A Priori and A Posteriori

Knowledge of a fact is a priori if and only if human beings can know it independently of the facts in the world. Logical and mathematical truths are a priori. By contrast, whether is is raining now is not a priori. This fact is a posteriori. Knowledge of a fact is a posteriori if and only if human beings cannot know it independently of the facts in the world.

Possible Worlds

A possible world is a total way things could have been. Every possible world specifies for every possible individual whether or not it exists in this possible world and which properties is possesses/exemplifies. Exactly one of the possible worlds is actual, all other possible worlds are merely possible and not actual.

Modality

A fact is necessary if and only if it obtains in every possible world. Logical and mathematical truths are necessary. By contrast, the fact that it is raining now is not necessary. It could have been the case that it is not raining. A fact which is true but could have been false is contingently true. A fact which is contingently true obtains in some possible worlds including the actual world and fails to obtain in some other possible worlds. A fact which either obtains or could have obtained is possible. A fact which is possible obtains in some possible worlds and fails to obtain in some other possible worlds. A fact which cannot obtain is impossible. A fact which is impossible fails to obtain in all possible worlds.

Impossibility

Here is an example of an impossibility. It is impossible that 'A and not A' obtains. 'A and not A' fails to obtain in all possible worlds. That 'A and not A' fails to obtain in all possible worlds is the Law of Non-Contradiction.

Rigid Designators

A rigid designator is a term which applies to the same individual in all possible worlds in which the individual exists. 'Morning Star' is a rigid designator of the planet Venus. The proper name 'Morning Star' refers to the planet Venus in all possible worlds in which the planet Venus exists. 'Evening Star' is also a rigid designator of the planet Venus. The proper name 'Evening Star' refers to the planet Venus in all possible worlds in which the planet Venus exists. It follows that the names 'Morning Star' and 'Evening Star' refer to the same object in all possible worlds. Hence, the identity statement 'The Morning Star is the Evening Star.' is true in all possible worlds. It is a necessary truth. Suppose Jonathan knows that the proper name 'Morning Star' refers to the planet Venus. But he does not know that the proper name 'Evening Star' refers to the planet Venus. Then he finds out that the proper name 'Evening Star' refers to the planet Venus. When this happens Jonathan learns a necessary truth. Some necessary truths can by learned by learning facts about this world. A convention with respect to which entity a particular name refers to is a fact about this world. Hence some necessary truths are a posteriori.

Descriptions

Proper names are rigid designators. By contrast, descriptions are not rigid designators. They do not refer to the same individual in all possible worlds. The description 'the biggest city in the world' refers to Tokio in the actual world. But there are possible worlds in which it refers to Sau Paulo or to Moskau.

Identity

A thing which exists or possibly exists is an entity. Every entity is identical with itself and with no other entity. Identity is the relation every thing has to itself. Every entity is identical with itself in every possible world in which it exists. Identity is a necessary relation.

Leibniz's Laws

If two things share every property they possess and lack every property they lack together, then they are identical. And vice versa. This is Leibniz's Law of the Indiscernability of Identicals.

If two things differ in at least one property with respect to whether they exemplify it, then they are not identical. And vice versa. This is Leibniz's Law of the Discernability of Non-Identicals.

Intentionality

An entity is intentional or representational if and only if it is about something, of something, referring to something. Peter's thought that Jacob is going to visit him is an intentional state. It is about Jacob. Antonia's desire for a drink of water is an intentional state. It is about a drink of water.

Consciousness

A state is conscious if and only if there is something it feels like to be in that state. A subject is conscious if and only if it is in a conscious state.

 
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