169 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] |
21489 | Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin] |
6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
14799 | Metaphysics rests on observations, but ones so common we hardly notice them [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] |
14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
14764 | I am saturated with the spirit of physical science [Peirce] |
14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
14779 | I reason in order to avoid disappointment and surprise [Peirce] |
14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
7661 | Truth is the opinion fated to be ultimately agreed by all investigators [Peirce] |
19095 | Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak] |
19097 | Peirce did not think a belief was true if it was useful [Peirce, by Misak] |
21494 | If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce] |
19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
15335 | Peirce's theory offers anti-realist verificationism, but surely how things are is independent of us? [Horsten on Peirce] |
14796 | Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce] |
14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
14186 | Logical connectives contain no information, but just record combination relations between facts [Read] |
19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
14775 | Numbers are just names devised for counting [Peirce] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
21492 | Realism is basic to the scientific method [Peirce] |
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] |
10352 | The real is the idea in which the community ultimately settles down [Peirce] |
6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
14778 | Facts are hard unmoved things, unaffected by what people may think of them [Peirce] |
11016 | Would a language without vagueness be usable at all? [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
13498 | Peirce and others began the mapping out of relations [Peirce, by Hart,WD] |
21491 | Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
14798 | All communication is vague, and is outside the principle of non-contradiction [Peirce] |
14797 | Vagueness is a neglected but important part of mathematical thought [Peirce] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
14804 | Is chance just unknown laws? But the laws operate the same, whatever chance occurs [Peirce] |
19252 | Objective chance is the property of a distribution [Peirce] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
14303 | Truth-functional conditionals have a simple falsification, when A is true and B is false [Peirce] |
14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
16376 | The possible can only be general, and the force of actuality is needed to produce a particular [Peirce] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
19089 | Our whole conception of an object is its possible practical consequences [Peirce] |
7660 | We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce] |
6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
14781 | A 'belief' is a habit which determines how our imagination and actions proceed [Peirce] |
19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
19107 | Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce] |
14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
14768 | Infallibility in science is just a joke [Peirce] |
14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
14765 | Association of ideas is the best philosophical idea of the prescientific age [Peirce] |
14794 | Instead of seeking Truth, we should seek belief that is beyond doubt [Peirce] |
14795 | Pragmatism is a way of establishing meanings, not a theory of metaphysics or a set of truths [Peirce] |
14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
19224 | Scientists will give up any conclusion, if experience opposes it [Peirce] |
6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
19243 | If each inference slightly reduced our certainty, science would soon be in trouble [Peirce] |
14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [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] |
14790 | 'Abduction' is beginning a hypothesis, particularly if it includes preference of one explanation over others [Peirce] |
14791 | Abduction involves original suggestions, and not just the testing involved in induction [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] |
14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
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] |
14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [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] |
14792 | A 'conception', the rational implication of a word, lies in its bearing upon the conduct of life [Peirce] |
14793 | The definition of a concept is just its experimental implications [Peirce] |
19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
14906 | Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce] |
7634 | Icons resemble their subject, an index is a natural sign, and symbols are conventional [Peirce, by Maund] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
14784 | Ethics is the science of aims [Peirce] |
14805 | Is there any such thing as death among the lower organisms? [Peirce] |
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] |
19244 | Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce] |
6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
19254 | Our laws of nature may be the result of evolution [Peirce] |
14806 | If the world is just mechanical, its whole specification has no more explanation than mere chance [Peirce] |
14803 | The more precise the observations, the less reliable appear to be the laws of nature [Peirce] |
6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |
6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |