37 ideas
14018 | Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne] |
14008 | The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne] |
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] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
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] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
14010 | All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne] |
14009 | It is a necessary condition for the existence of relations that both of the relata exist [Bourne] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
14016 | The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne] |
14019 | Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne] |
14013 | Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne] |
14015 | No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne] |
14007 | How can presentists talk of 'earlier than', and distinguish past from future? [Bourne] |
14011 | Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne] |
14017 | Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne] |
14003 | Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne] |
14005 | B-series objects relate to each other; A-series objects relate to the present [Bourne] |
14006 | Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne] |