174 ideas
3811 | Entailment and validity are relations, but inference is a human activity [Searle] |
3822 | Theory involves accepting conclusions, and so is a special case of practical reason [Searle] |
3806 | Rationality is built into the intentionality of the mind, and its means of expression [Searle] |
3812 | Rationality is the way we coordinate our intentionality [Searle] |
3508 | Correspondence to the facts HAS to be the aim of enquiry [Searle] |
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] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [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] |
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] |
3809 | If complex logic requires rules, then so does basic logic [Searle] |
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] |
7746 | We don't normally think of names as having senses (e.g. we don't give definitions of them) [Searle] |
7747 | How can a proper name be correlated with its object if it hasn't got a sense? [Searle] |
7748 | 'Aristotle' means more than just 'an object that was christened "Aristotle"' [Searle] |
7749 | Reference for proper names presupposes a set of uniquely referring descriptions [Searle] |
7750 | Proper names are logically connected with their characteristics, in a loose way [Searle] |
3810 | In real reasoning semantics gives validity, not syntax [Searle] |
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] |
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] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
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] |
3473 | Reduction can be of things, properties, ideas or causes [Searle] |
5791 | Reduction is either by elimination, or by explanation [Searle] |
5799 | Eliminative reduction needs a gap between appearance and reality, as in sunsets [Searle] |
3841 | Users of 'supervenience' blur its causal and constitutive meanings [Searle] |
3532 | Solidity in a piston is integral to its structure, not supervenient [Maslin on Searle] |
3533 | Is supervenience just causality? [Searle, by Maslin] |
3454 | Reality is entirely particles in force fields [Searle] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
5790 | A property is 'emergent' if it is caused by elements of a system, when the elements lack the property [Searle] |
3471 | Some properties depend on components, others on their relations [Searle] |
3472 | Fully 'emergent' properties contradict our whole theory of causation [Searle] |
3816 | Our beliefs are about things, not propositions (which are the content of the belief) [Searle] |
3833 | A belief is a commitment to truth [Searle] |
3837 | We can't understand something as a lie if beliefs aren't commitment to truth [Searle] |
3490 | Beliefs only make sense as part of a network of other beliefs [Searle] |
3491 | Beliefs are part of a network, and also exist against a background [Searle] |
3828 | Thinking must involve a self, not just an "it" [Searle] |
3482 | Perception is a function of expectation [Searle] |
3493 | Memory is mainly a guide for current performance [Searle] |
3831 | Reasons can either be facts in the world, or intentional states [Searle] |
3830 | In the past people had a reason not to smoke, but didn't realise it [Searle] |
3832 | Causes (usually events) are not the same as reasons (which are never events) [Searle] |
3463 | We don't have a "theory" that other people have minds [Searle] |
3457 | Other minds are not inferred by analogy, but are our best explanation [Searle] |
3480 | We experience unity at an instant and across time [Searle] |
5792 | Explanation of how we unify our mental stimuli into a single experience is the 'binding problem' [Searle] |
5786 | A system is either conscious or it isn't, though the intensity varies a lot [Searle] |
5794 | Consciousness has a first-person ontology, which only exists from a subjective viewpoint [Searle] |
5795 | There isn't one consciousness (information-processing) which can be investigated, and another (phenomenal) which can't [Searle] |
3479 | The mind experiences space, but it is not experienced as spatial [Searle] |
3470 | Conscious creatures seem able to discriminate better [Searle] |
3486 | Unconscious thoughts are those capable of causing conscious ones [Searle] |
3503 | Consciousness results directly from brain processes, not from some intermediary like information [Searle] |
3465 | Either there is intrinsic intentionality, or everything has it [Searle] |
3484 | Water flowing downhill can be described as if it had intentionality [Searle] |
3489 | Intentional phenomena only make sense within a background [Searle] |
3494 | Intentionality is defined in terms of representation [Searle] |
3481 | Consciousness is essential and basic to intentionality [Searle] |
5788 | The use of 'qualia' seems to imply that consciousness and qualia are separate [Searle] |
4088 | Pain is not intentional, because it does not represent anything beyond itself [Searle] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
3823 | Being held responsible for past actions makes no sense without personal identity [Searle] |
3821 | Giving reasons for action requires reference to a self [Searle] |
