122 ideas
2136 | Philosophers become as divine and orderly as possible, by studying divinity and order [Plato] |
23767 | The winds of the discussion should decide its destination [Plato] |
23682 | It would be absurd to be precise about the small things, but only vague about the big things [Plato] |
2151 | Dialectic is the only method of inquiry which uproots the things which it takes for granted [Plato] |
2154 | The ability to take an overview is the distinguishing mark of a dialectician [Plato] |
4011 | For Plato, rationality is a vision of and love of a cosmic rational order [Plato, by Taylor,C] |
2093 | You must never go against what you actually believe [Plato] |
2130 | People often merely practice eristic instead of dialectic, because they don't analyse the subject-matter [Plato] |
2145 | In mathematics certain things have to be accepted without further explanation [Plato] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
8726 | Geometry can lead the mind upwards to truth and philosophy [Plato] |
9863 | We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato] |
9864 | In pure numbers, all ones are equal, with no internal parts [Plato] |
8727 | Geometry is not an activity, but the study of unchanging knowledge [Plato] |
9861 | The same thing is both one and an unlimited number at the same time [Plato] |
9862 | To become rational, philosophers must rise from becoming into being [Plato] |
21818 | Being depends on the Good, which is not itself being, but superior to being [Plato] |
2061 | The best things (gods, healthy bodies, good souls) are least liable to change [Plato] |
6562 | Plato's reality has unchanging Parmenidean forms, and Heraclitean flux [Plato, by Fogelin] |
2142 | The plurality of beautiful things must belong to a single class, because they have a single particular character [Plato] |
5094 | Plato's Forms are said to have no location in space [Plato, by Aristotle] |
12043 | Forms are not universals, as they don't cover every general term [Plato, by Annas] |
2159 | Craftsmen making furniture refer to the form, but no one manufactures the form of furniture [Plato] |
17 | A Form applies to a set of particular things with the same name [Plato] |
12122 | Plato mistakenly thought forms were totally abstracted away from matter [Bacon on Plato] |
5574 | Plato's Forms not only do not come from the senses, but they are beyond possibility of sensing [Plato, by Kant] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
2133 | Knowledge must be of the permanent unchanging nature of things [Plato] |
2162 | If theory and practice conflict, the best part of the mind accepts theory, so the other part is of lower grade [Plato] |
2140 | True belief without knowledge is like blind people on the right road [Plato] |
2096 | Is the function of the mind management, authority and planning - or is it one's whole way of life? [Plato] |
6009 | Psychic conflict is clear if appetite is close to the body and reason fairly separate [Plato, by Modrak] |
6041 | There is a third element to the mind - spirit - lying between reason and appetite [Plato] |
2127 | The mind has parts, because we have inner conflicts [Plato] |
1737 | The soul seems to have an infinity of parts [Aristotle on Plato] |
5945 | The 'Republic' is a great work of rhetorical theory [Lawson-Tancred on Plato] |
23316 | For Plato and Aristotle there is no will; there is only rational desire for what is seen as good [Plato, by Frede,M] |
16 | We avoid evil either through a natural aversion, or because we have acquired knowledge [Plato] |
16565 | Without the surface decoration, poetry shows only appearances and nothing of what is real [Plato] |
2160 | Representation is two steps removed from the truth [Plato] |
2163 | Artists should be excluded from a law-abiding community, because they destroy the rational mind [Plato] |
2135 | Truth is closely related to proportion [Plato] |
2141 | I suggest that we forget about trying to define goodness itself for the time being [Plato] |
1869 | The good cannot be expressed in words, but imprints itself upon the soul [Plato, by Celsus] |
4115 | Plato found that he could only enforce rational moral justification by creating an authoritarian society [Williams,B on Plato] |
4547 | Plato measured the degree of reality by the degree of value [Nietzsche on Plato] |
2094 | A thing's function is what it alone can do, or what it does better than other things [Plato] |
2095 | If something has a function then it has a state of being good [Plato] |
2129 | Goodness is mental health, badness is mental sickness [Plato] |
12 | If we were invisible, would the just man become like the unjust? [Plato] |
2168 | Clever criminals do well at first, but not in the long run [Plato] |
2137 | The main aim is to understand goodness, which gives everything its value and advantage [Plato] |
2139 | Every person, and every activity, aims at the good [Plato] |
2143 | Good has the same role in the world of knowledge as the sun has in the physical world [Plato] |
2147 | The sight of goodness leads to all that is fine and true and right [Plato] |
4007 | For Plato we abandon honour and pleasure once we see the Good [Plato, by Taylor,C] |
2144 | Goodness makes truth and knowledge possible [Plato] |
2164 | Bad is always destructive, where good preserves and benefits [Plato] |
2138 | Pleasure is commonly thought to be the good, though the more ingenious prefer knowledge [Plato] |
2070 | Even people who think pleasure is the good admit that there are bad pleasures [Plato] |
2157 | Nice smells are intensive, have no preceding pain, and no bad after-effect [Plato] |
2134 | Philosophers are concerned with totally non-physical pleasures [Plato] |
2156 | There are three types of pleasure, for reason, for spirit and for appetite [Plato] |
2158 | Pleasure-seekers desperately seek illusory satisfaction, like filling a leaky vessel [Plato] |
2123 | Excessive pleasure deranges people, making the other virtues impossible [Plato] |
2166 | We should behave well even if invisible, for the health of the mind [Plato] |
2097 | Isn't it better to have a reputation for goodness than to actually be good? [Plato] |
19946 | Morality is a compromise, showing restraint, to avoid suffering wrong without compensation [Plato] |
5 | Justice is merely the interests of the stronger party [Plato] |
7 | Surely you don't return a borrowed weapon to a mad friend? [Plato] |
8 | Is right just the interests of the powerful? [Plato] |
15 | Sin first, then sacrifice to the gods from the proceeds [Plato] |
5944 | For Plato, virtue is its own reward [Lawson-Tancred on Plato] |
2155 | True goodness requires mental unity and harmony [Plato] |
2126 | A good community necessarily has wisdom, courage, self-discipline and morality [Plato] |
23562 | If the parts of our soul do their correct work, we will be just people, and will act justly [Plato] |
2092 | Simonides said morality is helping one's friends and harming one's enemies [Plato] |
19889 | People need society because the individual has too many needs [Plato] |
19890 | All exchanges in a community are for mutual benefit [Plato] |
10 | After a taste of mutual harm, men make a legal contract to avoid it [Plato] |
23561 | People doing their jobs properly is the fourth cardinal virtue for a city [Plato] |
2149 | Reluctant rulers make a better and more unified administration [Plato] |
2132 | Only rule by philosophers of integrity can keep a community healthy [Plato] |
2131 | Is there anything better for a community than to produce excellent people? [Plato] |
2152 | Dialectic is the highest and most important part of the curriculum [Plato] |
2148 | To gain knowledge, turn away from the world of change, and focus on true goodness [Plato] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
2153 | Compulsory intellectual work never remains in the mind [Plato] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
2630 | If Plato's God is immaterial, he will lack consciousness, wisdom, pleasure and movement, which are essential to him [Cicero on Plato] |
14 | If the gods are non-existent or indifferent, why bother to deceive them? [Plato] |
2165 | Something is unlikely to be immortal if it is imperfectly made from diverse parts [Plato] |
13 | Is the supreme reward for virtue to be drunk for eternity? [Plato] |
2120 | God is responsible for the good things, but we must look elsewhere for the cause of the bad things [Plato] |