100 ideas
| 5196 | Philosophy is a department of logic [Ayer] |
| Full Idea: Philosophy is a department of logic. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: Personally I would invert that. Philosophy is concerned with human rationality, of which precise logic appears to be a rather limited subdivision. I see philosophy as the 'master' subject, not the 'servant' subject (as Locke had implied). |
| 5189 | Philosophers should abandon speculation, as philosophy is wholly critical [Ayer] |
| Full Idea: We can overthrow speculative philosophy, and see that the function of philosophy is wholly critical. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This seems to imply that we CAN speculate, which appeared to be rendered impossible by the verification principle. Personally I think speculation is central to philosophy, but Ayer should always stand as a warning against bogus truth-claims. |
| 7919 | Humeans rejected the a priori synthetic, and so rejected even Kantian metaphysics [Ayer, by Macdonald,C] |
| Full Idea: Thinkers from Hume to the logical positivists took exception to Kant's view that some synthetic propositions could be known a priori, and so rejected the possibility of metaphysics as Kant conceived of it. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Cynthia Macdonald - Varieties of Things Ch.1 | |
| A reaction: See Idea 7918 for Kant's epistemological view of metaphysics. This strikes me as a big misunderstanding by empiricists, even though they are quite right to insist on evidence and proof. Metaphysics is essential, but its excess is the worst nonsense. |
| 5195 | Critics say analysis can only show the parts, and not their distinctive configuration [Ayer] |
| Full Idea: Critics say an analyst is obliged by his atomistic metaphysics to regard an object consisting of parts a, b, c and d in a distinctive configuration as being simply a+b+c+d, and thus giving an entirely false account of its nature. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: Ayer refers the critics to gestatl psychology. Personally I prefer to talk about the ontology rather than the psychology. If we include (as Russell suggests) relations as part of the analysis, there seems to be no problem. |
| 5179 | Philosophy deals with the questions that scientists do not wish to handle [Ayer] |
| Full Idea: If there are any questions which science leaves it to philosophy to answer, a straightforward process of elimination must lead to their discovery. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This is characteristic of the feeble-mindedness that British philosophy slipped into in the age of Wittgenstein, and for a while thereafter. Personally I regard scientists as servants, who are sent off on exploratory errands, and must report back. |
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
| From: Plato (Parmenides [c.364 BCE], 135e) |
| 232 | Opposites are as unlike as possible [Plato] |
| Full Idea: Opposites are as unlike as possible. | |
| From: Plato (Parmenides [c.364 BCE], 159a) |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
| A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
| 4749 | We cannot analyse the concept of 'truth', because it is simply a mark that a sentence is asserted [Ayer] |
| Full Idea: When one says that "Queen Anne is dead" is true or false, these terms 'true' and 'false' connote nothing, but function in the sentence simply as marks of assertion and denial, so there is no sense in asking us to analyse the concept of 'truth'. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.5) | |
| A reaction: "I am ill" may be true when you say it, and false when I say it. The word 'true' has a useful function in 'x is true if y'. "If that is true, Freddie, I will hit you". |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
| A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
| A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
| A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
| 13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
| Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
| 14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
| Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
| A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
| A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
| From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
| A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
| A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
| A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 5202 | Maths and logic are true universally because they are analytic or tautological [Ayer] |
| Full Idea: The principles of logic and mathematics are true universally simply because we never allow them to be anything else; …in other words, they are analytic propositions, or tautologies. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is obviously a very appealing idea, but it doesn's explain WHY we have invented these particular tautologies (which seem surprisingly useful). The 'science of patterns' can be empirical and a priori and useful (but not tautological). |
| 229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
| Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
| From: Plato (Parmenides [c.364 BCE], 155d) |
| 21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
| Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
| 6523 | Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H] |
| Full Idea: Positivists tend to be prejudiced against ontology, regarding very general questions about what sort of things exist either as meaningless, or as questions to be settled by stipulation. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