3824 | A 'self' must be capable of conscious reasonings about action [Searle] |
3834 | An intentional, acting, rational being must have a self [Searle] |
3825 | Action requires a self, even though perception doesn't [Searle] |
3829 | Selfs are conscious, enduring, reasonable, active, free, and responsible [Searle] |
3826 | A self must at least be capable of consciousness [Searle] |
3827 | The self is neither an experience nor a thing experienced [Searle] |
3820 | The bundle must also have agency in order to act, and a self to act rationally [Searle] |
3467 | Neither introspection nor privileged access makes sense [Searle] |
3483 | Introspection is just thinking about mental states, not a special sort of vision [Searle] |
3468 | I cannot observe my own subjectivity [Searle] |
3817 | Free will is most obvious when we choose between several reasons for an action [Searle] |
3808 | Rational decision making presupposes free will [Searle] |
3818 | We freely decide whether to make a reason for action effective [Searle] |
3469 | Mind and brain don't interact if they are the same [Searle] |
3487 | Without internal content, a zombie's full behaviour couldn't be explained [Searle] |
3458 | Mental states only relate to behaviour contingently, not necessarily [Searle] |
3485 | Wanting H2O only differs from wanting water in its mental component [Searle] |
3461 | Functionalists like the externalist causal theory of reference [Searle] |
2427 | Maybe understanding doesn't need consciousness, despite what Searle seems to think [Searle, by Chalmers] |
7389 | A program won't contain understanding if it is small enough to imagine [Dennett on Searle] |
7390 | If bigger and bigger brain parts can't understand, how can a whole brain? [Dennett on Searle] |
3496 | A program for Chinese translation doesn't need to understand Chinese [Searle] |
5789 | I now think syntax is not in the physics, but in the eye of the beholder [Searle] |
3499 | Computation presupposes consciousness [Searle] |
3501 | If we are computers, who is the user? [Searle] |
5798 | Consciousness has a first-person ontology, so it cannot be reduced without omitting something [Searle] |
3456 | Consciousness is a brain property as liquidity is a water property [Searle] |
3453 | Property dualism is the reappearance of Cartesianism [Searle] |
3455 | Property dualists tend to find the mind-body problem baffling [Searle] |
3475 | Property dualism denies reductionism [Searle] |
5787 | There is non-event causation between mind and brain, as between a table and its solidity [Searle] |
3477 | If mind-brain supervenience isn't causal, this implies epiphenomenalism [Searle] |
3531 | Mental events can cause even though supervenient, like the solidity of a piston [Searle] |
3476 | Mind and brain are supervenient in respect of cause and effect [Searle] |
3478 | Upwards mental causation makes 'supervenience' irrelevant [Searle] |
3466 | Consciousness seems indefinable by conditions or categories [Searle] |
5797 | The pattern of molecules in the sea is much more complex than the complexity of brain neurons [Searle] |
3500 | Can the homunculus fallacy be beaten by recursive decomposition? [Searle] |
9317 | Searle argues that biology explains consciousness, but physics won't explain biology [Searle, by Kriegel/Williford] |
3474 | If mind is caused by brain, does this mean mind IS brain? [Searle] |
5796 | If tree rings contain information about age, then age contains information about rings [Searle] |
3497 | If mind is multiply realisable, it is possible that anything could realise it [Searle] |
3462 | We don't postulate folk psychology, we experience it [Searle] |
3498 | Computation isn't a natural phenomenon, it is a way of seeing phenomena [Searle] |
3492 | Content is much more than just sentence meaning [Searle] |
3464 | There is no such thing as 'wide content' [Searle] |
3506 | We explain behaviour in terms of actual internal representations in the agent [Searle] |
9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
3451 | Meaning is derived intentionality [Searle] |
3450 | Philosophy of language is a branch of philosophy of mind [Searle] |
3507 | Universal grammar doesn't help us explain anything [Searle] |
3495 | Shared Background makes translation possible, though variation makes it hard [Searle] |
3814 | Preferences can result from deliberation, not just precede it [Searle] |
3840 | We don't accept practical reasoning if the conclusion is unpalatable [Searle] |
3815 | The essence of humanity is desire-independent reasons for action [Searle] |
3839 | Only an internal reason can actually motivate the agent to act [Searle] |
3835 | If it is true, you ought to believe it [Searle] |
3836 | If this is a man, you ought to accept similar things as men [Searle] |
3505 | The function of a heart depends on what we want it to do [Searle] |
3838 | Promises hold because I give myself a reason, not because it is an institution [Searle] |
3813 | 'Ought' implies that there is a reason to do something [Searle] |
3504 | Chemistry entirely explains plant behaviour [Searle] |
3502 | Mind involves fighting, fleeing, feeding and fornicating [Searle] |
3459 | You can only know the limits of knowledge if you know the other side of the limit [Searle] |