82 ideas
| 19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
| 19583 | Philosophy only begins when it studies itself [Novalis] |
| 22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
| 19588 | The highest aim of philosophy is to combine all philosophies into a unity [Novalis] |
| 19598 | Philosophy relies on our whole system of learning, and can thus never be complete [Novalis] |
| 19586 | Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis] |
| 19587 | Philosophy aims to produce a priori an absolute and artistic world system [Novalis] |
| 4739 | In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel] |
| 19574 | If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis] |
| 4737 | Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel] |
| 4750 | The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel] |
| 4744 | We can't explain the corresponding structure of the world except by referring to our thoughts [Engel] |
| 4738 | The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel] |
| 4745 | Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel] |
| 19571 | Delusion and truth differ in their life functions [Novalis] |
| 4753 | Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel] |
| 4755 | Deflationism cannot explain why we hold beliefs for reasons [Engel] |
| 4751 | Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel] |
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| 19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| 4752 | Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel] |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| 19581 | A problem is a solid mass, which the mind must break up [Novalis] |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| 19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
| 19575 | Refinement of senses increasingly distinguishes individuals [Novalis] |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 4762 | The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel] |
| 4754 | Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel] |
| 4763 | 'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel] |
| 22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
| 19572 | Experiences tests reason, and reason tests experience [Novalis] |
| 4746 | Pragmatism is better understood as a theory of belief than as a theory of truth [Engel] |
| 19590 | Empiricists are passive thinkers, given their philosophy by the external world and fate [Novalis] |
| 4764 | We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel] |
| 19594 | General statements about nature are not valid [Novalis] |
| 19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
| 19596 | The whole body is involved in the formation of thoughts [Novalis] |
| 4759 | Mental states as functions are second-order properties, realised by first-order physical properties [Engel] |
| 19573 | The seat of the soul is where our inner and outer worlds interpenetrate [Novalis] |
| 19577 | Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis] |
| 19585 | Every person has his own language [Novalis] |
| 19578 | Only self-illuminated perfect individuals are beautiful [Novalis] |
| 19582 | Morality and philosophy are mutually dependent [Novalis] |
| 22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
| 19589 | The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis] |
| 19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
| 19593 | Persons are shaped by a life history; splendid persons are shaped by world history [Novalis] |
| 19595 | Nature is a whole, and its individual parts cannot be wholly understood [Novalis] |
| 19592 | The basic relations of nature are musical [Novalis] |
| 19576 | Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis] |