| A reaction: So much the worse for positivists, because they are missing all the fun. I consider one of the central activities of philosophy to be speculating about explanations. Ontology is at the heart of what explanation aims at. |
| 221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
| Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
| From: Plato (Parmenides [c.364 BCE], 134c) |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
| From: Plato (Parmenides [c.364 BCE], 135c) |
| 227 | You must always mean the same thing when you utter the same name [Plato] |
| Full Idea: You must always mean the same thing when you utter the same name. | |
| From: Plato (Parmenides [c.364 BCE], 147d) |
| 210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
| Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 220 | The concept of a master includes the concept of a slave [Plato] |
| Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
| From: Plato (Parmenides [c.364 BCE], 133e) |
| 211 | If admirable things have Forms, maybe everything else does as well [Plato] |
| Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
| Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
| From: Plato (Parmenides [c.364 BCE], 133c) |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
| Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
| From: Plato (Parmenides [c.364 BCE], 149e) |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
| 213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
| Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
| From: Plato (Parmenides [c.364 BCE], 131b) |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
| From: Plato (Parmenides [c.364 BCE], 132e) |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
| Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
| From: Plato (Parmenides [c.364 BCE], 132c) |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
| From: Plato (Parmenides [c.364 BCE], 131a) |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
| Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
| From: Plato (Parmenides [c.364 BCE], 132a) |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
| A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
| 15851 | Parts must belong to a created thing with a distinct form [Plato] |
| Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
| From: Plato (Parmenides [c.364 BCE], 157d) | |
| A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
| 15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
| Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
| From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
| A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
| 15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
| Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
| From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
| A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
| 15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
| Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
| From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
| 15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
| Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
| From: Plato (Parmenides [c.364 BCE], 146b) | |
| A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
| 5183 | Only tautologies can be certain; other propositions can only be probable [Ayer] |
| Full Idea: No proposition, other than a tautology, can possibly be anything more than a probable hypothesis. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: A nice clear empiricist rejection of all attempts to assert necessary truths about nature. This also seems to be a rejection of empiricist foundationalism. A problem case seems to be introspective observations, which seem irrefutable and obvious. |
| 6525 | Logical positivists could never give the sense-data equivalent of 'there is a table next door' [Robinson,H on Ayer] |
| Full Idea: Logical positivist phenomenalism has few supporters these days; ..no one ever seemed clear what the sense-datum equivalent of 'there is a table in the next room' could be. | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
| A reaction: But do the critics know what they mean by 'there is a table in the next room'? Does it just mean 'I am hoping there is'? You can't refer to the table in the next room without sticking your ontological neck out - and that is 'best explanation'. |
| 5170 | Material things are constructions from actual and possible occurrences of sense-contents [Ayer] |
| Full Idea: The existence of a material thing is defined in terms of the actual and possible occurrence of the sense-contents which constitute it as a logical construction. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: Obviously we need 'possible' experiences so that unperceived trees can still exist, but it is a can of worms. Is speculation about a possible world an account of possible experiences? Realists want to know WHY we think certain experiences are possible. |
| 5198 | We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer] |
| Full Idea: It is possible to challenge the proposition 'a material thing cannot be in two places at once' empirically; if you destroy one object, the other should also instantly be destroyed if they are a single thing. | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936], Ch.2) by Virgil Ierubino - works | |
| A reaction: This leaves us having to decide whether the proposition is metaphysically necessary, or is empirical, or is tautological. This idea inclines me towards the view that it is empirical. Imagine two 'separate' objects which responded identically to stimuli. |
