171 ideas
| 15801 | Many philosophers aim to understand metaphysics by studying ourselves [Chisholm] |
| 15802 | I use variables to show that each item remains the same entity throughout [Chisholm] |
| 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] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [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] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 3137 | Varieties of singular terms are used to designate token particulars [Rey] |
| 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] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [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] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [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] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
| 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] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [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] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [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] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 3143 | Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 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] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 15832 | Events are states of affairs that occur at certain places and times [Chisholm] |
| 15829 | The mark of a state of affairs is that it is capable of being accepted [Chisholm] |
| 15809 | A state of affairs pertains to a thing if it implies that it has some property [Chisholm] |
| 15828 | I propose that events and propositions are two types of states of affairs [Chisholm] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 13120 | Chisholm divides things into contingent and necessary, and then individuals, states and non-states [Chisholm, by Westerhoff] |
| 15827 | Some properties, such as 'being a widow', can be seen as 'rooted outside the time they are had' [Chisholm] |
| 15830 | Some properties can never be had, like being a round square [Chisholm] |
| 15804 | If some dogs are brown, that entails the properties of 'being brown' and 'being canine' [Chisholm] |
| 15810 | Maybe we can only individuate things by relating them to ourselves [Chisholm] |
| 15805 | Being the tallest man is an 'individual concept', but not a haecceity [Chisholm] |
| 15807 | A haecceity is a property had necessarily, and strictly confined to one entity [Chisholm] |
| 15814 | A peach is sweet and fuzzy, but it doesn't 'have' those qualities [Chisholm] |
| 12852 | If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons] |
| 15808 | A traditional individual essence includes all of a thing's necessary characteristics [Chisholm] |
| 11966 | If there are essential properties, how do you find out what they are? [Chisholm] |
| 12851 | Intermittence is seen in a toy fort, which is dismantled then rebuilt with the same bricks [Chisholm, by Simons] |
| 15806 | The property of being identical with me is an individual concept [Chisholm] |
| 3145 | The Indiscernibility of Identicals is a truism; but the Identity of Indiscernibles depends on possible identical worlds [Rey] |
| 15826 | There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm] |
| 11965 | Could possible Adam gradually transform into Noah, and vice versa? [Chisholm] |
| 19569 | We have a basic epistemic duty to believe truth and avoid error [Chisholm, by Kvanvig] |
| 20298 | The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey] |
| 15819 | Do sense-data have structure, location, weight, and constituting matter? [Chisholm] |
| 15816 | 'I feel depressed' is more like 'he runs slowly' than like 'he has a red book' [Chisholm] |
| 15817 | If we can say a man senses 'redly', why not also 'rectangularly'? [Chisholm] |
| 15818 | So called 'sense-data' are best seen as 'modifications' of the person experiencing them [Chisholm] |
| 3172 | Empiricism says experience is both origin and justification of all knowledge [Rey] |
| 8790 | The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm] |
| 3166 | Animal learning is separate from their behaviour [Rey] |
| 15831 | Explanations have states of affairs as their objects [Chisholm] |
| 3232 | Abduction could have true data and a false conclusion, and may include data not originally mentioned [Rey] |
| 3128 | It's not at all clear that explanation needs to stop anywhere [Rey] |
| 3136 | The three theories are reduction, dualism, eliminativism [Rey] |
| 3141 | Is consciousness 40Hz oscillations in layers 5 and 6 of the visual cortex? [Rey] |
| 3148 | Dualist privacy is seen as too deep for even telepathy to reach [Rey] |
| 3164 | Intentional explanations are always circular [Rey] |
| 3138 | Arithmetic and unconscious attitudes have no qualia [Rey] |
| 3142 | Why qualia, and why this particular quale? [Rey] |
| 3224 | If qualia have no function, their attachment to thoughts is accidental [Rey] |
| 3227 | Are qualia a type of propositional attitude? [Rey] |
| 3226 | Are qualia irrelevant to explaining the mind? [Rey] |
| 3229 | If colour fits a cone mapping hue, brightness and saturation, rotating the cone could give spectrum inversion [Rey] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 15811 | I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm] |
| 3223 | Self-consciousness may just be nested intentionality [Rey] |
| 15815 | Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm] |
