204 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] |
19199 | Some say metaphysics is a highly generalised empirical study of objects [Tarski] |
19219 | Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce] |
14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
19193 | Disputes that fail to use precise scientific terminology are all meaningless [Tarski] |
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] |
19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten] |
19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski] |
19178 | Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski] |
19177 | A definition of truth should be materially adequate and formally correct [Tarski] |
19186 | A rigorous definition of truth is only possible in an exactly specified language [Tarski] |
19194 | We may eventually need to split the word 'true' into several less ambiguous terms [Tarski] |
19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
16296 | Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach] |
19095 | Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak] |
14796 | Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce] |
19097 | Peirce did not think a belief was true if it was useful [Peirce, by Misak] |
7661 | Truth is the opinion fated to be ultimately agreed by all investigators [Peirce] |
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] |
19196 | Scheme (T) is not a definition of truth [Tarski] |
15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten] |
16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach] |
19135 | Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski] |
19138 | Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski] |
4699 | Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady] |
19324 | Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski] |
10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack] |
13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
19180 | It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski] |
19181 | In the classical concept of truth, 'snow is white' is true if snow is white [Tarski] |
19182 | Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski] |
19183 | Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski] |
19198 | We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski] |
15410 | Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski] |
18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt] |
15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten] |
19314 | For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham] |
19316 | Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham] |
19175 | Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson] |
19184 | The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski] |
19191 | Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski] |
19188 | We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski] |
19189 | The metalanguage must contain the object language, logic, and defined semantics [Tarski] |
19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
2571 | Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack] |
10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H] |
10822 | A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski] |
10824 | If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski] |
10969 | Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read] |
17746 | Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki] |
10904 | Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski] |
16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten] |
19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
19190 | We need an undefined term 'true' in the meta-language, specified by axioms [Tarski] |
14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
19197 | Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski] |
19185 | Semantics is a very modest discipline which solves no real problems [Tarski] |
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
10152 | Set theory and logic are fairy tales, but still worth studying [Tarski] |
10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
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] |
19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee] |
19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham] |
13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
19187 | The Liar makes us assert a false sentence, so it must be taken seriously [Tarski] |
14775 | Numbers are just names devised for counting [Peirce] |
10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
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] |
10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
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] |
10151 | I am a deeply convinced nominalist [Tarski] |
14797 | Vagueness is a neglected but important part of mathematical thought [Peirce] |
14798 | All communication is vague, and is outside the principle of non-contradiction [Peirce] |
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] |
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] |
14771 | Only reason can establish whether some deliverance of revelation really is inspired [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] |
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] |
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] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
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] |