| 2619 | Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer] |
| Full Idea: Whether a geometry can be applied to the actual physical world or not, is an empirical question which falls outside the scope of the geometry itself. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is a key objection to rationalism by empiricists. You may say that geometry applies to your car, but your car may have been pulverised while you were talking. Why, though, did Einstein find non-Euclidean geometry so useful? |
| 5197 | By changing definitions we could make 'a thing can't be in two places at once' a contradiction [Ayer] |
| Full Idea: The proposition that 'a material thing cannot be in two places at once' is not empirical at all, but linguistic; ..we could so alter our definitions that the proposition came to express a self-contradiction instead of a necessary truth. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This seems a striking anticipation of Quine's famous challenge to the analytic/synthetic distinction. |
| 5204 | To say that a proposition is true a priori is to say that it is a tautology [Ayer] |
| Full Idea: To say that a proposition is true a priori is to say that it is a tautology. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is Ayer's splendidly clearcut anti-rationalism. However, one might concede that one cannot know a priori about remote possible worlds (though I'm not so sure), but still claim a priori extrapolations from our current experiences. |
| 6524 | Positivists prefer sense-data to objects, because the vocabulary covers both illusions and perceptions [Ayer, by Robinson,H] |
| Full Idea: Positivists prefer the sense-datum vocabulary because it is more inclusive than physical object vocabulary; it can report after-images, hallucinations, illusions and bodily sensations, as well as veridical perceptions. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
| A reaction: The assumption of this is that illusions and perceptions are frequently indistinguishable, but that is just nonsense. Illusions usually appeal to one sense only, when you are ill, and in an unclear way. Sensible people know objects when they see them. |
| 5193 | Causal and representative theories of perception are wrong as they refer to unobservables [Ayer] |
| Full Idea: The fact that all causal and representative theories of perception treat material things as if they were unobservable entities entitles us to rule them out a priori. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: It seems to me that we can accept a causal/representative account of perception if we think of it in terms of 'best explanation' rather than observables. Explanation requires speculation, which logical positivists can't cope with. |
| 5200 | The main claim of rationalism is that thought is an independent source of knowledge [Ayer] |
| Full Idea: The fundamental tenet of rationalism is that thought is an independent source of knowledge. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: Presumably one should add that thought gives synthetic knowledge. Thought is also an experience, so empiricists will always acknowledge that we could have some knowledge (of thought) by thought alone. |
| 4729 | Empiricism lacked a decent account of the a priori, until Ayer said it was entirely analytic [O'Grady on Ayer] |
| Full Idea: Ayer's gives an account of the a priori (as analytic) that readily meshes with empiricism, and empiricism had long been lacking an adequate account of the a priori | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: Ayer's logical positivist view was based on Hume's 'relations of ideas', as opposed to 'matters of fact'. Personally I see no reason why some facts about reality shouldn't be self-evident to thought, just as others are self-evident to the senses. |
| 5180 | All propositions (especially 'metaphysics') must begin with the senses [Ayer] |
| Full Idea: One way to attack a metaphysician would be to enquire from what premises his propositions were deduced. Must he not begin, as other men do, with the evidence of his senses? | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This simple idea is the core of empiricism. This is a heavily criticised doctrine, but you must start somewhere. Hume and Russell agreed. Don't forget, though, that Descartes's first move is to reject the senses as untrustworthy. |
| 5169 | My empiricism logically distinguishes analytic and synthetic propositions, and metaphysical verbiage [Ayer] |
| Full Idea: The empiricist doctrine to which we are committed is a logical doctrine concerning the distinction between analytic propositions, synthetic propositions, and metaphysical verbiage. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This is the tough logical positivist version of empiricism. The whole project stumbles on the relationship between a synthetic proposition and its verifying experiences. How close? What of wild speculations? The analytic part is interesting, though. |
| 5185 | It is further sense-experience which informs us of the mistakes that arise out of sense-experience [Ayer] |
| Full Idea: It is further sense-experience which informs us of the mistakes that arise out of sense-experience. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This is a wonderfull plain-spoken challenge to anyone who thinks they can demonstrate facts a priori about reality. 'I see this object in two places at once'? 'This object appears to be both red and green'? |
| 5199 | Empiricism, it is said, cannot account for our knowledge of necessary truths [Ayer] |
