94 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
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] |
10073 | There cannot be a set theory which is complete [Smith,P] |
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] |
10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [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] |
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] |
13120 | Chisholm divides things into contingent and necessary, and then individuals, states and non-states [Chisholm, by Westerhoff] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
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] |
15826 | There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
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] |
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] |
8790 | The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm] |
15831 | Explanations have states of affairs as their objects [Chisholm] |
15811 | I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm] |
15815 | Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm] |
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] |
9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
15821 | Determinism claims that every event has a sufficient causal pre-condition [Chisholm] |
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] |
3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
15824 | There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm] |
15822 | The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
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] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |