Numbers and abstract items

‘Abstract’ (Liggins)

it is acausal and lacks spatial location

Sempiternal

to exist at all moments of time

Acausal

does not take part in causal interactions (something that never affects anything and is never affected by anything)

Concrete (Liggins)

not abstract - that is, it fails to be both acausal and non‑spatial.

Necessarily existing

An object that exists in all possible worlds - it cannot fail to exist.

Contingently existing

An object that exists in this world but could have failed to exist - there are possible worlds where it does not exist.

The burden of proof

The responsibility to provide arguments or evidence for a claim, rather than assuming it by default.

Platonism

the view that at least one abstract object exists.

Nominalism

the view that there are no abstract objects - everything that exists is concrete.

Confirmation Holism

No individual statement can be confirmed or disconfirmed by an empirical test, but rather only a set of statements (a whole theory) can be.

Universal

a single entity which is ‘repeatable’ or ‘shareable’ in the sense of being capable of somehow existing, or being ‘instantiated’ or ‘exemplified’, at different places at the same time

Particular

a one-off, non-repeatable, non-shareable entity

realism about universals

the view that universals exist

nominalism about universals

the view that universals do not exist, though we can think and talk usefully in terms of universals

transcendent (platonic) realism

universals can exist even when ‘unexemplified’ - e.g. even when no object anywhere in the world can truly be said to ‘have’ the relevant property

Immanent (Aristotelian) realism

universals exist only at those times when they are ‘exemplified’ or ‘instantiated’, e.g. whenever some object actually is the relevant way of being