90 ideas
| 19250 | Everything interesting should be recorded, with records that can be rearranged [Peirce] |
| 19228 | Sciences concern existence, but philosophy also concerns potential existence [Peirce] |
| 19241 | An idea on its own isn't an idea, because they are continuous systems [Peirce] |
| 19227 | Philosophy is a search for real truth [Peirce] |
| 19218 | Metaphysics is pointless without exact modern logic [Peirce] |
| 19229 | Metaphysics is the science of both experience, and its general laws and types [Peirce] |
| 19219 | Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce] |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| 19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| 16324 | Any definition of truth requires a metalanguage [Halbach] |
| 16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
| 16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
| 19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
| 19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| 16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
| 16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
| 16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
| 16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
| 16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
| 16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
| 16309 | Every attempt at formal rigour uses some set theory [Halbach] |
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| 19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
| 19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| 16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
| 16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
| 16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
| 16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
| 19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| 19240 | Realism is the belief that there is something in the being of things corresponding to our reasoning [Peirce] |
| 19239 | There may be no reality; it's just our one desperate hope of knowing anything [Peirce] |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| 19252 | Objective chance is the property of a distribution [Peirce] |
| 19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
| 19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
| 19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
| 19224 | Scientists will give up any conclusion, if experience opposes it [Peirce] |
| 19243 | If each inference slightly reduced our certainty, science would soon be in trouble [Peirce] |
| 19225 | I classify science by level of abstraction; principles derive from above, and data from below [Peirce] |
| 19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce] |
| 19235 | How does induction get started? [Peirce] |
| 19236 | Induction can never prove that laws have no exceptions [Peirce] |
| 19251 | The worst fallacy in induction is generalising one recondite property from a sample [Peirce] |
| 19222 | Men often answer inner 'whys' by treating unconscious instincts as if they were reasons [Peirce] |
| 19220 | We may think animals reason very little, but they hardly ever make mistakes! [Peirce] |
| 19255 | Generalisation is the great law of mind [Peirce] |
| 19242 | Generalization is the true end of life [Peirce] |
| 19249 | 'Know yourself' is not introspection; it is grasping how others see you [Peirce] |
| 19257 | Whatever is First must be sentient [Peirce] |
| 19248 | Reasoning involves observation, experiment, and habituation [Peirce] |
| 19221 | Everybody overrates their own reasoning, so it is clearly superficial [Peirce] |
| 19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| 21375 | Reason can be vicious, and great crimes have to be rational [Schopenhauer] |
| 21379 | Man's three basic ethical incentives are egoism, malice and compassion [Schopenhauer] |
| 19230 | People should follow what lies before them, and is within their power [Peirce] |
| 19245 | We are not inspired by other people's knowledge; a sense of our ignorance motivates study [Peirce] |
| 21376 | Philosophy treats animals as exploitable things, ignoring the significance of their lives [Schopenhauer] |
| 19244 | Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce] |
| 19254 | Our laws of nature may be the result of evolution [Peirce] |