76 ideas
| 3695 | Philosophy is a priori if it is anything [Bonjour] |
| 3651 | Perceiving necessary connections is the essence of reasoning [Bonjour] |
| 3700 | Coherence can't be validated by appeal to coherence [Bonjour] |
| 8893 | For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour] |
| 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] |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| 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] |
| 4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| 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] |
| 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] |
| 3697 | The concept of possibility is prior to that of necessity [Bonjour] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 8888 | The concept of knowledge is so confused that it is best avoided [Bonjour] |
| 8887 | It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour] |
| 8897 | The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour] |
| 3707 | Our rules of thought can only be judged by pure rational insight [Bonjour] |
| 3704 | Moderate rationalists believe in fallible a priori justification [Bonjour] |
| 4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
| 4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
| 8896 | Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [Bonjour] |
| 3696 | A priori justification requires understanding but no experience [Bonjour] |
| 3703 | You can't explain away a priori justification as analyticity, and you can't totally give it up [Bonjour] |
| 3706 | A priori justification can vary in degree [Bonjour] |
| 4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
| 3699 | The induction problem blocks any attempted proof of physical statements [Bonjour] |
| 21506 | A coherence theory of justification can combine with a correspondence theory of truth [Bonjour] |
| 21509 | There will always be a vast number of equally coherent but rival systems [Bonjour] |
| 21503 | Empirical coherence must attribute reliability to spontaneous experience [Bonjour] |
| 21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
| 21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
| 21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
| 21505 | A coherent system can be justified with initial beliefs lacking all credibility [Bonjour] |
| 8891 | My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour] |
| 8892 | Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour] |
| 8894 | Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour] |
| 4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
| 3701 | Externalist theories of justification don't require believers to have reasons for their beliefs [Bonjour] |
| 8889 | Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour] |
| 4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
| 8890 | If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour] |
| 4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
| 3702 | Externalism means we have no reason to believe, which is strong scepticism [Bonjour] |
| 21508 | Anomalies challenge the claim that the basic explanations are actually basic [Bonjour] |
| 3709 | Induction must go beyond the evidence, in order to explain why the evidence occurred [Bonjour] |
| 8895 | If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [Bonjour] |
| 3708 | All thought represents either properties or indexicals [Bonjour] |
| 3698 | Indeterminacy of translation is actually indeterminacy of meaning and belief [Bonjour] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |