165 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] |
| 6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
| 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] |
| 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] |
| 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] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 23173 | If a syllogism admits one absurdity, others must follow [Aquinas] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 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] |
| 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] |
| 21250 | A proposition is self-evident if the predicate is included in the essence of the subject [Aquinas] |
| 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] |
| 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] |
| 1856 | Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas] |
| 1862 | However habituated you are, given time to ponder you can go against a habit [Aquinas] |
| 1849 | Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas] |
| 1861 | The will is not compelled to move, even if pleasant things are set before it [Aquinas] |
| 1853 | Because the will moves by examining alternatives, it doesn't compel itself to will [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] |
| 9096 | The mind must produce by its own power an image of the individual species [Aquinas] |
| 11206 | The mind constructs complete attributions, based on the unified elements of the real world [Aquinas] |
| 1847 | The will must aim at happiness, but can choose the means [Aquinas] |
| 1857 | We don't have to will even perfect good, because we can choose not to think of it [Aquinas] |
| 1846 | The will can only want what it thinks is good [Aquinas] |
| 23180 | The will is the rational appetite [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] |
| 6823 | Repay evil with good and your enemies will become friends (though this is hard) [Mohammed] |
| 6828 | You may break off a treaty if you fear treachery from your ally [Mohammed] |
| 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] |
| 6826 | Allah rewards those who are devout, sincere, patient, humble, charitable, chaste, and who fast [Mohammed] |
| 22399 | Temperance prevents our passions from acting against reason [Aquinas] |
| 6822 | Those who avenge themselves when wronged incur no guilt [Mohammed] |
| 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] |
| 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] |
| 22114 | Tyrannical laws are irrational, and so not really laws [Aquinas] |
| 6833 | Punish theft in men or women by cutting off their hands [Mohammed] |
| 7291 | For Aquinas a war must be in a just cause, have proper authority, and aim at good [Aquinas, by Grayling] |
| 6825 | Do not kill except for a just cause [Mohammed] |
| 6832 | Killing a human, except as just punishment, is like killing all mankind [Mohammed] |
| 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] |
| 6811 | Allah is lord of creation, compassionate, merciful, king of judgement-day [Mohammed] |
| 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] |
| 6819 | True believers see that Allah made the night for rest and the day to give light [Mohammed] |
| 21273 | Way 5: mindless things act towards an obvious end, so there is an intelligent director [Aquinas] |
| 6818 | Allah cannot have begotten a son, as He is self-sufficient [Mohammed] |
| 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] |
| 6829 | There shall be no compulsion in religion [Mohammed] |
| 6831 | He that kills a believer by design shall burn in Hell for ever [Mohammed] |
| 6827 | Make war on the unbelievers until Allah's religion reigns supreme [Mohammed] |
| 6834 | Unbelievers try to interpret the ambiguous parts of the Koran, simply to create dissension [Mohammed] |
| 6817 | The Koran is certainly composed by Allah; no one could compose a chapter like it [Mohammed] |
| 6824 | Do not split into sects, exulting in separate beliefs [Mohammed] |
| 6821 | I created mankind that it might worship Me [Mohammed] |
| 6815 | Be patient with unbelievers, and leave them to the judgement of Allah [Mohammed] |
| 23306 | Humans have a non-physical faculty of reason, so they can be immortal [Aquinas, by Sorabji] |
| 1863 | If the soul achieves well-being in another life, it doesn't follow that I do [Aquinas] |
| 6820 | The righteous shall dwell on couches in gardens, wedded to dark-eyed houris [Mohammed] |
| 6812 | Heaven will be reclining on couches, eating fruit, attended by virgins [Mohammed] |
| 4412 | Those in bliss have their happiness increased by seeing the damned punished [Aquinas] |
| 6830 | Unbelievers will have their skin repeatedly burned off in hell [Mohammed] |
| 6816 | The unbelievers shall drink boiling water [Mohammed] |
| 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] |