| Full Idea: The objection which is commonly brought against empiricism is that it is impossible on empiricist principles to account for our knowledge of necessary truths. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This criticism goes back at least to Leibniz. Ayer's distinctive contribution to empiricism (with help) is to emphasise that we can only know necessities if they are tautologies. Hume always challenged our knowledge of natural necessities. |
| 5190 | The induction problem is to prove generalisations about the future based on the past [Ayer] |
| Full Idea: The problem of induction is (roughly) finding a way to prove that certain empirical generalisations which are derived from past experience will hold good also in the future. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This doesn't seem to be the only problem. It seems self-evident (since Hume) that you cannot use deductive reasoning to prove that the future will be like the past. In fact, we should obviously be cautious, as things could easily change. |
| 5191 | We can't use the uniformity of nature to prove induction, as that would be circular [Ayer] |
| Full Idea: It is often said that we can justify induction by invoking the uniformity of nature, but that principle merely states (in a misleading fashion) the assumption that past experience is a reliable guide to the future. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: That is correct, but it seems to me that if you take the uniformity of nature as a provisional unproven axiom, then induction is an account of how rational creatures cope with the situation. If nature ceases to be uniform, our reason cannot cope. |
| 5177 | Other minds are 'metaphysical' objects, because I can never observe their experiences [Ayer] |
| Full Idea: On the view that we are discussing, I must regard other people as metaphysical objects; for it is assumed that their experiences are completely inaccessible to my observation. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: 'Metaphysical' is here a dirty word. This is the strictly empirical view of other minds, which pushes Ayer towards behaviourism on this subject. He should have asked about the 'best explanation' of the behaviour of others'. |
| 5178 | A conscious object is by definition one that behaves in a certain way, so behaviour proves consciousness [Ayer] |
| Full Idea: If I know that an object behaves in every way as a conscious being must, by definition, behave, then I know that it is really conscious. This is an analytical proposition. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This treats the Turing test as proof of consciousness, and is open to all the usual objections to behaviourism. To say behaviour IS consciousness is ridiculous. It just counts as evidence. Presumably Ayer would later have become a functionalist. |
| 5172 | If the self is meaningful, it must be constructed from sense-experiences [Ayer] |
| Full Idea: The self, if it is not to be treated as a metaphysical entity, must be held to be a logical construction out of sense-experiences. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: It is striking how people differ in their reports when they try to see the self by introspection. The self could be beyond sense-experience, and yet still be the best explanation of what we actually DO experience. It is a 'transcendental sensation'? |
| 5173 | Two experiences belong to one self if their contents belong with one body [Ayer] |
| Full Idea: For any two sense-experiences to belong to the sense-history of the same self it is necessary and sufficient that they should contain organic sense-contents which are elements of the same body. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This makes more sense if you are a realist about organic bodies, but less sense if (like Ayer) you define the body in terms of sense-experiences. It is a stab at what is now called 'animalism', but needs an account of brain transplant thought-experiments. |
| 5176 | Empiricists can define personal identity as bodily identity, which consists of sense-contents [Ayer] |
| Full Idea: We have solved Hume's problem by defining personal identity in terms of bodily identity, and bodily identity is to be defined in terms of the resemblance and continuity of sense-contents. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This is a phenomenalist account of personal identity, so it has no independent account of the body apart from the contents of the mind. Personally I think we must distinguish 'central' mental events from 'peripheral' ones. |
| 5171 | The supposed 'gulf' between mind and matter is based on the senseless concept of 'substances' [Ayer] |
| Full Idea: The problems of bridging the 'gulf' between mind and matter, in knowledge or in action, are all fictitious problems arising out of the senseless metaphysical conception of mind and matter as 'substances'. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: He is presumably implying that there is only one 'substance', the stuff of physics, thus voting for Spinoza's dual aspect theory. There could still be a 'gulf', between incommensurable properties, or untranslatable levels of description. |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
| A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
| A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
| A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
| 5181 | A sentence is factually significant to someone if they know how to verify its proposition [Ayer] |
| Full Idea: A sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: 'I can't verify it, but I know a bloke who can'? 'If only I could think of a way to verify x'? 'This is unverifiable, but it is the only remaining possibility'? 'X is unverifiable, but it would nice if it was true'? Etc. |
