Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and 'The Republic'

expand these ideas     |    start again     |     specify just one area for these texts


124 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Philosophers become as divine and orderly as possible, by studying divinity and order [Plato]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
The winds of the discussion should decide its destination [Plato]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
It would be absurd to be precise about the small things, but only vague about the big things [Plato]
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic is the only method of inquiry which uproots the things which it takes for granted [Plato]
The ability to take an overview is the distinguishing mark of a dialectician [Plato]
For Plato, rationality is a vision of and love of a cosmic rational order [Plato, by Taylor,C]
2. Reason / C. Styles of Reason / 2. Elenchus
You must never go against what you actually believe [Plato]
2. Reason / C. Styles of Reason / 3. Eristic
People often merely practice eristic instead of dialectic, because they don't analyse the subject-matter [Plato]
2. Reason / D. Definition / 2. Aims of Definition
Definitions should be replaceable by primitives, and should not be creative [Brown,JR]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
In mathematics certain things have to be accepted without further explanation [Plato]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Nowadays conditions are only defined on existing sets [Brown,JR]
Naïve set theory assumed that there is a set for every condition [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The 'iterative' view says sets start with the empty set and build up [Brown,JR]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
If a proposition is false, then its negation is true [Brown,JR]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is the only place where we are sure we are right [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Geometry can lead the mind upwards to truth and philosophy [Plato]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Mathematics represents the world through structurally similar models. [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
To see a structure in something, we must already have the idea of the structure [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
In pure numbers, all ones are equal, with no internal parts [Plato]
Geometry is not an activity, but the study of unchanging knowledge [Plato]
The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The same thing is both one and an unlimited number at the same time [Plato]
Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Does some mathematics depend entirely on notation? [Brown,JR]
The most brilliant formalist was Hilbert [Brown,JR]
For nomalists there are no numbers, only numerals [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
There are no constructions for many highly desirable results in mathematics [Brown,JR]
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
To become rational, philosophers must rise from becoming into being [Plato]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Being depends on the Good, which is not itself being, but superior to being [Plato]
7. Existence / B. Change in Existence / 1. Nature of Change
The best things (gods, healthy bodies, good souls) are least liable to change [Plato]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
David's 'Napoleon' is about something concrete and something abstract [Brown,JR]
7. Existence / D. Theories of Reality / 3. Reality
Plato's reality has unchanging Parmenidean forms, and Heraclitean flux [Plato, by Fogelin]
8. Modes of Existence / D. Universals / 2. Need for Universals
The plurality of beautiful things must belong to a single class, because they have a single particular character [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Plato's Forms are said to have no location in space [Plato, by Aristotle]
Craftsmen making furniture refer to the form, but no one manufactures the form of furniture [Plato]
Forms are not universals, as they don't cover every general term [Plato, by Annas]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
A Form applies to a set of particular things with the same name [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
Plato mistakenly thought forms were totally abstracted away from matter [Bacon on Plato]
Plato's Forms not only do not come from the senses, but they are beyond possibility of sensing [Plato, by Kant]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge must be of the permanent unchanging nature of things [Plato]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
If theory and practice conflict, the best part of the mind accepts theory, so the other part is of lower grade [Plato]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
True belief without knowledge is like blind people on the right road [Plato]
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
Is the function of the mind management, authority and planning - or is it one's whole way of life? [Plato]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Psychic conflict is clear if appetite is close to the body and reason fairly separate [Plato, by Modrak]
There is a third element to the mind - spirit - lying between reason and appetite [Plato]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
The mind has parts, because we have inner conflicts [Plato]
The soul seems to have an infinity of parts [Aristotle on Plato]
18. Thought / E. Abstraction / 1. Abstract Thought
'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR]
19. Language / F. Communication / 1. Rhetoric
The 'Republic' is a great work of rhetorical theory [Lawson-Tancred on Plato]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
For Plato and Aristotle there is no will; there is only rational desire for what is seen as good [Plato, by Frede,M]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
We avoid evil either through a natural aversion, or because we have acquired knowledge [Plato]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
