95 ideas
| 16440 | I don't think Lewis's cost-benefit reflective equilibrium approach offers enough guidance [Stalnaker] |
| Full Idea: Lewis articulated and made fashionable the cost-benefit reflective equilibrium methodology, but I have my reservations as it does not offer much guidance. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.1) | |
| A reaction: Stalnaker suggests that this approach has 'run amok' in Lewis's case, giving reality to possible worlds. He spends much effort on showing the 'benefits' of a profoundly implausible view. The same can be said of 4D Perdurantism. |
| 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. |
| 16468 | Non-S5 can talk of contingent or necessary necessities [Stalnaker] |
| Full Idea: One can make sense of necessary versus contingent necessities in a non-S5 modal semantics. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4.3 n17) | |
| A reaction: In S5 □φ → □□φ, so all necessities are necessary. Does it make any sense to say 'I suppose this might have been necessarily true'? |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed. |
| 16449 | In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker] |
| Full Idea: One principle of modal set theory should be uncontroversial: a set exists in a given possible world if and only if all of its members exist at that world. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 2.4) | |
| A reaction: Does this mean there can be no set containing all of my ancestors and future descendants? In no world can we coexist. |
| 16464 | We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker] |
| Full Idea: The point of regimentation is to give a perspicuous representation of the semantic structure of an expression, making it easier to evaluate the validity of arguments and to interpret complex statements. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4.2) | |
| A reaction: This is an authoritative summary from an expert of why all philosophers must take an interest in logical form. |
| 16465 | In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker] |
| Full Idea: In 'either Socrates was a philosopher or someone other than Socrates was a philosopher', both propositions expressed by the disjuncts depend for their existence on the existence of Socrates, but the whole disjunction does not. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4.2) | |
| A reaction: Nice example, just the sort of thing we pay philosophers to come up with. He is claiming that propositions can exist in possible worlds in which the individuals mentioned do not exist. |
| 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 |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets). | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2 | |
| A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist. |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts). | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3) | |
| A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means. |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3) | |
| A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means. |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4) | |
| A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging. |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| Full Idea: The real numbers stand to measurement as the natural numbers stand to counting. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4) |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us). |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3) | |
| A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero). |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us. |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2) |
| 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. |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3) | |
| A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'. |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1) | |
| A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it. |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2) |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to. |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction. |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2) | |
| A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction. |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described. |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I) | |
| A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers. |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| Full Idea: I construe arithmetic as an idealizing theory. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'. |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics. |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory. |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second. |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1) | |
| A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them? |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6) | |
| A reaction: Nice question! He's a fan of getting at the explanatory in mathematics. |
| 16434 | Some say what exists must do so, and nothing else could possible exist [Stalnaker] |
| Full Idea: Some philosophers deny there could have been anything other than what in fact exists, or that anything that exists could have failed to exist. This is developed in very different ways by Wittgenstein (in 'Tractatus'), Lewis and Williamson. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1) | |
| A reaction: This could come in various strengths. A weak version would say that, empirically, that all talk of what doesn't exist is vacuous. A strong necessity (Williamson?) that totally rules out other possible existence is a very odd view. |
| 16439 | A nominalist view says existence is having spatio-temporal location [Stalnaker] |
| Full Idea: A nominalist definition of existence is 'having spatio-temporal location'. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.1) | |
| A reaction: This would evidently be physicalist as well as nominalist. Presumably it fits the 'mosaic' of reality Lewis refers to. I find this view sympathetic. A process of abstraction is required to get the rest of the stuff we talk about. |
| 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. |
| 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) |
| 16443 | Properties are modal, involving possible situations where they are exemplified [Stalnaker] |
| Full Idea: I take properties and relations to be modal notions. Properties are to be understood in terms of what it would be for them to be exemplified, which means understanding them in terms of a range of possible situations. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.2) | |
| A reaction: I can't make head or tail of a property as anything other than a feature of some entity. Treating properties as a 'range of situations' is just as baffling to me as treating them as sets of objects. |
| 16471 | I accept a hierarchy of properties of properties of properties [Stalnaker] |
| Full Idea: I myself am prepared to accept higher-order properties and relations. There is the property of being Socrates, …and the property of being the property of being Socrates, ..and so on. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4.4) | |
| A reaction: Elsewhere I have quoted such a hierarchy of vacuous properties as an absurdity that arises if all predicates are treated as properties. Logicians can live with such stuff, given their set hierarchy and so on, but in science and life this is a nonsense. |
| 16452 | Dispositions have modal properties, of which properties things would have counterfactually [Stalnaker] |
| Full Idea: Dispositional properties deserve special mention since they seem to be properties that have modal consequences - consequences for what properties the individuals that instantiate them would have in counterfactual circumstances. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 3.4) | |
| A reaction: I take this to be the key idea in trying to understand modality, but Stalnaker makes this point and then moves swiftly on, because it is so far away from his possible worlds models, in which he has invested a lifetime. |
| 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) |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing. |
| 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. |
| 16467 | 'Socrates is essentially human' seems to say nothing could be Socrates if it was not human [Stalnaker] |
| Full Idea: It seems natural to paraphrase the claim that Socrates is essentially human as the claim that nothing could be Socrates if it was not human. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4.3) | |
| A reaction: In ordinary speech it would be emphasising how very human Socrates was (in comparison with Frege, for example). By this token Socrates essentially breathes oxygen, but that is hardly part of his essence. |
| 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. |
| 16453 | The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties [Stalnaker] |
| Full Idea: On the bundle theory, the identity of indiscernibles (for 'individuals') is a necessary truth, since an individual is just the co-instantiation of all the properties represented by a point in the space of properties. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 3.6) | |
| A reaction: So much the worse for the bundle theory, I presume. Leibniz did not, I think, hold a bundle theory, but his belief in the identity of indiscernibles seems to have had a theologicial underpinning. |
| 16466 | Strong necessity is always true; weak necessity is cannot be false [Stalnaker] |
| Full Idea: Prior had a strong and a weak reading of necessity, where strong necessity is truth in all possible worlds, while weak necessity is falsity in no possible world. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4.3) | |
| A reaction: [K.Fine 2005:Ch.9 is also cited] The point of the weak one is that in some worlds there might not exist the proposition which is the candidate for truth or falsehood. |
| 16438 | Necessity and possibility are fundamental, and there can be no reductive analysis of them [Stalnaker] |
| Full Idea: My view is that if there were a nonmodal analysis of the modal concepts, that would be a sure sign that we were on the wrong track. Necessity and possibility are fundamental concepts, like truth and existence. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.1) | |
| A reaction: The mystery of modality is tied up with the mystery of time (which is a very big mystery indeed). You get a nice clear grip on the here and now, but time and motion whisk you away to something else. Modality concerns the something else. |
| 16436 | Modal concepts are central to the actual world, and shouldn't need extravagant metaphysics [Stalnaker] |
| Full Idea: Modal concepts are central to our understanding of the world - the actual world - and understanding them should not require extravagant metaphysical commitments. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1) | |
| A reaction: I agree. Personally I think powers and dispositions do the job nicely. You just have to embrace Leibniz's emphasis on the active nature of reality, and the implausible metaphysics starts to recede. |
| 16433 | Given actualism, how can there be possible individuals, other than the actual ones? [Stalnaker] |
| Full Idea: My main focus is on how, on an actualist interpretation of possible worlds as ways a world might be, one is to account for the possibility that there be individuals other than those that actually exist. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], Pref) | |
| A reaction: The obvious thought would be that they are constructions from components of actual individuals, such as the chimaera, or fictional characters. We need some psychology here, which is not Stalnaker's style. |
| 16437 | Possible worlds are properties [Stalnaker] |
| Full Idea: Possible worlds are (to a first approximation) properties. [p.12] They are properties of the total universe. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1) |
| 16444 | Possible worlds don't reduce modality, they regiment it to reveal its structure [Stalnaker] |
| Full Idea: It is not reduction (of modality) but regimentation that the possible-worlds framework provides - a procedure for representing modal discourse, using primitive modal notions, in a way that helps reveal its structure. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.2) | |
