55 ideas
| 3811 | Entailment and validity are relations, but inference is a human activity [Searle] |
| 3822 | Theory involves accepting conclusions, and so is a special case of practical reason [Searle] |
| 3806 | Rationality is built into the intentionality of the mind, and its means of expression [Searle] |
| 3812 | Rationality is the way we coordinate our intentionality [Searle] |
| 21953 | For Heidegger there is 'ontic' truth or 'uncoveredness', as in "he is a true friend" [Heidegger, by Wrathall] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 3809 | If complex logic requires rules, then so does basic logic [Searle] |
| 3810 | In real reasoning semantics gives validity, not syntax [Searle] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 3841 | Users of 'supervenience' blur its causal and constitutive meanings [Searle] |
| 3816 | Our beliefs are about things, not propositions (which are the content of the belief) [Searle] |
| 3833 | A belief is a commitment to truth [Searle] |
| 3837 | We can't understand something as a lie if beliefs aren't commitment to truth [Searle] |
| 3828 | Thinking must involve a self, not just an "it" [Searle] |
| 3831 | Reasons can either be facts in the world, or intentional states [Searle] |
| 3830 | In the past people had a reason not to smoke, but didn't realise it [Searle] |
| 3832 | Causes (usually events) are not the same as reasons (which are never events) [Searle] |
| 3823 | Being held responsible for past actions makes no sense without personal identity [Searle] |
| 3821 | Giving reasons for action requires reference to a self [Searle] |
| 3824 | A 'self' must be capable of conscious reasonings about action [Searle] |
| 3834 | An intentional, acting, rational being must have a self [Searle] |
| 3825 | Action requires a self, even though perception doesn't [Searle] |
| 3829 | Selfs are conscious, enduring, reasonable, active, free, and responsible [Searle] |
| 3826 | A self must at least be capable of consciousness [Searle] |
| 3827 | The self is neither an experience nor a thing experienced [Searle] |
| 3820 | The bundle must also have agency in order to act, and a self to act rationally [Searle] |
| 3817 | Free will is most obvious when we choose between several reasons for an action [Searle] |
| 3808 | Rational decision making presupposes free will [Searle] |
| 3818 | We freely decide whether to make a reason for action effective [Searle] |
| 3814 | Preferences can result from deliberation, not just precede it [Searle] |
| 3840 | We don't accept practical reasoning if the conclusion is unpalatable [Searle] |
| 3815 | The essence of humanity is desire-independent reasons for action [Searle] |
| 3839 | Only an internal reason can actually motivate the agent to act [Searle] |
| 3835 | If it is true, you ought to believe it [Searle] |
| 3836 | If this is a man, you ought to accept similar things as men [Searle] |
| 3838 | Promises hold because I give myself a reason, not because it is an institution [Searle] |
| 3813 | 'Ought' implies that there is a reason to do something [Searle] |