49 ideas
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
From: Epictetus (fragments/reports [c.57], 15) | |
A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
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 |
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) |
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. |
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. |
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? |
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. |
23308 | Reasoning relates to understanding as time does to eternity [Boethius, by Sorabji] |
Full Idea: Boethius says that reasoning [ratiocinatio] is related to intellectual understanding [intellectus] as time to eternity, involving as it does movement from one stage to another. | |
From: report of Boethius (The Consolations of Philosophy [c.520], 4, prose 6) by Richard Sorabji - Rationality 'Shifting' | |
A reaction: This gives true understanding a quasi-religious aura, as befits a subject which is truly consoling. |
5771 | Knowledge of present events doesn't make them necessary, so future events are no different [Boethius] |
Full Idea: Just as the knowledge of present things imposes no necessity on what is happening, so foreknowledge imposes no necessity on what is going to happen. | |
From: Boethius (The Consolations of Philosophy [c.520], V.IV) | |
A reaction: This, I think, is the key idea if you are looking for a theological answer to the theological problem of free will. Don't think of God as seeing the future 'now'. God is outside time, and so only observes all of history just as we observe the present. |
5767 | Rational natures require free will, in order to have power of judgement [Boethius] |
Full Idea: There is freedom of the will, for it would be impossible for any rational nature to exist without it. Whatever by nature has the use of reason has the power of judgement to decide each matter. | |
From: Boethius (The Consolations of Philosophy [c.520], V.II) | |
A reaction: A view taken up by Aquinas (Idea 1849) and Kant (Idea 3740). The 'power of judgement' pinpoints the core of rationality, and it is not clear how a robot could fulfil such a power, if it lacked consciousness. Does a machine 'judge' barcodes? |
5768 | God's universal foreknowledge seems opposed to free will [Boethius] |
Full Idea: God's universal foreknowledge and freedom of the will seem clean contrary and opposite. | |
From: Boethius (The Consolations of Philosophy [c.520], V.III) | |
A reaction: The original source of the great theological and philosophical anguish over free will. The problem is anything which fixes future facts, be it oracular knowledge or scientific prediction. Personally I think free will was an invention by religions. |
5769 | Does foreknowledge cause necessity, or necessity cause foreknowledge? [Boethius] |
Full Idea: Does foreknowledge of the future cause the necessity of events, or necessity cause the foreknowledge? | |
From: Boethius (The Consolations of Philosophy [c.520], V.III) | |
A reaction: An intriguing question, though not one that bothers me. I don't understand how foreknowledge causes necessity, unless God's vision of the future is a kind of 'freezing ray'. Even the gods must bow to necessity (Idea 3016). |
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. |
5762 | The wicked want goodness, so they would not be wicked if they obtained it [Boethius] |
Full Idea: If the wicked obtained what they want - that is goodness - they could not be wicked. | |
From: Boethius (The Consolations of Philosophy [c.520], IV.II) | |
A reaction: This is a nice paradox which arises from Boethius being, like Socrates, an intellectualist. The question is whether the wicked want the good de re or de dicto. If they wanted to good de re (as its true self) they would obviously not be wicked. |
5770 | Rewards and punishments are not deserved if they don't arise from free movement of the mind [Boethius] |
Full Idea: If there is no free will, then in vain is reward offered to the good and punishment to the bad, because they have not been deserved by any free and willed movement of the mind. | |
From: Boethius (The Consolations of Philosophy [c.520], V.III) | |
A reaction: I just don't see why decisions have to come out of nowhere in order to have any merit. People are different from natural forces, because the former can be persuaded by reasons. A moral agent is a mechanism which decides according to reasons. |
5764 | When people fall into wickedness they lose their human nature [Boethius] |
Full Idea: When people fall into wickedness they lose their human nature. | |
From: Boethius (The Consolations of Philosophy [c.520], IV.III) | |
A reaction: This is a view I find quite sympathetic, but which is a million miles from the modern view. Today's paper showed a picture of a famous criminal holding a machine gun and a baby. We seem to delight in the idea that human nature is partly wicked. |
5756 | Happiness is a good which once obtained leaves nothing more to be desired [Boethius] |
Full Idea: Happiness is a good which once obtained leaves nothing more to be desired. | |
From: Boethius (The Consolations of Philosophy [c.520], III.I) | |
A reaction: This sounds like the ancient 'eudaimonism' of Socrates and Aristotle, which might not be entirely compatible with orthodox Christianity. It is not true, though, that happy people lack ambition. To be happy, an unfilfilled aim may be needed. |
5763 | The bad seek the good through desire, but the good through virtue, which is more natural [Boethius] |
Full Idea: The supreme good is the goal of good men and bad men alike, and the good seek it by means of a natural activity - the exercise of virtue - while the bad strive to acquire it by means of their desires, which is not a natural way of obtaining the good. | |
From: Boethius (The Consolations of Philosophy [c.520], IV.II) | |
A reaction: Interesting here is the slightly surprising claim that the pursuit of virtue is 'natural', implying that the mere pursuit of desire is not. Doesn't nature have to be restrained to achieve the good? Boethius is in the tradition of Aristotle and stoicism. |
5759 | Varied aims cannot be good because they differ, but only become good when they unify [Boethius] |
Full Idea: The various things that men pursue are not perfect and good, because they differ from one another; ..when they differ they are not good, but when they begin to be one they become good, so it is through the acquisition of unity that these things are good. | |
From: Boethius (The Consolations of Philosophy [c.520], III.XI) | |
A reaction: This is a criticism of Aristotle's pluralism about the good(s) for man. Boethius' thought is appealing, and ties in with the Socratic notion that the virtues might be unified in some way. I think it is right that true virtues merge together, ideally. |
5754 | You can't control someone's free mind, only their body and possessions [Boethius] |
Full Idea: The only way one man can exercise power over another is over his body and what is inferior to it, his possessions. You cannot impose anything on a free mind. | |
From: Boethius (The Consolations of Philosophy [c.520], II.VI) | |
A reaction: Written, of course, in prison. Boethius had not met hypnotism, or mind-controlling drugs, or invasive brain surgery. He hadn't read '1984'. He hadn't seen 'The Ipcress File'. (In fact, he should have got out more…) |
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') |
16692 | Divine eternity is the all-at-once and complete possession of unending life [Boethius] |
Full Idea: Divine eternity is the all-at-once [tota simul] and complete possession of unending life. | |
From: Boethius (The Consolations of Philosophy [c.520], V.6), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.1 | |
A reaction: This is a famous definition, and 'tota simul' became the phrase used for 'entia successiva', such as a day, or the Olympic Games. |
5752 | Where does evil come from if there is a god; where does good come from if there isn't? [Boethius] |
Full Idea: A philosopher (possibly Epicurus) asked where evil comes from if there is a god, and where good comes from if there isn't. | |
From: Boethius (The Consolations of Philosophy [c.520], I.IV) | |
A reaction: A nice question. The best known answer to the first question is 'Satan'. Some would say that in the second case good is impossible, but I would have thought that the only possible answer is 'mankind'. |
5758 | God is the good [Boethius] |
Full Idea: God is the good. | |
From: Boethius (The Consolations of Philosophy [c.520], III.XI) | |
A reaction: This summary follows on from the rather dubious discussion in Idea 5757. If God IS the good, it is not clear how God could be usefully described as 'good'. We would know that he was good a priori, without any enquiry into his nature being needed. |
5757 | God is the supreme good, so no source of goodness could take precedence over God [Boethius] |
Full Idea: That which by its own nature is something distinct from supreme good, cannot be supreme good. ..It is impossible for anything to be by nature better than that from which it is derived, so that which is the origin of all things is supreme good. | |
From: Boethius (The Consolations of Philosophy [c.520], III.X) | |
A reaction: This is the contortion early Christians got into once they decided God had to be 'supreme' in the moral world (and every other world). Boethius allows a possible external source of all morality, but then has to say that this source is morally inferior. |
5760 | The power through which creation remains in existence and motion I call 'God' [Boethius] |
Full Idea: For this power, whatever it is, through which creation remains in existence and in motion, I use the word which all people use, namely God. | |
From: Boethius (The Consolations of Philosophy [c.520], III.XII) | |
A reaction: An interesting caution in the phrase 'whatever it is'. Boethius would have been very open-minded in discussion with modern science about the stability of nature. Personally I reject Boethius' theory, but don't have a better one. Cf Idea 1431. |
5753 | The regular events of this life could never be due to chance [Boethius] |
Full Idea: I could never believe that events of such regularity as we find in this life are due to the haphazards of chance. | |
From: Boethius (The Consolations of Philosophy [c.520], I.VI) | |
A reaction: It depends what you mean by 'chance'. Boethius infers a conscious mind, and presumes this to be God, but that is two large and unsupported steps. Modern atheists must acknowledge Boethius' problem. Why is there order? |
5765 | The reward of the good is to become gods [Boethius] |
Full Idea: Goodness is happiness, ..but we agree that those who attain happiness are divine. The reward of the good, then, is to become gods. | |
From: Boethius (The Consolations of Philosophy [c.520], IV.III) | |
A reaction: Kant offered a similar argument (see Idea 1455). Most of us are unlikely to agree with the second premise of Boethius' argument. The idea that we might somehow become gods gripped the imagination for the next thousand years. |
5761 | God can do anything, but he cannot do evil, so evil must be nothing [Boethius] |
Full Idea: 'There is nothing that an omnipotent power could not do?' 'No.' 'Then can God do evil?' 'No.' 'So evil is nothing, since that is what He cannot do who can do anthing.' | |
From: Boethius (The Consolations of Philosophy [c.520], III.XII) | |
A reaction: A lovely example of the contortions necessary once you insist that God must be 'omnipotent', in some absolute sense of the term. Saying that evil is 'nothing' strikes me as nothing more than a feeble attempt to insult it. |
5766 | If you could see the plan of Providence, you would not think there was evil anywhere [Boethius] |
Full Idea: If you could see the plan of Providence, you would not think there was evil anywhere. | |
From: Boethius (The Consolations of Philosophy [c.520], IV.VI) | |
A reaction: This brings out the verificationist in me. See Idea 1467, by Antony Flew. Presumably Boethius would retain his faith as Europe moved horribly from 1939 to 1945, and even if the whole of humanity sank into squalid viciousness. |