| A reaction: I think this is exactly my view. All discussion of the ontology of possible worlds is irrelevant. They no more exist than variables in logic exist. They're good when they clarify, but dubious when they over-simplify. |
| 16445 | I think of worlds as cells (rather than points) in logical space [Stalnaker] |
| Full Idea: I prefer to think of the possible worlds not as points in logical space but as cells of a relatively fine-grained partition of logical space - a partition that makes all the distinctions we need. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.2) | |
| A reaction: Since he regards possible worlds as simply a means of regimenting our understanding of modality, he can think of possible worlds in any way that suits him. I find it hard work tuning in to his vision. |
| 16454 | Modal properties depend on the choice of a counterpart, which is unconstrained by metaphysics [Stalnaker] |
| Full Idea: Things have modal properties only relative to the choice of a counterpart relation, and the choice between alternative counterpart relations is not constrained by the metaphysics. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 3.6) | |
| A reaction: Stalnaker is sympathetic to counterparts, but this strikes me as a powerful objection to the theory. I take the modal properties of something to be fixed by its actuality. |
| 16450 | Anti-haecceitism says there is no more to an individual than meeting some qualitative conditions [Stalnaker] |
| Full Idea: The anti-haecceitist strategy holds that a purely qualitative characterisation of a possible world would be a complete characterisation; there is, on this view, nothing to being a particular individual other than meeting certain qualitative conditions. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 3) | |
| A reaction: Not quite the same as the bundle theory of objects, which says the objects are the qualities. This is about individuation, not about ontology (I think). I don't like anti-haecceitism, but I also don't like haecceitism. Hmm. |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4) | |
| A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start. |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2) | |
| A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2. |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3) | |
| A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view. |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6) | |
| A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates. |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2) | |
| A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention. |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence. | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3 | |
| A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man. |
| 16474 | How can we know what we are thinking, if content depends on something we don't know? [Stalnaker] |
| Full Idea: How can we know what we ourselves are thinking if the very existence of the content of our thought may depend on facts of which we are ignorant? | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 5) | |
| A reaction: This has always been my main doubt about externalism. I may defer to experts about what I intend by an 'elm' (Putnam's example), but what I mean by elm is thereby a fuzzy tall tree with indeterminate leaves. I don't know the meaning of 'elm'! |
| 16461 | We still lack an agreed semantics for quantifiers in natural language [Stalnaker] |
| Full Idea: We still do not know how to give a direct semantics for the quantifiers of a natural language; that is something that we still do not know how to do (or at least how it is done remains controversial). | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 4) | |
| A reaction: I am struck by how rapidly the domain of quantification changes, even in mid-sentence, in the course of an ordinary conversation. This is decided almost entirely by context, not by pure ('direct'?) semantics. |
| 16448 | Possible world semantics may not reduce modality, but it can explain it [Stalnaker] |
| Full Idea: Most theorists agree that possible worlds semantics cannot provide an analysis of modal concepts which is an eliminative reduction, but it can still provide an explanation of the meanings of modal expressions. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 2.2) | |
| A reaction: Stalnaker cites Kit Fine for the view that there is no reduction of modality, which Fine takes to be primitive. Stalnaker defends the semantics, while denying the reduction which Lewis thought possible. |
| 16442 | I take propositions to be truth conditions [Stalnaker] |
| Full Idea: I will defend the view that propositions are truth conditions. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 1.2) | |
| A reaction: This sounds close to the Russellian view, which I take to equate propositions (roughly) with facts or states of affairs. But are 'truth conditions' in the world or in the head? |
| 16447 | A theory of propositions at least needs primitive properties of consistency and of truth [Stalnaker] |
| Full Idea: A minimal theory of propositions can make do with just two primitive properties: a property of consistency applied to sets of propositions, and a property of truth applied to propositions. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 2) | |
| A reaction: I would have thought a minimal theory would need some account of what a proposition is supposed to be (since there seems to be very little agreement about that). Stalnaker goes on to sketch a theory. |
| 16446 | Propositions presumably don't exist if the things they refer to don't exist [Stalnaker] |
| Full Idea: It seems plausible that singular propositions are object-dependent in the sense that the proposition would not exist if the individual did not. It is also plausible that some objects exist contingently, and there are singular propositions about them. | |
| From: Robert C. Stalnaker (Mere Possibilities [2012], 2) | |
| A reaction: This replies to the view that possible worlds are maximal sets of propositions, and so must exist for the worlds to exist; e.g. Lowe 1999:248. That is yet another commonplace of contemporary philosophy which I find utterly bewildering. |
| 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. |
| 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) |