151 ideas
22115 | Wise people should contemplate and discuss the truth, and fight against falsehood [Aquinas] |
22101 | Philosophy aims to know the truth about the way things are [Aquinas] |
1848 | We are coerced into assent to a truth by reason's violence [Aquinas] |
1858 | The mind is compelled by necessary truths, but not by contingent truths [Aquinas] |
21267 | Supposing many principles is superfluous if a few will do it [Aquinas] |
22102 | Arguing with opponents uncovers truths, and restrains falsehoods [Aquinas] |
9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
13070 | If definitions must be general, and general terms can't individuate, then Socrates can't be defined [Aquinas, by Cover/O'Leary-Hawthorne] |
11197 | The definitions expressing identity are used to sort things [Aquinas] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
23176 | Truth is universal, but knowledge of it is not [Aquinas] |
20621 | Types of lying: Speak lies, intend lies, intend deception, aim at deceptive goal? [Aquinas, by Tuckness/Wolf] |
1852 | For the mind Good is one truth among many, and Truth is one good among many [Aquinas] |
21248 | If the existence of truth is denied, the 'Truth does not exist' must be true! [Aquinas] |
22104 | Truth is the conformity of being to intellect [Aquinas] |
6345 | Minimalism is incoherent, as it implies that truth both is and is not a property [Boghossian, by Horwich] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
23173 | If a syllogism admits one absurdity, others must follow [Aquinas] |
9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
11195 | If affirmative propositions express being, we affirm about what is absent [Aquinas] |
22103 | Being is basic to thought, and all other concepts are additions to being [Aquinas] |
15812 | Being implies distinctness, which implies division, unity, and multitude [Aquinas] |
21268 | Non-human things are explicable naturally, and voluntary things by the will, so God is not needed [Aquinas] |
16655 | Different genera are delimited by modes of predication, which rest on modes of being [Aquinas] |
16641 | Whiteness does not exist, but by it something can exist-as-white [Aquinas] |
11201 | Properties have an incomplete essence, with definitions referring to their subject [Aquinas] |
11205 | If the form of 'human' contains 'many', Socrates isn't human; if it contains 'one', Socrates is Plato [Aquinas] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
13090 | The principle of diversity for corporeal substances is their matter [Aquinas, by Cover/O'Leary-Hawthorne] |
17555 | 'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas] |
16765 | Humans only have a single substantial form, which contains the others and acts for them [Aquinas] |
16766 | One thing needs a single thing to unite it; if there were two forms, something must unite them [Aquinas] |
11202 | It is by having essence that things exist [Aquinas] |
11203 | Specific individual essence is defined by material, and generic essence is defined by form [Aquinas] |
11200 | The definition of a physical object must include the material as well as the form [Aquinas] |
11196 | Essence is something in common between the natures which sort things into categories [Aquinas] |
11208 | A simple substance is its own essence [Aquinas] |
22170 | Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas] |
23175 | The conclusions of speculative reason about necessities are certain [Aquinas] |
21337 | A knowing being possesses a further reality, the 'presence' of the thing known [Aquinas] |
21249 | Some things are self-evident to us; others are only self-evident in themselves [Aquinas] |
22169 | Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas] |
9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
21250 | A proposition is self-evident if the predicate is included in the essence of the subject [Aquinas] |
9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
22168 | Minds take in a likeness of things, which activates an awaiting potential [Aquinas] |
20224 | Sensation prepares the way for intellectual knowledge, which needs the virtues of reason [Aquinas] |
1860 | Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas] |
9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
22109 | The fullest knowledge places a conclusion within an accurate theory [Aquinas, by Kretzmann/Stump] |
11198 | Definition of essence makes things understandable [Aquinas] |
22107 | Sensations are transmitted to 'internal senses' in the brain, chiefly to 'phantasia' and 'imagination' [Aquinas, by Kretzmann/Stump] |
9098 | Mental activity combines what we sense with imagination of what is not present [Aquinas] |
9092 | Abstracting A from B generates truth, as long as the connection is not denied [Aquinas] |
9093 | We understand the general nature of things by ignoring individual peculiarities [Aquinas] |
9097 | The mind abstracts generalities from images, but also uses images for understanding [Aquinas] |
9095 | Very general ideas (being, oneness, potentiality) can be abstracted from thought matter in general [Aquinas] |
9099 | Particular instances come first, and (pace Plato) generalisations are abstracted from them [Aquinas] |
10508 | Species are abstracted from appearances by ignoring individual conditions [Aquinas] |
22111 | Aquinas attributes freedom to decisions and judgements, and not to the will alone [Aquinas, by Kretzmann/Stump] |
1855 | If we saw something as totally and utterly good, we would be compelled to will it [Aquinas] |
