58 ideas
12926 | Wisdom is the science of happiness [Leibniz] |
12903 | Wise people have fewer acts of will, because such acts are linked together [Leibniz] |
12914 | Metaphysics is geometrical, resting on non-contradiction and sufficient reason [Leibniz] |
12915 | Definitions can only be real if the item is possible [Leibniz] |
19333 | A truth is just a proposition in which the predicate is contained within the subject [Leibniz] |
12910 | The predicate is in the subject of a true proposition [Leibniz] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
12920 | There is no multiplicity without true units [Leibniz] |
12319 | What is not truly one being is not truly a being either [Leibniz] |
12922 | A thing 'expresses' another if they have a constant and fixed relationship [Leibniz] |
13079 | A substance contains the laws of its operations, and its actions come from its own depth [Leibniz] |
12745 | Philosophy needs the precision of the unity given by substances [Leibniz] |
12921 | Accidental unity has degrees, from a mob to a society to a machine or organism [Leibniz] |
12746 | We find unity in reason, and unity in perception, but these are not true unity [Leibniz] |
12916 | A body is a unified aggregate, unless it has an indivisible substance [Leibniz] |
12919 | Unity needs an indestructible substance, to contain everything which will happen to it [Leibniz] |
12923 | Every bodily substance must have a soul, or something analogous to a soul [Leibniz] |
12704 | Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance [Leibniz] |
13077 | Basic predicates give the complete concept, which then predicts all of the actions [Leibniz] |
12908 | Essences exist in the divine understanding [Leibniz] |
12706 | Bodies need a soul (or something like it) to avoid being mere phenomena [Leibniz] |
12906 | Truths about species are eternal or necessary, but individual truths concern what exists [Leibniz] |
12904 | If varieties of myself can be conceived of as distinct from me, then they are not me [Leibniz] |
11981 | If someone's life went differently, then that would be another individual [Leibniz] |
12905 | I cannot think my non-existence, nor exist without being myself [Leibniz] |
19334 | I can't just know myself to be a substance; I must distinguish myself from others, which is hard [Leibniz] |
5033 | Nothing should be taken as certain without foundations [Leibniz] |
12913 | Nature is explained by mathematics and mechanism, but the laws rest on metaphysics [Leibniz] |
13089 | To fully conceive the subject is to explain the resulting predicates and events [Leibniz] |
5034 | Mind is a thinking substance which can know God and eternal truths [Leibniz] |
5032 | It seems probable that animals have souls, but not consciousness [Leibniz] |
5031 | Everything which happens is not necessary, but is certain after God chooses this universe [Leibniz] |
12911 | Concepts are what unite a proposition [Leibniz] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
12925 | Beauty increases with familiarity [Leibniz] |
12927 | Happiness is advancement towards perfection [Leibniz] |
15955 | I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena [Leibniz] |
12907 | Each possible world contains its own laws, reflected in the possible individuals of that world [Leibniz] |
12924 | Motion alone is relative, but force is real, and establishes its subject [Leibniz] |
12909 | Everything, even miracles, belongs to order [Leibniz] |
5030 | Miracles are extraordinary operations by God, but are nevertheless part of his design [Leibniz] |
12912 | Immortality without memory is useless [Leibniz] |
12917 | The soul is indestructible and always self-aware [Leibniz] |
12918 | Animals have souls, but lack consciousness [Leibniz] |