Formal glossary of philosophy
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The formal glossary of philosophy is a collection of definitions of 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. If you want to use the terms in this glossary, the recommended way is to transclude them with the Template:Formal glossary of philosophy.
Contents
- 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 Theories
- 5 Notes and references
Guidelines[edit]
- When defining a term, link only the first appearance of each other term in to its definition in the dictionary.
- Try not to link outside of the dictionary (except Wikipedia articles when explaining primitive terms). 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).
Definitions[edit]
Accessibility relation[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Accidental property[edit]
Let P be a property, x an entity and w a possible world. Then P is an accidental property of x in w means: x has P in w, but in at least one possible world, x exists without P.^{[1]}
Actual property[edit]
Let P be a property, x an entity and w a possible world. Then P is an actual property of x in w means: P is a property of x in w.
Aristotelian change[edit]
Let x be an entity and w_{1} and w_{2} two possible worlds. Then x changes aristotelically from w_{1} to w_{2} means: there is at least one possible world w accessible from w_{1} and with access to w_{2} (or identical to w_{2}) such that P is a potential property of x in w_{1} and an actual property in w.
Causal chain[edit]
A sequence of events (e_{1}, e_{2}, e_{3} ..., e_{n}) is a causal chain means: e_{1} is a cause of e_{2}, e_{2} is a cause of e_{3} and so on until e_{n-1} is a cause of e_{n}
Causal independence[edit]
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.
Cause[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Change (1)[edit]
Let x be an entity, and w_{1} and w_{2} two possible worlds. Then x changes from w_{1} to w_{2} means: there is at least one property P and at least one possible world w accessible from w_{1} and with access to w_{2} (or identical to w_{2}) such that x has P in w_{1} and lacks it in w, or lacks it in w_{1} and has it in w.
Change (2)[edit]
Let x be an entity, and w_{1} and w_{2} two possible worlds. Then x changes from w_{1} to w_{2} means: there is at least one property P such that x has P in w_{1} and lacks it in w_{2}, or lacks it in w_{1} and has it in w_{2}.
Determinism[edit]
Determinism means: every possible world has direct access to exactly one possible world.
Direct cause[edit]
Let c, d and e be events. Then c is a direct cause of e means: c is a cause of e and there is no d such that c is a cause of d and d is a cause of e.
Element[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Effect[edit]
Let c and e be events. Then e is an effect of c means: c is a cause of e.
Entity[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Essence[edit]
Let x be an entity. Then the essence of x is the set of all its essential properties.
Essential property[edit]
Let P be a property and x be an entity. Then P is an essential property of x means: in every possible world where x exists, x has P.^{[1]}
Event[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
First cause[edit]
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[edit]
Let e be an event and ε be a set of events. Then ε is a full set of causes of e means: for every event c that is a cause of e, c is an element of ε.
Identity[edit]
Let x and y be two entities. Then x and y are identical means: they have the same properties.
Indirect cause[edit]
Let c and e be events. Then c is an indirect cause of e means: c is a cause of e, but c is not a direct cause of e.
Metaphysical probability[edit]
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.
Object[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Possible world[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Potential property[edit]
Let P be a property, x an event and w a possible world. Then P is a potential property of x in w means: x exists without P in w, but in at least one accessible possible world, x has P.
Property[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Sequence[edit]
Set[edit]
This is a primitive notion or term—an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term here.
Supervenience (1)[edit]
Let A and B be two sets of properties. Then A-properties supervene on B-properties means: all entities that are B-indiscernible are A-indiscernible.
Supervenience (2)[edit]
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.
Theorems[edit]
Potential properties are not actual[edit]
If P is a potential property of x in w, then P is not an actual property of x in w.
Actual properties are not potential[edit]
If P is an actual property of x in w, then P is not a potential property of x in w.
Essential properties are actual[edit]
If P is an essential property of x, and x exists in w, then P is an actual property of x in w.
Potential properties are not essential[edit]
If P is a potential property of x in w, then P is not an essential property of x.
Essential properties do not change[edit]
If x changes a property P from w_{1} to w_{2}, then P is not an essential property of x.
Suppose x changes a property P from w_{1} to w_{2}. Then, by the definition of change, there's at least one possible world w accessible from w_{1} and with access to w_{2} (or identical to w_{2}) where x exists, and x has P in w_{1} but lacks it in w, or lacks it in w_{1} 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[edit]
Theories[edit]
Notes and references[edit]
- ↑ ^{1.0} ^{1.1} Essential vs Accidental Properties in the Stanford Encyclopedia of Philosophy