79 ideas
| 9777 | Kant was the first philosopher [Zizek] |
| 9778 | There is no dialogue in philosophy [Zizek] |
| 9779 | Philosophy is transcendental questioning (not supporting science or constructing ontology) [Zizek] |
| 2463 | A standard naturalist view is realist, externalist, and computationalist, and believes in rationality [Fodor] |
| 2435 | Psychology has to include the idea that mental processes are typically truth-preserving [Fodor] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 2442 | Inferences are surely part of the causal structure of the world [Fodor] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 2462 | Control of belief is possible if you know truth conditions and what causes beliefs [Fodor] |
| 2460 | Participation in an experiment requires agreement about what the outcome will mean [Fodor] |
| 2461 | An experiment is a deliberate version of what informal thinking does all the time [Fodor] |
| 2454 | We can deliberately cause ourselves to have true thoughts - hence the value of experiments [Fodor] |
| 2455 | Interrogation and experiment submit us to having beliefs caused [Fodor] |
| 2458 | Theories are links in the causal chain between the environment and our beliefs [Fodor] |
| 2443 | I say psychology is intentional, semantics is informational, and thinking is computation [Fodor] |
| 9780 | Consciousness is a malfunction of evolution [Zizek] |
| 2453 | We are probably the only creatures that can think about our own thoughts [Fodor] |
| 2446 | Cartesians consider interaction to be a miracle [Fodor] |
| 2445 | Semantics v syntax is the interaction problem all over again [Fodor] |
| 2464 | Type physicalism equates mental kinds with physical kinds [Fodor] |
| 2447 | Hume has no theory of the co-ordination of the mind [Fodor] |
| 2440 | Propositional attitudes are propositions presented in a certain way [Fodor] |
| 2450 | Rationality has mental properties - autonomy, productivity, experiment [Fodor] |
| 2437 | XYZ (Twin Earth 'water') is an impossibility [Fodor] |
| 2441 | Truth conditions require a broad concept of content [Fodor] |
| 3114 | Concepts aren't linked to stuff; they are what is caused by stuff [Fodor] |
| 2452 | Knowing the cause of a thought is almost knowing its content [Fodor] |
| 2432 | Is content basically information, fixed externally? [Fodor] |
| 2438 | In the information view, concepts are potentials for making distinctions [Fodor] |
| 2439 | Semantic externalism says the concept 'elm' needs no further beliefs or inferences [Fodor] |
| 2457 | If meaning is information, that establishes the causal link between the state of the world and our beliefs [Fodor] |
| 2451 | To know the content of a thought is to know what would make it true [Fodor] |
| 2433 | For holists no two thoughts are ever quite the same, which destroys faith in meaning [Fodor] |
| 2436 | It is claimed that reference doesn't fix sense (Jocasta), and sense doesn't fix reference (Twin Earth) [Fodor] |
| 2434 | Broad semantics holds that the basic semantic properties are truth and denotation [Fodor] |
| 2459 | Externalist semantics are necessary to connect the contents of beliefs with how the world is [Fodor] |
| 9781 | Tolerance and love are strategies to avoid encountering our neighbours [Zizek] |