26 ideas
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| Full Idea: Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165) | |
| A reaction: Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology. |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| Full Idea: Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166) | |
| A reaction: This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it. |
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
| Full Idea: If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164) | |
| A reaction: It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412. |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |
| Full Idea: No account of an individual number is adequate unless it relates that number to the series of which it is a member. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169) | |
| A reaction: Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism. |
| 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). |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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…) |
| 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. |