Without the surface decoration, poetry shows only appearances and nothing of what is real [Plato]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
Representation is two steps removed from the truth [Plato]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
Truth is closely related to proportion [Plato]
Artists should be excluded from a law-abiding community, because they destroy the rational mind [Plato]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
I suggest that we forget about trying to define goodness itself for the time being [Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
The good cannot be expressed in words, but imprints itself upon the soul [Plato, by Celsus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Plato found that he could only enforce rational moral justification by creating an authoritarian society [Williams,B on Plato]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Plato measured the degree of reality by the degree of value [Nietzsche on Plato]
22. Metaethics / B. Value / 2. Values / b. Successful function
A thing's function is what it alone can do, or what it does better than other things [Plato]
If something has a function then it has a state of being good [Plato]
22. Metaethics / B. Value / 2. Values / d. Health
Goodness is mental health, badness is mental sickness [Plato]
22. Metaethics / B. Value / 2. Values / i. Self-interest
If we were invisible, would the just man become like the unjust? [Plato]
Clever criminals do well at first, but not in the long run [Plato]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
Bad is always destructive, where good preserves and benefits [Plato]
For Plato we abandon honour and pleasure once we see the Good [Plato, by Taylor,C]
Every person, and every activity, aims at the good [Plato]
Goodness makes truth and knowledge possible [Plato]
Good has the same role in the world of knowledge as the sun has in the physical world [Plato]
The main aim is to understand goodness, which gives everything its value and advantage [Plato]
The sight of goodness leads to all that is fine and true and right [Plato]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Pleasure is commonly thought to be the good, though the more ingenious prefer knowledge [Plato]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Even people who think pleasure is the good admit that there are bad pleasures [Plato]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
Nice smells are intensive, have no preceding pain, and no bad after-effect [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Philosophers are concerned with totally non-physical pleasures [Plato]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
There are three types of pleasure, for reason, for spirit and for appetite [Plato]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
Excessive pleasure deranges people, making the other virtues impossible [Plato]
Pleasure-seekers desperately seek illusory satisfaction, like filling a leaky vessel [Plato]
23. Ethics / A. Egoism / 1. Ethical Egoism
We should behave well even if invisible, for the health of the mind [Plato]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Justice is merely the interests of the stronger party [Plato]
Isn't it better to have a reputation for goodness than to actually be good? [Plato]
Morality is a compromise, showing restraint, to avoid suffering wrong without compensation [Plato]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
Surely you don't return a borrowed weapon to a mad friend? [Plato]
23. Ethics / B. Contract Ethics / 4. Value of Authority
Is right just the interests of the powerful? [Plato]
23. Ethics / B. Contract Ethics / 5. Free Rider
Sin first, then sacrifice to the gods from the proceeds [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
For Plato, virtue is its own reward [Lawson-Tancred on Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
True goodness requires mental unity and harmony [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
A good community necessarily has wisdom, courage, self-discipline and morality [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Simonides said morality is helping one's friends and harming one's enemies [Plato]
If the parts of our soul do their correct work, we will be just people, and will act justly [Plato]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
People need society because the individual has too many needs [Plato]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
All exchanges in a community are for mutual benefit [Plato]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
After a taste of mutual harm, men make a legal contract to avoid it [Plato]
24. Political Theory / B. Nature of a State / 4. Citizenship
People doing their jobs properly is the fourth cardinal virtue for a city [Plato]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Reluctant rulers make a better and more unified administration [Plato]
Only rule by philosophers of integrity can keep a community healthy [Plato]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Is there anything better for a community than to produce excellent people? [Plato]
25. Social Practice / E. Policies / 5. Education / b. Education principles
To gain knowledge, turn away from the world of change, and focus on true goodness [Plato]
Dialectic is the highest and most important part of the curriculum [Plato]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Compulsory intellectual work never remains in the mind [Plato]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]
28. God / A. Divine Nature / 4. Divine Contradictions
If Plato's God is immaterial, he will lack consciousness, wisdom, pleasure and movement, which are essential to him [Cicero on Plato]
28. God / C. Attitudes to God / 3. Deism
If the gods are non-existent or indifferent, why bother to deceive them? [Plato]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Something is unlikely to be immortal if it is imperfectly made from diverse parts [Plato]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
Is the supreme reward for virtue to be drunk for eternity? [Plato]
29. Religion / D. Religious Issues / 3. Problem of Evil / d. Natural Evil
God is responsible for the good things, but we must look elsewhere for the cause of the bad things [Plato]