1849 | Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas] |
1853 | Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas] |
1861 | The will is not compelled to move, even if pleasant things are set before it [Aquinas] |
1862 | However habituated you are, given time to ponder you can go against a habit [Aquinas] |
1856 | Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas] |
1854 | We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas] |
22105 | The human intellectual soul is an incorporeal, subsistent principle [Aquinas] |
20700 | Without God's influence every operation would stop, so God causes everything [Aquinas] |
22108 | First grasp what it is, then its essential features; judgement is their compounding and division [Aquinas] |
10503 | We abstract forms from appearances, and acquire knowledge of immaterial things [Aquinas] |
10509 | Understanding consists entirely of grasping abstracted species [Aquinas] |
10506 | Mathematics can be abstracted from sensible matter, and from individual intelligible matter [Aquinas] |
9094 | Mathematical objects abstract both from perceived matter, and from particular substance [Aquinas] |
10505 | We can just think of an apple's colour, because the apple is not part of the colour's nature [Aquinas] |
10504 | Abstracting either treats something as separate, or thinks of it separately [Aquinas] |
10507 | Numbers and shapes are abstracted by ignoring their sensible qualities [Aquinas] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9096 | The mind must produce by its own power an image of the individual species [Aquinas] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
11206 | The mind constructs complete attributions, based on the unified elements of the real world [Aquinas] |
17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
1857 | We don't have to will even perfect good, because we can choose not to think of it [Aquinas] |
23180 | The will is the rational appetite [Aquinas] |
1846 | The will can only want what it thinks is good [Aquinas] |
1847 | The will must aim at happiness, but can choose the means [Aquinas] |
1850 | Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas] |
22112 | For humans good is accordance with reason, and bad is contrary to reason [Aquinas] |
22494 | We must know the end, know that it is the end, and know how to attain it [Aquinas] |
1851 | Good applies to goals, just as truth applies to ideas in the mind [Aquinas] |
23181 | All acts of virtue relate to justice, which is directed towards the common good [Aquinas] |
8009 | Aquinas wanted, not to escape desire, but to transform it for moral ends [Aquinas, by MacIntyre] |
23182 | Legal justice is supreme, because it directs the other virtues to the common good [Aquinas] |
22399 | Temperance prevents our passions from acting against reason [Aquinas] |
23177 | Justice directs our relations with others, because it denotes a kind of equality [Aquinas] |
23179 | People differ in their social degrees, and a particular type of right applies to each [Aquinas] |
22114 | Tyrannical laws are irrational, and so not really laws [Aquinas] |
23174 | Natural law is a rational creature's participation in eternal law [Aquinas] |
22113 | Right and wrong actions pertain to natural law, as perceived by practical reason [Aquinas] |
7291 | For Aquinas a war must be in a just cause, have proper authority, and aim at good [Aquinas, by Grayling] |
5508 | Aquinas says a fertilized egg is not human, and has no immortal soul [Aquinas, by Martin/Barresi] |
16687 | Bodies are three-dimensional substances [Aquinas] |
11207 | A cause can exist without its effect, but the effect cannot exist without its cause [Aquinas] |
1859 | Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas] |
15202 | Eternity coexists with passing time, as the centre of a circle coexists with its circumference [Aquinas] |
23178 | Divine law commands some things because they are good, while others are good because commanded [Aquinas] |
21251 | We can't know God's essence, so his existence can't be self-evident for us [Aquinas] |
5614 | If you assume that there must be a necessary being, you can't say which being has this quality [Kant on Aquinas] |
21269 | Way 1: the infinite chain of potential-to-actual movement has to have a first mover [Aquinas] |
21270 | Way 2: no effect without a cause, and this cannot go back to infinity, so there is First Cause [Aquinas] |
21271 | Way 3: contingent beings eventually vanish, so continuity needs a necessary being [Aquinas] |
21272 | Way 4: the source of all qualities is their maximum, so something (God) causes all perfections [Aquinas] |
21273 | Way 5: mindless things act towards an obvious end, so there is an intelligent director [Aquinas] |
20211 | Life aims at the Beatific Vision - of perfect happiness, and revealed truth [Aquinas, by Zagzebski] |
22106 | Aquinas saw angels as separated forms, rather than as made of 'spiritual matter' [Aquinas, by Kretzmann/Stump] |
16711 | Heretics should be eradicated like wolves [Aquinas] |
1863 | If the soul achieves well-being in another life, it doesn't follow that I do [Aquinas] |
23306 | Humans have a non-physical faculty of reason, so they can be immortal [Aquinas, by Sorabji] |
4412 | Those in bliss have their happiness increased by seeing the damned punished [Aquinas] |
21266 | God does not exist, because He is infinite and good, and so no evil should be discoverable [Aquinas] |
21274 | It is part of God's supreme goodness that He brings good even out of evil [Aquinas] |