75 ideas
326 | For relaxation one can consider the world of change, instead of eternal things [Plato] |
315 | Philosophy is the supreme gift of the gods to mortals [Plato] |
306 | Nothing can come to be without a cause [Plato] |
9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
9677 | Φ indicates the empty set, which has no members [Priest,G] |
9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
9681 | X = Y means the set X equals the set Y [Priest,G] |
9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
9686 | A 'set' is a collection of objects [Priest,G] |
9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
9688 | A 'singleton' is a set with only one member [Priest,G] |
9689 | The 'empty set' or 'null set' has no members [Priest,G] |
9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
324 | Before the existence of the world there must have been being, space and becoming [Plato] |
20364 | The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato] |
458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
12042 | Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas] |
307 | Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato] |
318 | In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato] |
321 | For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato] |
317 | The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato] |
13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
462 | One vision is produced by both eyes [Empedocles] |
5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
330 | No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato] |
22765 | Wisdom and thought are shared by all things [Empedocles] |
1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
316 | Music has harmony like the soul, and serves to reorder disharmony within us [Plato] |
552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
332 | One should exercise both the mind and the body, to avoid imbalance [Plato] |
328 | Everything that takes place naturally is pleasant [Plato] |
322 | Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato] |
331 | Bad governments prevent discussion, and discourage the study of virtue [Plato] |
589 | 'Nature' is just a word invented by people [Empedocles] |
310 | The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato] |
311 | The cosmos must be unique, because it resembles the creator, who is unique [Plato] |
21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
459 | All change is unity through love or division through hate [Empedocles] |
13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
325 | We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato] |
327 | There are two types of cause, the necessary and the divine [Plato] |
314 | Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato] |
312 | Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato] |
309 | Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato] |
308 | If the cosmos is an object of perception then it must be continually changing [Plato] |
5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
461 | God is a pure, solitary, and eternal sphere [Empedocles] |
466 | God is pure mind permeating the universe [Empedocles] |
1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
1522 | It is wretched not to want to think clearly about the gods [Empedocles] |