90 ideas
| 19648 | Since Kant we think we can only access 'correlations' between thinking and being [Meillassoux] |
| 19674 | The Copernican Revolution decentres the Earth, but also decentres thinking from reality [Meillassoux] |
| 19657 | In Kant the thing-in-itself is unknowable, but for us it has become unthinkable [Meillassoux] |
| 18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
| 18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein] |
| 18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
| 18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
| 18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
| 19675 | Since Kant, philosophers have claimed to understand science better than scientists do [Meillassoux] |
| 19649 | Since Kant, objectivity is defined not by the object, but by the statement's potential universality [Meillassoux] |
| 19666 | If we insist on Sufficient Reason the world will always be a mystery to us [Meillassoux] |
| 19656 | Non-contradiction is unjustified, so it only reveals a fact about thinking, not about reality? [Meillassoux] |
| 18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
| 18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
| 18735 | Talking nonsense is not following the rules [Wittgenstein] |
| 18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
| 18707 | All thought has the logical form of reality [Wittgenstein] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 19663 | We can allow contradictions in thought, but not inconsistency [Meillassoux] |
| 19664 | Paraconsistent logics are to prevent computers crashing when data conflicts [Meillassoux] |
| 19665 | Paraconsistent logic is about statements, not about contradictions in reality [Meillassoux] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 18724 | In logic nothing is hidden [Wittgenstein] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
| 18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
| 18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
| 18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
| 18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
| 19677 | What is mathematically conceivable is absolutely possible [Meillassoux] |
| 18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
| 19659 | The absolute is the impossibility of there being a necessary existent [Meillassoux] |
| 19662 | It is necessarily contingent that there is one thing rather than another - so something must exist [Meillassoux] |
| 19654 | We must give up the modern criterion of existence, which is a correlation between thought and being [Meillassoux] |
| 18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
| 18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
| 19660 | Possible non-being which must be realised is 'precariousness'; absolute contingency might never not-be [Meillassoux] |
| 19671 | The idea of chance relies on unalterable physical laws [Meillassoux] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 18726 | For each necessity in the world there is an arbitrary rule of language [Wittgenstein] |
| 18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
| 19651 | Unlike speculative idealism, transcendental idealism assumes the mind is embodied [Meillassoux] |
| 19647 | The aspects of objects that can be mathematical allow it to have objective properties [Meillassoux] |
| 18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
| 18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
| 18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
| 19652 | How can we mathematically describe a world that lacks humans? [Meillassoux] |
| 19668 | Hume's question is whether experimental science will still be valid tomorrow [Meillassoux] |
| 18721 | Explanation and understanding are the same [Wittgenstein] |
| 18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
| 18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
| 18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
| 19650 | The transcendental subject is not an entity, but a set of conditions making science possible [Meillassoux] |
| 18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
| 18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
| 18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
| 18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
| 18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
| 19667 | If the laws of nature are contingent, shouldn't we already have noticed it? [Meillassoux] |
| 19670 | Why are contingent laws of nature stable? [Meillassoux] |
| 18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |
| 19653 | The ontological proof of a necessary God ensures a reality external to the mind [Meillassoux] |
| 19658 | Now that the absolute is unthinkable, even atheism is just another religious belief (though nihilist) [Meillassoux] |