43 ideas
| 3879 | Philosophy aims to provide a theory of everything [Scruton] |
| 3891 | If p entails q, then p is sufficient for q, and q is necessary for p [Scruton] |
| 3894 | We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton] |
| 3883 | A true proposition is consistent with every other true proposition [Scruton] |
| 3884 | The pragmatist does not really have a theory of truth [Scruton] |
| 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] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 3906 | If possible worlds are needed to define properties, maybe we should abandon properties [Scruton] |
| 3888 | Hume assumes that necessity can only be de dicto, not de re [Scruton] |
| 3903 | The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton] |
| 3897 | Epistemology is about the justification of belief, not the definition of knowledge [Scruton] |
| 3881 | In the Cogito argument consciousness develops into self-consciousness [Scruton] |
| 3887 | Maybe our knowledge of truth and causation is synthetic a priori [Scruton] |
| 3901 | Touch only seems to reveal primary qualities [Scruton] |
| 3885 | We only conceive of primary qualities as attached to secondary qualities [Scruton] |
| 3910 | If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton] |
| 3899 | The representational theory says perceptual states are intentional states [Scruton] |
| 3898 | My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton] |
| 3880 | Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton] |
| 3878 | Why should you believe someone who says there are no truths? [Scruton] |
| 3892 | Every event having a cause, and every event being determined by its cause, are not the same [Scruton] |
| 3911 | The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton] |
| 3882 | Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton] |
| 3896 | Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton] |
| 3886 | Membership is the greatest source of obligation [Scruton] |
| 3895 | The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 3890 | 'Cause' used to just mean any valid explanation [Scruton] |
| 3904 | Measuring space requires no movement while I do it [Scruton] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 3905 | 'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton] |