full Idea: In addition to scientific or causal explanation, there maybe a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some causal mechanism, but through some constitutive form of determination. | |
| From: Kit Fine (Guide to Ground [2012], Intro) | |
| A reaction: I'm unclear why determination has to be 'constitutive', since I would take determination to be a family of concepts, with constitution being one of them, as when chess pieces determine a chess set. Skip 'metaphysical'; just have Determinative Explanation. |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 17277 | If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K] |
| Full Idea: It is not enough to require that the mental should modally supervene on the physical, since that still leaves open the possibility that the physical is itself ultimately to be understood in terms of the mental. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: See Horgan on supervenience. Supervenience is a question, not an answer. The first question is whether the supervenience is mutual, and if not, which 'direction' does it go in? |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help! |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| Full Idea: An argument for conceptual priority is greater simplicity in explanation. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?). |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872. |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14 | |
| A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981. |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14) | |
| A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction... |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'. |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc. |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval? | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |