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All the ideas for 'Parmenides', 'Timaeus' and 'New Foundations for Mathematical Logic'

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63 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
For relaxation one can consider the world of change, instead of eternal things [Plato]
     Full Idea: If, for relaxation, one gives up discussing eternal things, it is pleasant to consider likely accounts of the world of change.
     From: Plato (Timaeus [c.349 BCE], 59c)
     A reaction: To understand this, examine Plato's example of the Line at 'Republic' 509d.
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Philosophy is the supreme gift of the gods to mortals [Plato]
     Full Idea: Philosophy is the greatest gift the gods have ever given or ever will give to mortals.
     From: Plato (Timaeus [c.349 BCE], 47b)
     A reaction: I wonder why they gave it to us?
2. Reason / A. Nature of Reason / 1. On Reason
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)
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Nothing can come to be without a cause [Plato]
     Full Idea: Nothing can come to be without a cause.
     From: Plato (Timaeus [c.349 BCE], 28a)
2. Reason / B. Laws of Thought / 5. Opposites
Opposites are as unlike as possible [Plato]
     Full Idea: Opposites are as unlike as possible.
     From: Plato (Parmenides [c.364 BCE], 159a)
2. Reason / C. Styles of Reason / 1. Dialectic
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.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett]
     Full Idea: Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions.
     From: report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18
     A reaction: The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded.
5. Theory of Logic / L. Paradox / 3. Antinomies
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'
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
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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.
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
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)
Before the existence of the world there must have been being, space and becoming [Plato]
     Full Idea: There were, before the world came into existence, being, space, and becoming, three distinct realities.
     From: Plato (Timaeus [c.349 BCE], 52d)
The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato]
     Full Idea: That which is apprehended by intelligence and reason is always in the same state, but that which is conceived by opinion with the help of sensation and without reason is always in a process of becoming and perishing, and never really is.
     From: Plato (Timaeus [c.349 BCE], 28a)
     A reaction: Lots of problems with this, of which I take the main one to be the idea that sensation is 'without reason', as if there were a sharp dichotomy in our ways of evaluating reality. Laws of nature seem to be laws of change, not of stasis.
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
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.
7. Existence / D. Theories of Reality / 3. Reality
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)
8. Modes of Existence / D. Universals / 2. Need for Universals
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)
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)
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
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)
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)
Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas]
     Full Idea: In the ancient world Plato's Theory of Forms was mostly seen as one aspect of Plato's 'physics' or theory of the world (rather than as 'metaphysics').
     From: report of Plato (Timaeus [c.349 BCE]) by Julia Annas - Ancient Philosophy: very short introduction Ch.5
     A reaction: This is how I also see the theory, but then I am inclined to see religion as a rather startling branch of speculative physics. Annas cites 'Timaeus' as the key text for this.
Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato]
     Full Idea: Whenever the maker of anything keeps his eye on the eternally unchanging and uses it as his pattern for the form and function of his product the result must be good.
     From: Plato (Timaeus [c.349 BCE], 28b)
In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato]
     Full Idea: In addition to an eternal unchanging model and a visible and changing copy of reality, there must be a third part, the receptacle and nurse of all becoming and change.
     From: Plato (Timaeus [c.349 BCE], 49b)
     A reaction: cf Aristotle's criticism in Metaphysics
For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato]
     Full Idea: If intelligence and true opinion are different, then the forms must exist, but if they are the same, then what our senses perceive must be the most certain reality.
     From: Plato (Timaeus [c.349 BCE], 51d)
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)
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)
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)
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.
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato]
     Full Idea: Our basic description of the universe contained an intelligible and unchanging model, and a visible and changing copy of it.
     From: Plato (Timaeus [c.349 BCE], 48e)
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)
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)
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)
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)
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)
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
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)
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)
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
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.
9. Objects / C. Structure of Objects / 5. Composition of an Object
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?
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
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.
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.
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
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.
9. Objects / F. Identity among Objects / 6. Identity between Objects
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.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Only bird-brained people think astronomy is entirely a matter of evidence [Plato]
     Full Idea: Birds are empty-headed men who grew feathers instead of hair, because they were interested in astronomy but thought it was entirely a matter of physical evidence.
     From: Plato (Timaeus [c.349 BCE], 91d)
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Plato says the soul is ordered by number [Plato, by Plutarch]
     Full Idea: Plato regards the substance of soul not as number but as being ordered by number.
