82 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] |
| 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] |
| 19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
| 19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
| 19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
| 14684 | A world is 'accessible' to another iff the first is possible according to the second [Salmon,N] |
| 14669 | For metaphysics, T may be the only correct system of modal logic [Salmon,N] |
| 14667 | System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N] |
| 14668 | In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N] |
| 14692 | System B implies that possibly-being-realized is an essential property of the world [Salmon,N] |
| 14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
| 14686 | S5 modal logic ignores accessibility altogether [Salmon,N] |
| 14691 | S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N] |
| 14693 | The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N] |
| 14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
| 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] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 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] |
| 14678 | Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N] |
| 14680 | Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N] |
| 14677 | Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N] |
| 14679 | Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N] |
| 14685 | Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N] |
| 14688 | Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N] |
| 14690 | In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N] |
| 14681 | Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N] |
| 14676 | Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N] |
| 19252 | Objective chance is the property of a distribution [Peirce] |
| 19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
| 14689 | Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N] |
| 14674 | Impossible worlds are also ways for things to be [Salmon,N] |
| 14682 | Denial of impossible worlds involves two different confusions [Salmon,N] |
| 14687 | Without impossible worlds, how things might have been is the only way for things to be [Salmon,N] |
| 14683 | Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N] |
| 14672 | Possible worlds are maximal abstract ways that things might have been [Salmon,N] |
| 14675 | Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N] |
| 14673 | You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N] |
| 19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
| 19224 | Scientists will give up any conclusion, if experience opposes it [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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 19233 | Indexicals are unusual words, because they stimulate the hearer to look around [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] |
| 19254 | Our laws of nature may be the result of evolution [Peirce] |