102 ideas
7113 | Phenomenology assumes that all consciousness is of something [Sartre] |
10073 | There cannot be a set theory which is complete [Smith,P] |
10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
10075 | A 'partial function' maps only some elements to another set [Smith,P] |
10074 | A 'total function' maps every element to one element in another set [Smith,P] |
10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
10605 | Two functions are the same if they have the same extension [Smith,P] |
10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
10613 | No nice theory can define truth for its own language [Smith,P] |
10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
22227 | For Sartre there is only being for-itself, or being in-itself (which is beyond experience) [Sartre, by Daigle] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
7112 | The Cogito depends on a second-order experience, of being conscious of consciousness [Sartre] |
7114 | The consciousness that says 'I think' is not the consciousness that thinks [Sartre] |
7119 | Is the Cogito reporting an immediate experience of doubting, or the whole enterprise of doubting? [Sartre] |
20743 | Appearances do not hide the essence; appearances are the essence [Sartre] |
7125 | A consciousness can conceive of no other consciousness than itself [Sartre] |
7122 | We can never, even in principle, grasp other minds, because the Ego is self-conceiving [Sartre] |
7108 | The eternal truth of 2+2=4 is what gives unity to the mind which regularly thinks it [Sartre] |
24016 | Consciousness always transcends itself [Sartre] |
6151 | Sartre says consciousness is just directedness towards external objects [Sartre, by Rowlands] |
7111 | Consciousness exists as consciousness of itself [Sartre] |
22226 | Since we are a consciousness, Sartre entirely rejected the unconscious mind [Sartre, by Daigle] |
7107 | Intentionality defines, transcends and unites consciousness [Sartre] |
3847 | Man is nothing else but the sum of his actions [Sartre] |
7109 | If you think of '2+2=4' as the content of thought, the self must be united transcendentally [Sartre] |
7106 | The Ego is not formally or materially part of consciousness, but is outside in the world [Sartre] |
7117 | How could two I's, the reflective and the reflected, communicate with each other? [Sartre] |
7123 | Knowing yourself requires an exterior viewpoint, which is necessarily false [Sartre] |
22225 | My ego is more intimate to me, but not more certain than other egos [Sartre] |
7124 | The Ego never appears except when we are not looking for it [Sartre] |
7116 | When we are unreflective (as when chasing a tram) there is no 'I' [Sartre] |
7120 | It is theoretically possible that the Ego consists entirely of false memories [Sartre] |
7110 | If the 'I' is transcendental, it unnecessarily splits consciousness in two [Sartre] |
7115 | Maybe it is the act of reflection that brings 'me' into existence [Sartre] |
7121 | The Ego only appears to reflection, so it is cut off from the World [Sartre] |
3846 | Man IS freedom [Sartre] |
24013 | An emotion and its object form a unity, so emotion is a mode of apprehension [Sartre] |
24017 | Emotion is one of our modes of understanding our Being-in-the-World [Sartre] |
24014 | Emotions are a sort of bodily incantation which brings a magic to the world [Sartre] |
24015 | Emotions makes us believe in and live in a new world [Sartre] |
6164 | Sartre rejects mental content, and the idea that the mind has hidden inner features [Sartre, by Rowlands] |
6687 | Man is the desire to be God [Sartre] |
7074 | Man is a useless passion [Sartre] |
3843 | There is no human nature [Sartre] |
20762 | There are no values to justify us, and no excuses [Sartre] |
3852 | If values depend on us, freedom is the foundation of all values [Sartre] |
22228 | Sartre's freedom is not for whimsical action, but taking responsibility for our own values [Sartre, by Daigle] |
22233 | Love is the demand to be loved [Sartre] |
20764 | In becoming what we want to be we create what we think man ought to be [Sartre] |
3848 | Cowards are responsible for their cowardice [Sartre] |
20763 | When my personal freedom becomes involved, I must want freedom for everyone else [Sartre] |
22229 | Existentialists says that cowards and heroes make themselves [Sartre] |
20755 | Fear concerns the world, but 'anguish' comes from confronting my self [Sartre] |
3842 | Existence before essence (or begin with the subjective) [Sartre] |
6868 | 'Existence precedes essence' means we have no pre-existing self, but create it through existence [Sartre, by Le Poidevin] |
3844 | Existentialism says man is whatever he makes of himself [Sartre] |
20760 | Sincerity is not authenticity, because it only commits to one particular identity [Sartre, by Aho] |
22231 | We flee from the anguish of freedom by seeing ourselves objectively, as determined [Sartre] |
20754 | It is dishonest to offer passions as an excuse [Sartre] |
22230 | Sartre gradually realised that freedom is curtailed by the weight of situation [Sartre, by Daigle] |
22232 | Authenticity is taking responsibility for a situation, with all its risks and emotions [Sartre] |
3851 | If I do not choose, that is still a choice [Sartre] |
6571 | When a man must choose between his mother and the Resistance, no theory can help [Sartre, by Fogelin] |
20491 | States have a monopoly of legitimate violence [Sartre, by Wolff,J] |
21240 | The truth about events always comes from the oppressed and disadvantaged [Sartre, by Bakewell] |
3845 | Without God there is no intelligibility or value [Sartre] |