     From: report of Plato (Timaeus [c.349 BCE]) by Plutarch - 68: Generation of the soul in 'Timaeus' 1023
     A reaction: This remark points towards Plato's esoteric doctrines, which are some sort of mathematical metaphysics. The idea that order and numbers are in some way connected is one of the most powerful in western civilization, with undeniable appeal.
16. Persons / F. Free Will / 6. Determinism / a. Determinism
No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato]
     Full Idea: No one wishes to be bad, but a bad man is bad because of some flaw in his physical makeup and failure in his education, neither of which he likes or chooses.
     From: Plato (Timaeus [c.349 BCE], 86e)
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
Music has harmony like the soul, and serves to reorder disharmony within us [Plato]
     Full Idea: Music has harmonic motions like the orbits of the soul, and is not for irrational pleasure, but to reduce to order any disharmony in the revolutions within us.
     From: Plato (Timaeus [c.349 BCE], 47d)
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
One should exercise both the mind and the body, to avoid imbalance [Plato]
     Full Idea: One should preserve a balance and avoid exercising the mind or body without the other; mathematicians should exercise physically, and athletes mentally.
     From: Plato (Timaeus [c.349 BCE], 88c)
     A reaction: Excellent, and very modern. Use it or lose it. It suggests that Plato had a fairly holistic view of a human being, and saw mind and body as closely integrated.
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Everything that takes place naturally is pleasant [Plato]
     Full Idea: Everything that takes place naturally is pleasant.
     From: Plato (Timaeus [c.349 BCE], 81e)
     A reaction: Not many people would agree with this. I recently watched a sparrowhawk eat a pigeon in my garden. This is the source of the stoic formula of living according to nature.
25. Social Practice / E. Policies / 5. Education / a. Aims of education
Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato]
     Full Idea: Intelligence is produced by teaching, involves truth and reason, and cannot be moved; true opinion involves persuasion, is irrational and can be moved.
     From: Plato (Timaeus [c.349 BCE], 51e)
25. Social Practice / E. Policies / 5. Education / b. Education principles
Bad governments prevent discussion, and discourage the study of virtue [Plato]
     Full Idea: Under a bad government discussion, both public and private, is bad, and no courses of study are available to cure faults of character.
     From: Plato (Timaeus [c.349 BCE], 87b)
25. Social Practice / E. Policies / 5. Education / c. Teaching
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)
26. Natural Theory / A. Speculations on Nature / 1. Nature
The cosmos must be unique, because it resembles the creator, who is unique [Plato]
     Full Idea: So that our universe can resemble the perfect living creature in being unique, the universe was, is and will continue to be its maker's only creation.
     From: Plato (Timaeus [c.349 BCE], 31c)
The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato]
     Full Idea: This changing cosmos was made because its maker is good, and therefore lacks envy; he therefore wished all things to be as like himself as possible.
     From: Plato (Timaeus [c.349 BCE], 29e)
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
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)
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
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
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)
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.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato]
     Full Idea: We must think of the individual units of all four basic shapes as being far too small to be visible, and only becoming visible when massed together in large numbers.
     From: Plato (Timaeus [c.349 BCE], 56c)
26. Natural Theory / C. Causation / 1. Causation
There are two types of cause, the necessary and the divine [Plato]
     Full Idea: We must distinguish two types of cause, the necessary and the divine.
     From: Plato (Timaeus [c.349 BCE], 68e)
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato]
     Full Idea: Days, months, years and solstices have caused the invention of number, given us the notion of time, and caused us to inquire into the nature of the universe.
     From: Plato (Timaeus [c.349 BCE], 47a)
27. Natural Reality / D. Time / 3. Parts of Time / a. Beginning of time
Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato]
     Full Idea: Time came into being with the heavens, so that they should be dissolved together if ever they are dissolved.
     From: Plato (Timaeus [c.349 BCE], 38c)
27. Natural Reality / E. Cosmology / 1. Cosmology
Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato]
     Full Idea: If the world is beautiful and its maker good, he had an eye on the eternal; if not, on that which is subject to change; clearly the world is the fairest of things, and he the best of causes, so it is eternal.
     From: Plato (Timaeus [c.349 BCE], 29a)
27. Natural Reality / E. Cosmology / 3. The Beginning
If the cosmos is an object of perception then it must be continually changing [Plato]
     Full Idea: The cosmos is visible, tangible and corporeal, and therefore perceptible by the senses; therefore it is an object of opinion and sensation, and therefore change and coming into being.
     From: Plato (Timaeus [c.349 BCE], 28d)
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
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)