Formal glossary of philosophy
The formal glossary of philosophy is a collection of definitions for philosophical terms that are sufficiently formal to allow proofs about them.
You can use the terms in this glossary to prove theorems and build philosophical theories, such as this one. If you want to use the terms in this glossary, the recommended way is to transclude them with the Template:Formal glossary of philosophy.
- 1 Guidelines
- 2 Definitions
- 2.1 Accessibility relation
- 2.2 Accidental property
- 2.3 Actual property
- 2.4 Aristotelian change
- 2.5 Causal chain
- 2.6 Causal independence
- 2.7 Cause
- 2.8 Change (1)
- 2.9 Change (2)
- 2.10 Determinism
- 2.11 Direct cause
- 2.12 Element
- 2.13 Effect
- 2.14 Entity
- 2.15 Essence
- 2.16 Essential property
- 2.17 Event
- 2.18 First cause
- 2.19 Full set of causes
- 2.20 Identity
- 2.21 Indirect cause
- 2.22 Metaphysical probability
- 2.23 Object
- 2.24 Possible world
- 2.25 Potential property
- 2.26 Property
- 2.27 Sequence
- 2.28 Set
- 2.29 Supervenience (1)
- 2.30 Supervenience (2)
- 3 Theorems
- 4 Notes and references
- When defining a term, link only the first appearance of each other term in to its definition in the dictionary.
- Do not link outside of the dictionary (to Wikipedia articles for example). One of the goals of the dictionary is to be able to track the definitions back to the primitives. Linking out of the dictionary defeats this purpose. If you want to link to a term that hasn't been defined yet, just create a section for it and leave its definition for later, or mark it as a primitive term.
- If you want to add a different definition for an already existing term, distinguish them with numbers between parenthesis, like in Change (1) and Change (2).
Let x be an entity and w1 and w2 two possible worlds. Then x changes aristotelically from w1 to w2 means: there is at least one possible world w accessible from w1 and with access to w2 (or identical to w2) such that P is a potential property of x in w1 and an actual property in w.
Let c and e be events. Then c is causally independent of e means: c is not a cause of e and e is not a cause of c.
Let x be an entity, and w1 and w2 two possible worlds. Then x changes from w1 to w2 means: there is at least one property P and at least one possible world w accessible from w1 and with access to w2 (or identical to w2) such that x has P in w1 and lacks it in w, or lacks it in w1 and has it in w.
Let x be an entity, and w1 and w2 two possible worlds. Then x changes from w1 to w2 means: there is at least one property P such that x has P in w1 and lacks it in w2, or lacks it in w1 and has it in w2.
Determinism means: every possible world has direct access to one possible world.
Let e be an event. Then e is a first cause means: there is no event c that is a cause of e.
Full set of causes
Let p be a proposition, w a possible world and n a real number between 0 and 1. Then the metaphysical probability of p in w is n means: the number of possible worlds accessible from w where p is true divided by the total number of possible worlds accessible from w equals n.
Note: we assume that the total number of possible worlds accessible from w is a finite number, else all metaphysical probabilities collapse to zero.
Let A and B be two sets of properties. Then A-properties supervene on B-properties means: anything that has an A-property has some B-property such that anything that has that B-property also has that A-property.
Potential properties are not actual
Actual properties are not potential
Essential properties are actual
Potential properties are not essential
Essential properties do not change
Suppose x changes a property P from w1 to w2. Then, by the definition of change, there's at least one possible world w accessible from w1 and with access to w2 (or identical to w2) where x exists, and x has P in w1 but lacks it in w, or lacks it in w1 but has it in w. In either case, there's at least one possible world where x exists without P, so by the definition of essential property, P is not an essential property of x. QED
Some changes are not Aristotelian
Notes and references
- Essential vs Accidental Properties in the Stanford Encyclopedia of Philosophy