33 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
| From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
| A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 22744 | Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus] |
| Full Idea: If the whole is nothing more than the sum of the parts, the parts will not be parts. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.343) | |
| A reaction: Nice. Bricks lying on the ground are not parts of a wall. For them to be parts of a wall there has to be a wall which is not just the bricks. Nihilists like Van Inwagen can deny the wall in ontology, but in thought we need walls. Conceptual dependence. |
| 22748 | Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus] |
| Full Idea: Some assert that motion is perceived by sense, but others that it is not perceived at all by sense but by the intellect through sensation. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.062) | |
| A reaction: Descartes' wax argument defends the idea that change is perceived by intellect. The intellect has to distinguish the relative aspect of each motion, such as when someone is walking around on a moving ship. Even sense also need memory. |
| 22746 | If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus] |
| Full Idea: When we have gone so far as to deprive the length of its breadth altogether, we no longer conceive even the length, but along with the removal of the breadth the conception of the length is also removed. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.392) | |
| A reaction: The only explanation of our retaining an understanding of a line even after we have removed its breadth is that we have abandoned experience and conceptualised the line - by idealising it. |
| 22741 | The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus] |
| Full Idea: The incorporeal will never come into existence from body because the nature of the incorporeal does not exist in body. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.225) | |
| A reaction: So nothing high could be made of pebbles because pebbles are not high? His argument depends on incorporeality having an intrinsically incorporeal nature. Pebbles have some height which can be extended. |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 22747 | A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus] |
| Full Idea: If a ship moves forward and a man carries a rod backwards on it, then it is possible for an object to move without quitting its place. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.056) | |
| A reaction: [summary of a verbose paragraph] The point is that you cannot define movement as change of place (contrary to Russell's proposal!). The concept of a place seems to be relative. Walking on a treadmill. |
| 22749 | Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus] |
| Full Idea: It is absurd to say that when the Universe is destroyed time does not exist; for the statement that it was destroyed once and that it is being destroyed are indicative of times. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.188) | |
| A reaction: Intriguing. He takes it that a proposition can be true even though nothing exists. This is not merely an affirmation of the tensed A-series view of time, but he even offers tenses as evidence that the A-series is correct. That time could cease was a view. |
| 22750 | Time is divisible, into past, present and future [Sext.Empiricus] |
| Full Idea: Time cannot be indivisible, since it is divided into past, present and future. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.193) | |
| A reaction: Does the fact that you can name the parts of something prove that it is divisible? Do electrons have left and right-hand sides? |
| 22742 | Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus] |
| Full Idea: Socrates either dies when existing, or when not existing. …He does not die when he exists, for he is alive, and he does not die when he has died, for then he will be dying twice, which is absurd. So then, Socrates does not die. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.269) | |
| A reaction: A nice dramatisation of a major dilemma. The present moment is just the boundary between the past and the future, and so has no magnitude, and hence nothing can occur during the present. Perhaps my favourite philosophical dilemma. |
| 22751 | If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus] |
| Full Idea: If the present is the limit of the past, and the limit of the past has passed away together with that of which it is the limit, the present no longer exists. And if the present begins the future, which doesn't exist, the present does not yet exist. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.201) | |
| A reaction: If I mark a line on the ground where the wall will begin, the limit seems prior to the object. The gun starts the race, but is not part of it. That said, I cannot think of any more mysterious entity than the present moment. It isn't a line or a bang. |
| 22730 | All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus] |
| Full Idea: All men have one common preconception about God, according to which he is a blessed creature and imperishable and perfect in happiness and receptive of nothing evil. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.033) | |
| A reaction: He observes this after he has pointed the enormous variety of religious beliefs. He offers this unanimity as a reason to believe that it is true. |
| 22739 | God must suffer to understand suffering [Sext.Empiricus] |
| Full Idea: God cannot have a notion of suffering if he has not experience it. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.163) | |
| A reaction: Christians like to portray God as suffering because of his son's horrible death. We can imagine experiences we have never had, and presumably God is better at that than we are. |
| 22738 | The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus] |
| Full Idea: If the Divine is all-virtuous, it possesses all the virtues. But it does not possess the virtues of continence and fortitude unless there are certain things which are hard for God to abstain from and hard to endure. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.151) | |
| A reaction: Courage would also be unnecessary, we assume. Good people are not tempted to steal, and hence do not need to resist it. It is a mistake to attribute human virtues to the Divine. Humans lack the virtues of a good frog. |
| 22734 | God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus] |
| Full Idea: Arguments for God have four modes: from universal agreement, from the orderly arrangement of the universe, from the absurd consequences of denying God, and from undermining the opposing arguments. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.060) | |
| A reaction: [compressed] The loss of status of the argument from universal agreement has had a huge influence. We now realise that a very wide consensus is no guarantee of truth in anything. |
| 22736 | God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus] |
| Full Idea: If God has sensation he is altered, …so he is receptive of change, including change for the worse. If so, he is also perishable, but that is absurd; therefore it is absurd also to claim that God exists. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.146) | |
| A reaction: [compressed] It is certainly paradoxical to think that God is eternal and unchanging, but also capable of perception and thought, which necessitate change. Some theological ingenuity is needed to explain this. |
| 22740 | God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus] |
| Full Idea: If the Divine exists it either has or has not virtue. If it has not it is base and unhappy, which is absurd. But if it has it, there will exist something which is better than God, just as a virtue of a horse is better than the horse itself. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.176) | |
| A reaction: It is obviously better to think of a virtue as some mode of a thing, rather than as a separate attachment. This is an ontological argument, because it is inferred from the concept of God. |
| 22735 | The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus] |
| Full Idea: They say that the substance of existing things being of itself motionless and shapeless must be put in motion and shape by some cause. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.075) | |
| A reaction: Interestingly, Sextus doesn't seem to think that the existence of the original substance also needs a cause. This substance sounds like a relative of Aristotle's Prime Matter. The source of motion isn't really a 'design' argument. |
| 22732 | The perfections of God were extrapolations from mankind [Sext.Empiricus] |
| Full Idea: It is said that …the idea that God is eternal and imperishable and perfect in happiness was introduced by way of transference from mankind. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.045) | |
| A reaction: This view is found in Hume, and in Feuerbach. I presume 'transference' means extrapolation and idealisation. If God exists, we may have no option but to think of God anthropomorphically. |
| 22728 | Gods were invented as watchers of people's secret actions [Sext.Empiricus] |
| Full Idea: It is asserted that those who first led mankind …invented gods as watchers of all the sinful and righteous acts of men, so that none should dare to do wrong even in secret. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.016) | |
| A reaction: Sextus is a sceptic about everything, so this scepticism about the gods is nothing special. I'm not sure if this is why the gods were invented, but it seems to be the main role assigned to God by the Christian church, as the basis of religious morality. |
| 22737 | An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus] |
| Full Idea: The Divine is not incorporeal, since that is inanimate and insensitive and incapable of any action; nor is it a body, since that is subject to change and perishable; so the Divine does not exist. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.151) | |
| A reaction: I find this quite persuasive. An incorporeal God has to be ascribed magical powers in order to interact with what is corporeal. A corporeal God is subject to entropy and all the depredations of the physical world. |
| 22731 | It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus] |
| Full Idea: To suppose that lakes and rivers, and whatsoever else is of a nature to be useful to us, are gods surpasses the height of lunacy. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.040) | |
| A reaction: He also points out the what is useful to us decays and changes. Sextus lived in a time when monotheism was becoming dominant. |