| 3162 | Experiments prove that people are often unaware of their motives [Rey] |
| 3163 | Brain damage makes the unreliability of introspection obvious [Rey] |
| 15813 | People use 'I' to refer to themselves, with the meaning of their own individual essence [Chisholm] |
| 15803 | Bad theories of the self see it as abstract, or as a bundle, or as a process [Chisholm] |
| 3444 | If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm] |
| 3446 | For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm] |
| 15821 | Determinism claims that every event has a sufficient causal pre-condition [Chisholm] |
| 9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
| 3196 | Free will isn't evidence against a theory of thought if there is no evidence for free will [Rey] |
| 3195 | If reason could be explained in computational terms, there would be no need for the concept of 'free will' [Rey] |
| 3180 | Maybe behaviourists should define mental states as a group [Rey] |
| 3165 | Behaviourism is eliminative, or reductionist, or methodological [Rey] |
| 3167 | Animals don't just respond to stimuli, they experiment [Rey] |
| 3173 | How are stimuli and responses 'similar'? [Rey] |
| 3179 | Behaviour is too contingent and irrelevant to be the mind [Rey] |
| 3186 | If a normal person lacked a brain, would you say they had no mind? [Rey] |
| 3127 | Dualism and physicalism explain nothing, and don't suggest any research [Rey] |
| 3188 | Homuncular functionalism (e.g. Freud) could be based on simpler mechanical processes [Rey] |
| 3216 | Is the room functionally the same as a Chinese speaker? [Rey] |
| 3220 | Searle is guilty of the fallacy of division - attributing a property of the whole to a part [Rey] |
| 3206 | One computer program could either play chess or fight a war [Rey] |
| 3134 | Human behaviour can show law-like regularity, which eliminativism can't explain [Rey] |
| 3140 | If you explain water as H2O, you have reduced water, but not eliminated it [Rey] |
| 3199 | Connectionism assigns numbers to nodes and branches, and plots the outcomes [Rey] |
| 3201 | Connectionism explains well speed of perception and 'graceful degradation' [Rey] |
| 3202 | Connectionism explains irrationality (such as the Gamblers' Fallacy) quite well [Rey] |
| 3200 | Pattern recognition is puzzling for computation, but makes sense for connectionism [Rey] |
| 3150 | Can identity explain reason, free will, non-extension, intentionality, subjectivity, experience? [Rey] |
| 3129 | Physicalism offers something called "complexity" instead of mental substance [Rey] |
| 3139 | Some attitudes are information (belief), others motivate (hatred) [Rey] |
| 3174 | Good grammar can't come simply from stimuli [Rey] |
| 3171 | Children speak 90% good grammar [Rey] |
| 3213 | Animals may also use a language of thought [Rey] |
| 3170 | We train children in truth, not in grammar [Rey] |
| 3215 | Images can't replace computation, as they need it [Rey] |
| 3194 | CRTT is good on deduction, but not so hot on induction, abduction and practical reason [Rey] |
| 3147 | Problem-solving clearly involves manipulating images [Rey] |
| 3175 | Animals map things over time as well as over space [Rey] |
| 3207 | Simple externalism is that the meaning just is the object [Rey] |
| 3176 | Anything bears a family resemblance to a game, but obviously not anything counts as one [Rey] |
| 3181 | A one hour gap in time might be indirectly verified, but then almost anything could be [Rey] |
| 3204 | The meaning of "and" may be its use, but not of "animal" [Rey] |
| 3205 | Semantic holism means new evidence for a belief changes the belief, and we can't agree on concepts [Rey] |
| 20300 | Externalist synonymy is there being a correct link to the same external phenomena [Rey] |
| 3209 | Causal theories of reference (by 'dubbing') don't eliminate meanings in the heads of dubbers [Rey] |
| 3210 | If meaning and reference are based on causation, then virtually everything has meaning [Rey] |
| 3149 | Referential Opacity says truth is lost when you substitute one referring term ('mother') for another ('Jocasta') [Rey] |
| 20293 | Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey] |
| 20294 | 'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey] |
| 20297 | Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey] |
| 20301 | The meaning properties of a term are those which explain how the term is typically used [Rey] |
| 20302 | An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey] |
| 20303 | Research throws doubts on the claimed intuitions which support analyticity [Rey] |
| 20299 | If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey] |
| 3169 | A simple chaining device can't build sentences containing 'either..or', or 'if..then' [Rey] |
| 20062 | If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm] |
| 20054 | There has to be a brain event which is not caused by another event, but by the agent [Chisholm] |
| 3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
| 3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
| 15824 | There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm] |
| 3221 | Our desires become important when we have desires about desires [Rey] |
| 15822 | The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm] |
| 15823 | Some propose a distinct 'agent causation', as well as 'event causation' [Chisholm] |
| 3445 | Causation among objects relates either events or states [Chisholm] |
| 15820 | A 'law of nature' is just something which is physically necessary [Chisholm] |