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All the ideas for 'Logic (Port-Royal Art of Thinking)', 'Timaeus' and 'Phil of Mathematics: why nothing works'

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33 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 / 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)
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
How can you contemplate Platonic entities without causal transactions with them? [Putnam]
     Full Idea: Platonism has the attendant problem of how we can succeed in thinking about and referring to entities we can have no causal transactions with.
     From: Hilary Putnam (Phil of Mathematics: why nothing works [1979], Modalism)
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
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 / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
     Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things.
     From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
     A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer.
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
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)
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)
12. Knowledge Sources / B. Perception / 3. Representation
We can only know the exterior world via our ideas [Arnauld,A/Nicole,P]
     Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us.
     From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc'
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)
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
     Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties.
     From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6
     A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea.
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.
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P]
     Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example).
     From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
     A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology.
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
     Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles.
     From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
     A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power.
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P]
     Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width.
     From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
     A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives.
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)
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 / 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)