| 5184 | Factual propositions imply (in conjunction with a few other premises) possible experiences [Ayer] |
| Full Idea: The mark of a genuinely factual proposition is that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those premises alone. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: I.Berlin showed that any statement S could pass this test, because if you assert 'S' and 'If S then O', these two statements entail O, which could be some random observation. Verificationism kept meeting problems of this kind. |
| 5186 | Tautologies and empirical hypotheses form the entire class of significant propositions [Ayer] |
| Full Idea: Tautologies and empirical hypotheses form the entire class of significant propositions. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This appears to be false. Possibly the problem is that Ayer takes the whole proposition to be the unit of meaning, but actually meaninfulness only requires that we build up a claim about a possible world from semantic units. Blue bees live on square suns. |
| 5205 | Moral intuition is worthless if there is no criterion to decide between intuitions [Ayer] |
| Full Idea: Unless it is possible to provide some criterion by which one may decide between conflicting intuitions, a mere appeal to intuition is worthless as a test of a proposition's validity. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: It is a bit much to expect a 'proof' of its 'validity'! If moral judgements are reflected in consequences, then reliable intuitions (i.e. wisdom) could be demonstrated by getting it right (for happiness, or flourishing). |
| 23725 | Ayer defends the emotivist version of expressivism [Ayer, by Smith,M] |
| Full Idea: Ayer defends emotivism, which is his own favoured form of expressivism. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936], Ch.6) by Michael Smith - The Moral Problem 2.1 | |
| A reaction: A helpful distinction of terminology. Expressivism is the broad theory, and emotivism is a sub-type, saying that it is emotions which are expressed. The alternative (such as Prescriptivism) is to express pro- and con- attitudes. |
| 5206 | To say an act is wrong makes no further statement about it, but merely expresses disapproval [Ayer] |
| Full Idea: In adding 'You acted wrongly in…' to 'you stole my money' I am not making any further statement about it; I am simply evincing my moral disapproval of it. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: A basic claim of emotivism. Perhaps an understandable response to (e.g.) Kantian claims that we have duties, but to no one in particular. Most people mean by moral criticism that there will be long-term bad consequences, or virtue is lacking. |
| 222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
| Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
| From: Plato (Parmenides [c.364 BCE], 135a) |
| 225 | The unlimited has no shape and is endless [Plato] |
| Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
| From: Plato (Parmenides [c.364 BCE], 137e) |
| 233 | Some things do not partake of the One [Plato] |
| Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
| From: Plato (Parmenides [c.364 BCE], 159d) | |
| A reaction: Compare Idea 231 |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
| From: Plato (Parmenides [c.364 BCE], 138b) |
| 231 | Everything partakes of the One in some way [Plato] |
| Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: Compare Idea 233. |
| 5208 | A person with non-empirical attributes is unintelligible. [Ayer] |
| Full Idea: The notion of a person whose essential attributes are non-empirical is not an intelligible notion at all. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: Non-empirical and non-causal are not quite the same thing. A being which never had any effects is a bizarre, and probably pointless, fantasy. A being which affected our world (through ideas, say) but is unobservable is a perfectly good theory. |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
| Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
| From: Plato (Parmenides [c.364 BCE], 160d) |
| 5187 | When we ascribe an attribute to a thing, we covertly assert that it exists [Ayer] |
| Full Idea: When we ascribe an attribute to a thing, we covertly assert that it exists. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This is an unsurprising endorsement from logical positivism that Kant's claim that the ontological argument is probably tautological is correct. We could of course say "Imagine a non-existent being with dirty toenails". |
| 5207 | If theism is non-sensical, then so is atheism. [Ayer] |
| Full Idea: If the assertion that there is a god is non-sensical, then the atheist's assertion that there is no god is equally non-sensical. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: Ayer urgently needs the concept of 'best explanation'. If we observe only footprints, we infer creatures; if there are no footprints, lack of creatures looks like a good theory. The design argument is perfectly meaningful. |
| 5209 | The 'truths' expressed by theists are not literally significant [Ayer] |
| Full Idea: There cannot be any transcendent truths of religion, for the sentences which the theist uses to express such 'truths' are not literally significant. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: Ayer claims that only tautologies or empirically verifiable statements have literal significance. I say speculations, wild theories and fantasies are perfectly meaningful. Nevertheless, the words of many hymns and prayers look like empty rhetoric. |