99 ideas
| 9136 | The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen] |
| 9131 | Two long understandable sentences can have an unintelligible conjunction [Sorensen] |
| 12249 | 'Animal' is a genus and 'rational' is a specific difference [Oderberg] |
| 12242 | Definition distinguishes one kind from another, and individuation picks out members of the kind [Oderberg] |
| 9139 | If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen] |
| 9140 | Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen] |
| 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] |
| 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] |
| 9119 | No attempt to deny bivalence has ever been accepted [Sorensen] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 9135 | We now see that generalizations use variables rather than abstract entities [Sorensen] |
| 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] |
| 9125 | Denying problems, or being romantically defeated by them, won't make them go away [Sorensen] |
| 9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
| 12238 | The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg] |
| 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] |
| 12254 | Being is substantial/accidental, complete/incomplete, necessary/contingent, possible, relative, intrinsic.. [Oderberg] |
| 9116 | Vague words have hidden boundaries [Sorensen] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 12253 | If tropes are in space and time, in what sense are they abstract? [Oderberg] |
| 12256 | We need to distinguish the essential from the non-essential powers [Oderberg] |
| 12252 | Empiricists gave up 'substance', as unknowable substratum, or reducible to a bundle [Oderberg] |
| 9132 | An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen] |
| 12241 | Essences are real, about being, knowable, definable and classifiable [Oderberg, by PG] |
| 12244 | Nominalism is consistent with individual but not with universal essences [Oderberg] |
| 12240 | Essentialism is the main account of the unity of objects [Oderberg] |
| 12247 | Essence is not explanatory but constitutive [Oderberg] |
| 12258 | Properties are not part of an essence, but they flow from it [Oderberg] |
| 12257 | Could we replace essence with collections of powers? [Oderberg] |
| 12236 | Leibniz's Law is an essentialist truth [Oderberg] |
| 12250 | Bodies have act and potency, the latter explaining new kinds of existence [Oderberg] |
| 12234 | Realism about possible worlds is circular, since it needs a criterion of 'possible' [Oderberg] |
| 12235 | Necessity of identity seems trivial, because it leaves out the real essence [Oderberg] |
| 12237 | Rigid designation has at least three essentialist presuppositions [Oderberg] |
| 9128 | It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen] |
| 9130 | Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen] |
| 9118 | The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen] |
| 9124 | We are unable to perceive a nose (on the back of a mask) as concave [Sorensen] |
| 9126 | Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen] |
| 9121 | Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 9134 | The negation of a meaningful sentence must itself be meaningful [Sorensen] |
| 9133 | Propositions are what settle problems of ambiguity in sentences [Sorensen] |
| 9129 | I can buy any litre of water, but not every litre of water [Sorensen] |
| 12245 | Essence is the source of a thing's characteristic behaviour [Oderberg] |
| 12246 | What makes Parmenidean reality a One rather than a Many? [Oderberg] |
| 12239 | The real essentialist is not merely a scientist [Oderberg] |
| 12243 | The reductionism found in scientific essentialism is mistaken [Oderberg] |
| 9122 | God cannot experience unwanted pain, so God cannot understand human beings [Sorensen] |