44 ideas
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 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] |
| 22919 | A thing which makes no difference seems unlikely to exist [Le Poidevin] |
| 15201 | That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 22926 | In addition to causal explanations, they can also be inferential, or definitional, or purposive [Le Poidevin] |
| 22932 | We don't just describe a time as 'now' from a private viewpoint, but as a fact about the world [Le Poidevin] |
| 22927 | The logical properties of causation are asymmetry, transitivity and irreflexivity [Le Poidevin] |
| 22922 | We can identify unoccupied points in space, so they must exist [Le Poidevin] |
| 22924 | If spatial points exist, then they must be stationary, by definition [Le Poidevin] |
| 22923 | Absolute space explains actual and potential positions, and geometrical truths [Le Poidevin] |
| 22928 | For relationists moving an object beyond the edge of space creates new space [Le Poidevin] |
| 22931 | We distinguish time from space, because it passes, and it has a unique present moment [Le Poidevin] |
| 22917 | Since nothing occurs in a temporal vacuum, there is no way to measure its length [Le Poidevin] |
| 22921 | Temporal vacuums would be unexperienced, unmeasured, and unending [Le Poidevin] |
| 22934 | Time can't speed up or slow down, so it doesn't seem to be a 'process' [Le Poidevin] |
| 22899 | 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN] |
| 22938 | To say that the past causes the present needs them both to be equally real [Le Poidevin] |
| 22939 | The B-series doesn't seem to allow change [Le Poidevin] |
| 22940 | If the B-universe is eternal, why am I trapped in a changing moment of it? [Le Poidevin] |
| 22947 | An ordered series can be undirected, but time favours moving from earlier to later [Le Poidevin] |
| 22952 | If time's arrow is causal, how can there be non-simultaneous events that are causally unconnected? [Le Poidevin] |
| 22951 | If time's arrow is psychological then different minds can impose different orders on events [Le Poidevin] |
| 22948 | There are Thermodynamic, Psychological and Causal arrows of time [Le Poidevin] |
| 22949 | Presumably if time's arrow is thermodynamic then time ends when entropy is complete [Le Poidevin] |
| 22950 | If time is thermodynamic then entropy is necessary - but the theory says it is probable [Le Poidevin] |
| 22953 | Time's arrow is not causal if there is no temporal gap between cause and effect [Le Poidevin] |
| 22943 | Instantaneous motion is an intrinsic disposition to be elsewhere [Le Poidevin] |
| 22945 | The dynamic view of motion says it is primitive, and not reducible to objects, properties and times [Le Poidevin] |
| 22937 | If the present could have diverse pasts, then past truths can't have present truthmakers [Le Poidevin] |
| 22925 | The present is the past/future boundary, so the first moment of time was not present [Le Poidevin] |
| 22944 | The primitive parts of time are intervals, not instants [Le Poidevin] |
| 22942 | If time is infinitely divisible, then the present must be infinitely short [Le Poidevin] |
| 22946 | The multiverse is distinct time-series, as well as spaces [Le Poidevin] |
| 22941 | How could a timeless God know what time it is? So could God be both timeless and omniscient? [Le Poidevin] |