80 ideas
1695 | Without extensive examination firm statements are hard, but studying the difficulties is profitable [Aristotle] |
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
1697 | The contrary of good is bad, but the contrary of bad is either good or another evil [Aristotle] |
1698 | Both sides of contraries need not exist (as health without sickness, white without black) [Aristotle] |
11034 | The differentiae of genera which are different are themselves different in kind [Aristotle] |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
18367 | A true existence statement has its truth caused by the existence of the thing [Aristotle] |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
11033 | Predications of predicates are predications of their subjects [Aristotle] |
18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
11044 | One is prior to two, because its existence is implied by two [Aristotle] |
18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
11042 | Parts of a line join at a point, so it is continuous [Aristotle] |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
11041 | Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle] |
11286 | Primary being must be more than mere indeterminate ultimate subject of predication [Politis on Aristotle] |
1700 | There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place [Aristotle] |
1699 | A thing is prior to another if it implies its existence [Aristotle] |
18366 | Of interdependent things, the prior one causes the other's existence [Aristotle] |
3311 | The categories (substance, quality, quantity, relation, action, passion, place, time) peter out inconsequentially [Benardete,JA on Aristotle] |
11035 | There are ten basic categories for thinking about things [Aristotle] |
13121 | Substance,Quantity,Quality,Relation,Place,Time,Being-in-a-position,Having,Doing,Being affected [Aristotle, by Westerhoff] |
16116 | Aristotle derived categories as answers to basic questions about nature, size, quality, location etc. [Aristotle, by Gill,ML] |
21345 | Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil] |
16155 | Aristotle promoted the importance of properties and objects (rather than general and particular) [Aristotle, by Frede,M] |
11032 | Some things said 'of' a subject are not 'in' the subject [Aristotle] |
11038 | We call them secondary 'substances' because they reveal the primary substances [Aristotle] |
16739 | Four species of quality: states, capacities, affects, and forms [Aristotle, by Pasnau] |
11037 | Colour must be in an individual body, or it is not embodied [Aristotle] |
16154 | Aristotle gave up his earlier notion of individuals, because it relied on universals [Aristotle, by Frede,M] |
12351 | Genus and species are substances, because only they reveal the primary substance [Aristotle, by Wedin] |
1694 | Substances have no opposites, and don't come in degrees (including if the substance is a man) [Aristotle] |
16091 | Is primary substance just an ultimate subject, or some aspect of a complex body? [Aristotle, by Gill,ML] |
11280 | Primary being is 'that which lies under', or 'particular substance' [Aristotle, by Politis] |
11040 | A single substance can receive contrary properties [Aristotle] |
16140 | Secondary substances do have subjects, so they are not ultimate in the ontology [Aristotle, by Frede,M] |
10965 | In earlier Aristotle the substances were particulars, not kinds [Aristotle, by Lawson-Tancred] |
11036 | A 'primary' substance is in each subject, with species or genera as 'secondary' substances [Aristotle] |
8287 | Earlier Aristotle had objects as primary substances, but later he switched to substantial form [Aristotle, by Lowe] |
12350 | Things are called 'substances' because they are subjects for everything else [Aristotle] |
18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
11039 | A primary substance reveals a 'this', which is an individual unit [Aristotle] |
12361 | Primary substances are ontological in 'Categories', and explanatory in 'Metaphysics' [Aristotle, by Wedin] |
3315 | Aristotle denigrates the category of relation, but for modern absolutists self-relation is basic [Benardete,JA on Aristotle] |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
18825 | S5 is the logic of logical necessity [Rumfitt] |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
12349 | Only what can be said of many things is a predicable [Aristotle, by Wedin] |
11837 | Some predicates signify qualification of a substance, others the substance itself [Aristotle] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
11043 | It is not possible for fire to be cold or snow black [Aristotle] |
1696 | Change goes from possession to loss (as in baldness), but not the other way round [Aristotle] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |