177 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] |
| 9198 | It is no longer possible to be a sage, but we can practice the exercise of wisdom [Hadot] |
| 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] |
| 9197 | The logos represents a demand for universal rationality [Hadot] |
| 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] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 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] |
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 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] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 14775 | Numbers are just names devised for counting [Peirce] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 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] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 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] |
| 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] |
| 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] |
| 14303 | Truth-functional conditionals have a simple falsification, when A is true and B is false [Peirce] |
| 19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
| 16376 | The possible can only be general, and the force of actuality is needed to produce a particular [Peirce] |
| 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] |
| 19255 | Generalisation is the great law of mind [Peirce] |
| 19242 | Generalization is the true end of life [Peirce] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 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] |
| 19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
| 14784 | Ethics is the science of aims [Peirce] |
| 14805 | Is there any such thing as death among the lower organisms? [Peirce] |
| 9196 | The pleasure of existing is the only genuine pleasure [Hadot] |
| 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] |