162 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] |
14796 | Independent truth (if there is any) is the ultimate result of sufficient enquiry [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] |
14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
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] |
14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
14775 | Numbers are just names devised for counting [Peirce] |
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] |
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] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
19252 | Objective chance is the property of a distribution [Peirce] |
14804 | Is chance just unknown laws? But the laws operate the same, whatever chance occurs [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] |
13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
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] |
6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [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] |
19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
14781 | A 'belief' is a habit which determines how our imagination and actions proceed [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] |
14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
14773 | A truth is hard for us to understand if it rests on nothing but inspiration [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] |
19225 | I classify science by level of abstraction; principles derive from above, and data from below [Peirce] |
14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce] |
19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [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] |
19235 | How does induction get started? [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] |
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] |
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] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |