25 ideas
13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
13029 | Set Existence: ∃x (x = x) [Kunen] |
13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
10789 | Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)] |
10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
12697 | Indivisibles are not parts, but the extrema of parts [Leibniz] |
10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |