44 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
| From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
| 10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
| Full Idea: The Axiom of Choice seems better treated as a non-logical principle of set-theory. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4 n8) | |
| A reaction: This reinforces the idea that set theory is not part of logic (and so pure logicism had better not depend on set theory). |
| 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
| Full Idea: We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
| Full Idea: We might reduce sets to ordinal numbers, thereby reversing the standard set-theoretical reduction of ordinals to sets. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) | |
| A reaction: He has demonstrated that there are as many ordinals as there are sets. |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
| Full Idea: Extensional mereology defs: 'distinct' things have no parts in common; a 'fusion' has some things all of which are parts, with no further parts. Axioms: (transitivity) a part of a part is part of the whole; (sums) any things have a unique fusion. | |
| From: Keith Hossack (Plurals and Complexes [2000], 5) |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think. | |
| From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans' | |
| A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention. |
| 10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
| Full Idea: If we extend the power of language with plural definite descriptions, these would pick out the largest class of things that fit the description. | |
| From: Keith Hossack (Plurals and Complexes [2000], 3) |
| 10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
| Full Idea: It may be that plural reference gives atomism the resources to state complex facts without needing to refer to complex things. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: This seems the most interesting metaphysical implication of the possibility of plural quantification. |
| 10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
| Full Idea: If all properties are distributive, plural reference is just a handy abbreviation to avoid repetition (as in 'A and B are hungry', to avoid 'A is hungry and B is hungry'), but not all properties are distributive (as in 'some people surround a table'). | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: The characteristic examples to support plural quantification involve collective activity and relations, which might be weeded out of our basic ontology, thus leaving singular quantification as sufficient. |
| 10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
| Full Idea: Singular comprehension principles have a bad reputation, but the plural comprehension principle says that given a condition on individuals, there are some things such that something is one of them iff it meets the condition. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
| Full Idea: In a plural language we can discuss without fear of inconsistency the things that are not members of themselves. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) | |
| A reaction: [see Hossack for details] |
| 10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
| Full Idea: The theory of the transfinite needs the ordinal numbers. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 10684 | I take the real numbers to be just lengths [Hossack] |
| Full Idea: I take the real numbers to be just lengths. | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) | |
| A reaction: I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged. |
| 10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
| Full Idea: A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
| Full Idea: In arithmetic singularists need sets as the instantiator of numeric properties. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 10685 | Set theory is the science of infinity [Hossack] |
| Full Idea: Set theory is the science of infinity. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
| Full Idea: By Quine's test of ontological commitment, if some children are sitting in a circle, no individual child can sit in a circle, so a singular paraphrase will have us committed to a 'group' of children. | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: Nice of why Quine is committed to the existence of sets. Hossack offers plural quantification as a way of avoiding commitment to sets. But is 'sitting in a circle' a real property (in the Shoemaker sense)? I can sit in a circle without realising it. |
| 10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
| Full Idea: Complex particulars are of at least three types: masses (which sum, of which we do not ask 'how many?' but 'how much?'); composite individuals (how many?, and summing usually fails); and sets (only divisible one way, unlike composites). | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: A composite pile of grains of sand gradually becomes a mass, and drops of water become 'water everywhere'. A set of people divides into individual humans, but redescribe the elements as the union of males and females? |
| 10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
| Full Idea: The relation of composition seems to be indispensable in a correct account of the part-whole relation for individuals. | |
| From: Keith Hossack (Plurals and Complexes [2000], 7) | |
| A reaction: This is the culmination of a critical discussion of mereology and ontological atomism. At first blush it doesn't look as if 'composition' has much chance of being a precise notion, and it will be plagued with vagueness. |
| 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. |
| 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
| Full Idea: We can employ Leibniz's Law against mereological atomism. Water is wet, but no water molecule is wet. The set of infinite numbers is infinite, but no finite number is infinite. ..But with plural reference the atomist can resist this argument. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: The idea of plural reference is to state plural facts without referring to complex things, which is interesting. The general idea is that we have atomism, and then all the relations, unities, identities etc. are in the facts, not in the things. I like it. |
| 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
| Full Idea: The fusion of five rectangles may have a decomposition into more than five parts that are rectangles. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 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. |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge. | |
| From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall. |
| 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. |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| Full Idea: A thought can refer to a particular or a universal or a state of affairs, but it can predicate only a universal and it can affirm only a state of affairs. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: Hossack is summarising Armstrong's view, which he is accepting. To me, 'thought' must allow for animals, unlike language. I think Hossack's picture is much too clear-cut. Do animals grasp universals? Doubtful. Can they predicate? Yes. |
| 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. |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
| Full Idea: We might dispense with substantival space, and say that if the distribution of matter in space could have been different, that just means the matter of the Universe could have been shaped differently (with geometry as the science of shapes). | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) |
| 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. |