103 ideas
20910 | Everything happens necessarily, and for a reason [Democritus] |
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] |
9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [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] |
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] |
9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
9678 | X⊆Y means set X is a '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] |
9682 | X∪Y indicates the 'union' of all the things in sets X and Y [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] |
9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
9688 | A 'singleton' is a set with only one member [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] |
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] |
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] |
16146 | Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle] |
20901 | True Being only occurs when it is completely full, with atoms and no void [Democritus, by Aristotle] |
20902 | Being does not exist more than non-being [Democritus, by Aristotle] |
20904 | The non-existent exists as much as the existent, because it has causal powers [Democritus] |
20903 | The only distinctions are Configuration (shape), Disposition (order) and Turning (position) [Democritus, by Aristotle] |
20893 | Nothing comes from non-existence, or passes into it [Democritus, by Diog. Laertius] |
20896 | It is not possible to know what sort each thing is [Democritus] |
3357 | Democritus denies reality to large objects, because atomic entities can't combine to produce new ones [Benardete,JA on Democritus] |
598 | Democritus said that substances could never be mixed, so atoms are the substances [Democritus, by Aristotle] |
6346 | The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz] |
6351 | Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz] |
6374 | To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz] |
6355 | Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz] |
6359 | Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz] |
6366 | Perception causes beliefs in us, without inference or justification [Pollock/Cruz] |
1532 | Sensible qualities can't be real if they appear different to different creatures [Democritus, by Theophrastus] |
20894 | Man is separated from reality [Democritus] |
6362 | Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz] |
20897 | Obscure knowledge belongs to the five senses, and genuine knowledge is the other type [Democritus] |
517 | All evidence comes from senses, so they are indispensable to the mind [Democritus] |
6371 | Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz] |
6373 | Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz] |
6353 | People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz] |
6361 | Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz] |
6357 | Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz] |
6363 | Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz] |
6365 | Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz] |
6354 | Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz] |
6367 | Coherence theories isolate justification from the world [Pollock/Cruz] |
6370 | Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz] |
6358 | One belief may cause another, without being the basis for the second belief [Pollock/Cruz] |
577 | Democritus says there is either no truth, or it is concealed from us [Democritus, by Aristotle] |
20895 | We actually know nothing, and opinions are mere flux [Democritus] |
1528 | We in fact know nothing, but we each restructure our reality with beliefs [Democritus] |
492 | It is obviously impossible to understand the reality of each thing [Democritus] |
515 | We know nothing in reality; for truth lies in an abyss [Democritus] |
6364 | We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz] |
6352 | Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz] |
6372 | Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz] |
20892 | Democritus was devoted to discovering causal explanations [Democritus, by Eusebius] |
6360 | Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz] |
5882 | Democritus says soul consists of smooth round bodies brought together in accidental collision [Democritus, by Cicero] |
6034 | Atomists say soul has a rational part in the chest, and a diffused non-rational part [Democritus, by Aetius] |
20912 | The soul is the same as the mind [Democritus, by Aristotle] |
20916 | Animals have a share of reason [Democritus, by Porphyry] |
20914 | The directive centre is located in the whole head [Democritus, by Ps-Plutarch] |
6033 | Democritus said everything happens of necessity, by natural motion of atoms [Democritus, by Cicero] |
5088 | Some say there is a determinate cause for every apparently spontaneous event [Democritus, by Aristotle] |
21670 | Democritus said atoms only move by their natural motions, which are therefore necessary [Democritus, by Cicero] |
24041 | Democritus says spherical atoms are fire, and constitute the soul [psuche] [Democritus, by Aristotle] |
20913 | Democritus says the soul is the body, and thinking is thus the mixture of the body [Democritus, by Theophrastus] |
1540 | Pleasure and pain guide our choices of good and bad [Democritus] |
495 | Wisdom creates a healthy passion-free soul [Democritus] |
1537 | Happiness is identifying and separating the pleasures [Democritus, by Stobaeus] |
20917 | Contentment comes from moderation and proportion in life [Democritus, by Stobaeus] |
13551 | Democritus says wealth is a burden to the virtuous mind [Democritus, by Seneca] |
20899 | Atoms cling together, until a stronger necessity disperses them [Democritus, by Aristotle] |
20898 | Atoms are irregular, hooked, concave, convex, and many other shapes [Democritus, by Aristotle] |
20908 | There could be an atom the size of the world [Democritus, by Ps-Plutarch] |
1527 | There must be atoms, to avoid the absurdity of infinite division down to nothing [Democritus, by Aristotle] |
493 | Experiences are merely convention; only atoms and the void are real [Democritus] |
20909 | The basic atoms are without qualities - which only arise from encounters between atoms [Democritus, by Galen] |
1536 | If a cone is horizontally sliced the surfaces can't be equal, so it goes up in steps [Democritus] |
17542 | 'Full' and 'Void' secularised Parmenides's Being and Not-being [Democritus, by Heisenberg] |
1525 | Atomists say there are only three differences - in shape, arrangement and position [Democritus, by Aristotle] |
5947 | If only atoms are real and the rest is convention, we wouldn't bother to avoid pain [Democritus, by Diogenes of Oen.] |
13219 | When atoms touch, why don't they coalesce, like water drops? [Aristotle on Democritus] |
1533 | Because appearance is infinitely varied, atomists assume infinitely many shapes of atom [Democritus, by Aristotle] |
23314 | Greeks explained regularity by intellectual design, not by laws [Democritus, by Frede,M] |
24059 | Democritus is wrong: in a void we wouldn't see a distant ant in exact detail [Aristotle on Democritus] |
5101 | Movement is impossible in a void, because nothing can decide the direction of movement [Aristotle on Democritus] |
20905 | Growth and movement would not exist if there were no void to receive them [Democritus] |
20911 | There are unlimited worlds of varying sizes, some without life or water [Democritus, by Hippolytus] |
1535 | Democritus said people imagined gods as the source of what awed or frightened them [Democritus, by Sext.Empiricus] |
20915 | The soul is destroyed with the body [Democritus, by Ps-Plutarch] |