Combining Texts

All the ideas for 'Gorgias', 'Parmenides' and 'Maths as a Science of Patterns'

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70 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Is a gifted philosopher unmanly if he avoids the strife of the communal world? [Plato]
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]
2. Reason / B. Laws of Thought / 5. Opposites
Opposites are as unlike as possible [Plato]
2. Reason / C. Styles of Reason / 1. Dialectic
Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato]
2. Reason / C. Styles of Reason / 2. Elenchus
In "Gorgias" Socrates is confident that his 'elenchus' will decide moral truth [Vlastos on Plato]
We should test one another, by asking and answering questions [Plato]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
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]
Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
There are too many mathematical objects for them all to be mental or physical [Resnik]
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
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]
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]
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]
7. Existence / D. Theories of Reality / 3. Reality
Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato]
8. Modes of Existence / D. Universals / 2. Need for Universals
If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato]
You must always mean the same thing when you utter the same name [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato]
If admirable things have Forms, maybe everything else does as well [Plato]
If absolute ideas existed in us, they would cease to be absolute [Plato]
Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M]
It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato]
The concept of a master includes the concept of a slave [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
The whole idea of each Form must be found in each thing which participates in it [Plato]
If things are made alike by participating in something, that thing will be the absolute idea [Plato]
Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato]
If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato]
Participation is not by means of similarity, so we are looking for some other method of participation [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato]
Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato]
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]
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]
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]
Anything which has parts must be one thing, and parts are of a one, not of a many [Plato]
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]
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]
19. Language / F. Communication / 1. Rhetoric
Rhetoric can produce conviction, but not educate people about right and wrong [Plato]
Rhetoric is irrational about its means and its ends [Plato]
20. Action / B. Preliminaries of Action / 1. Intention to Act / b. Types of intention
All activity aims at the good [Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
Moral rules are made by the weak members of humanity [Plato]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
A good person is bound to act well, and this brings happiness [Plato]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Is it natural to simply indulge our selfish desires? [Plato]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
In slaking our thirst the goodness of the action and the pleasure are clearly separate [Plato]
Good should be the aim of pleasant activity, not the other way round [Plato]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Good and bad people seem to experience equal amounts of pleasure and pain [Plato]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [Plato]
If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato]
23. Ethics / A. Egoism / 2. Hedonism
Is the happiest state one of sensual, self-indulgent freedom? [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Should we avoid evil because it will bring us bad consequences? [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
I would rather be a victim of crime than a criminal [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
Self-indulgent desire makes friendship impossible, because it makes a person incapable of co-operation [Plato]
If absence of desire is happiness, then nothing is happier than a stone or a corpse [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
A criminal is worse off if he avoids punishment [Plato]
Do most people praise self-discipline and justice because they are too timid to gain their own pleasure? [Plato]
23. Ethics / C. Virtue Theory / 4. External Goods / b. Health
The popular view is that health is first, good looks second, and honest wealth third [Plato]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
As with other things, a good state is organised and orderly [Plato]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
A good citizen won't be passive, but will redirect the needs of the state [Plato]
25. Social Practice / B. Equalities / 1. Grounds of equality
Do most people like equality because they are second-rate? [Plato]
25. Social Practice / B. Equalities / 4. Economic equality
Does nature imply that it is right for better people to have greater benefits? [Plato]
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]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
The unlimited has no shape and is endless [Plato]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
Everything partakes of the One in some way [Plato]
The only movement possible for the One is in space or in alteration [Plato]
Some things do not partake of the One [Plato]
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]