57 ideas
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. |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
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 |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
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. |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
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. |
18680 | To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi] |
Full Idea: It is no part of supervenience that 'if p then q' entails 'if not p then not q'. To avoid such misunderstandings, it is common (though not more accurate) to describe supervenience in negative terms: no difference in A without a difference in B. | |
From: Francesco Orsi (Value Theory [2015], 5.2) | |
A reaction: [compressed] In other words it is important to avoid the presupposition that the given supervenience is a two-way relation. The paradigm case of supervenience is stalking. |
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) |
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) |
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) |
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. |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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. |
18684 | Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi] |
Full Idea: Many have suggested alternative roles or sorts of reasons, which are not mandatory. Dancy says some reasons are 'enticing' rather than peremptory; Raz makes options 'eligible' rather than required; Gert says they justify rather than require action. | |
From: Francesco Orsi (Value Theory [2015], 6.4) | |
A reaction: The third option is immediately attractive - but then it would only justify the action because it was a good reason, which would need explaining. 'Enticing' captures the psychology in a nice vague way. |
18685 | Final value is favoured for its own sake, and personal value for someone's sake [Orsi] |
Full Idea: Final value is to be favoured for its own sake; personal value is to be favoured for someone's sake. | |
From: Francesco Orsi (Value Theory [2015], 7.2) | |
A reaction: This gives another important dimension for discussions of value. I like the question 'what gives rise to this value?', but we can also ask (given the value) why we should then promote it. Health isn't a final value, and truth isn't a personal value? |
18666 | Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi] |
Full Idea: Examples of value-maker concepts are courageous, honest, cowardly, corrupt, elegant, tacky, melodious, insightful. Employing these concepts normally means both evaluating and describing the thing or person one way or another. | |
From: Francesco Orsi (Value Theory [2015], 1.2) | |
A reaction: The point being that they tell you two things - that this thing has a particular value, and also why it has that value. Since I am flirting with the theory that all values must have 'value-makers' this is very interesting. |
18667 | The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi] |
Full Idea: The '-able' concepts, such as valuable, enviable, contemptible, wear on their sleeve the idea that the thing so evaluated merits or is worth a certain attitude or response (of valuing, envying, despising). | |
From: Francesco Orsi (Value Theory [2015], 1.2) | |
A reaction: Compare Idea 18666. Hence some concepts point to the source of value in the thing, and others point to the source of the value in the normative attitude of the speaker. Interesting. |
18679 | Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi] |
Full Idea: If a certain object is valuable, then something other than its being valuable must make it so. ...One is always in principle entitled to an answer as to why it is good or bad. | |
From: Francesco Orsi (Value Theory [2015], 5.2) | |
A reaction: What Orsi calls the 'chemistry' of value. I am inclined to think that this is the key to a philosophical study of value. Without this assumption the values float free, and we drift into idealised waffle. Note that here he only refers to 'objects'. |
18682 | A complex value is not just the sum of the values of the parts [Orsi] |
Full Idea: The whole 'being pleased by cats being tortured' is definitely not better, and is likely worse, than cats being tortured. So its value cannot result from a sum of the intrinsic values of the parts. | |
From: Francesco Orsi (Value Theory [2015], 5.3) | |
A reaction: This example is simplistic. It isn't a matter of just adding 'pleased' and 'tortured'. 'Pleased' doesn't have a standalone value. Only a rather gormless utilitarian would think it was always good if someone was pleased. I suspect values don't sum at all. |
18683 | Trichotomy Thesis: comparable values must be better, worse or the same [Orsi] |
Full Idea: It is natural to assume that if we can compare two objects or states of affairs, X and Y, then X is either better than, or worse than, or as good as Y. This has been called the Trichotomy Thesis. | |
From: Francesco Orsi (Value Theory [2015], 6.2) | |
A reaction: This is the obvious starting point for a discussion of the difficult question of the extent to which values can be compared. Orsi says even if there was only one value, like pleasure, it might have incommensurable aspects like duration and intensity. |
18686 | The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi] |
Full Idea: The main claims of the Fitting Attitude view of value are Reduction: values such are goodness are reduced to fitting attitudes, having reasons, and Normative Redundancy: goodness provides no reasons for attitudes beyond the thing's features. | |
From: Francesco Orsi (Value Theory [2015], 8.2) | |
A reaction: Orsi's book is a sustained defence of this claim. I like the Normative Redundancy idea, but I am less persuaded by the Reduction. |
18672 | Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi] |
Full Idea: A support for the fittingness account (against the buck-passing reasons account) is the 'wrong kind of reasons' problem. There are many reasons for positive attitudes towards things which are not good. We might admire a demon because he threatens torture. | |
From: Francesco Orsi (Value Theory [2015], 1.4) | |
A reaction: [compressed] I like the Buck-Passing view, but was never going to claim that all reasons for positive attitudes bestow value. I only think that there is no value without a reason |
18677 | A thing may have final value, which is still derived from other values, or from relations [Orsi] |
Full Idea: Many believe that final values can be extrinsic: objects which are valuable for their own sake partly thanks to their relations to other objects. ...This might depend on the value of other things...or an object's relational properties. | |
From: Francesco Orsi (Value Theory [2015], 2.3) | |
A reaction: It strikes me that virtually nothing (or even absolutely nothing) has final value in total isolation from other things (Moore's 'isolation test'). Values arise within a tangled network of relations. Your final value is my instrumental value. |
18668 | Truths about value entail normative truths about actions or attitudes [Orsi] |
Full Idea: My guiding assumption is that truths about value, at least, regularly entail normative truths of some sort about actions or attitudes. | |
From: Francesco Orsi (Value Theory [2015], 1.4) | |
A reaction: Not quite as clear as it sounds. If I say 'the leaf is green' I presume a belief that it is green, which is an attitude. If I say 'shut the door' that implies an action with no value. One view says that values are entirely normative in this way. |
18669 | Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi] |
Full Idea: Version one of the normative view of values is the Fitting Attitude account, which says that 'x is good' means 'it is fitting to respond favourably to (or 'favour') x'. | |
From: Francesco Orsi (Value Theory [2015], 1.4) | |
A reaction: Brentano is mentioned. Orsi favours this view. The rival normative view is Scanlon's [1998:95-8] Buck-Passing account, in Idea 18670. I am interested in building a defence of the Buck-Passing account, which seems to suit a naturalistic realist like me. |
18670 | The Buck-Passing view of normative values says other properties are reasons for the value [Orsi] |
Full Idea: Version two of the normative view of values is the Buck-Passing account, which says that 'x is good' means 'x has the property of having other properties that provide reasons to favour x'. | |
From: Francesco Orsi (Value Theory [2015], 1.4) | |
A reaction: [He cites Scanlon 1998:95-8] I think this is the one to explore. We want values in the world, bridging the supposed 'is-ought gap', and not values that just derive from the way human beings are constituted (and certainly not supernatural values!). |
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) |