286 ideas
21875 | The wisdom of a free man is a meditation on life, not on death [Spinoza] |
17230 | If we are not wholly wise, we should live by good rules and maxims [Spinoza] |
18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
17200 | We must be careful to keep words distinct from ideas and images [Spinoza] |
17194 | Reason only explains what is universal, so it is timeless, under a certain form of eternity [Spinoza] |
4840 | Reason perceives things under a certain form of eternity [Spinoza] |
19917 | Without reason and human help, human life is misery [Spinoza] |
17213 | In so far as men live according to reason, they will agree with one another [Spinoza] |
4819 | There is necessarily for each existent thing a cause why it should exist [Spinoza] |
16541 | All the intrinsic properties of a thing should be deducible from its definition [Spinoza] |
21864 | Truth is its own standard [Spinoza] |
8018 | Spinoza's life shows that love of truth which he proclaims as the highest value [MacIntyre on Spinoza] |
5641 | For Spinoza, 'adequacy' is the intrinsic mark of truth [Spinoza, by Scruton] |
4816 | A true idea must correspond with its ideate or object [Spinoza] |
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] |
20309 | If our ideas are adequate, what follows from them is also adequate [Spinoza] |
10605 | Two functions are the same if they have the same extension [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] |
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] |
10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
10077 | A 'surjective' ('onto') function creates every element of the output set [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] |
17185 | Mathematics deals with the essences and properties of forms [Spinoza] |
17222 | The sum of its angles follows from a triangle's nature [Spinoza] |
17197 | The idea of a triangle involves truths about it, so those are part of its essence [Spinoza] |
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] |
10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
10618 | All numbers are related to zero by the ancestral of the successor relation [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] |
17174 | Outside the mind, there are just things and their properties [Spinoza] |
17176 | The more reality a thing has, the more attributes it has [Spinoza] |
17179 | There must always be a reason or cause why some triangle does or does not exist [Spinoza] |
17186 | Men say they prefer order, not realising that we imagine the order [Spinoza] |
20127 | Laws of nature are universal, so everything must be understood through those laws [Spinoza] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
17170 | An 'attribute' is what the intellect takes as constituting an essence [Spinoza] |
17171 | A 'mode' is an aspect of a substance, and conceived through that substance [Spinoza] |
18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
17195 | Things persevere through a force which derives from God [Spinoza] |
17206 | The essence of a thing is its effort to persevere [Spinoza] |
15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
17192 | The 'universal' term 'man' is just imagining whatever is the same in a multitude of men [Spinoza] |
18459 | Diversity arises from the power of unity [Porphyry] |
17188 | A thing is unified if its parts produce a single effect [Spinoza] |
5639 | Spinoza implies that thought is impossible without the notion of substance [Spinoza, by Scruton] |
21857 | Substance is the power of self-actualisation [Spinoza, by Lord] |
4813 | Substance is that of which an independent conception can be formed [Spinoza] |
4828 | The essence of a thing is what is required for it to exist or be conceived [Spinoza] |
17187 | Essence gives existence and conception to things, and is inseparable from them [Spinoza] |
17191 | Nothing is essential if it is in every part, and is common to everything [Spinoza] |
17184 | All natures of things produce some effect [Spinoza] |
4869 | Experience does not teach us any essences of things [Spinoza] |
17205 | Only an external cause can destroy something [Spinoza] |
17175 | There cannot be two substances with the same attributes [Spinoza] |
17173 | Two substances can't be the same if they have different attributes [Spinoza] |
17183 | Things are impossible if they imply contradiction, or their production lacks an external cause [Spinoza] |
4299 | Contingency is an illusion, resulting from our inadequate understanding [Spinoza, by Cottingham] |
4824 | We only call things 'contingent' in relation to the imperfection of our knowledge [Spinoza] |
4839 | Reason naturally regards things as necessary, and only imagination considers them contingent [Spinoza] |
4822 | Divine nature makes all existence and operations necessary, and nothing is contingent [Spinoza] |
17182 | Necessity is in reference to essence or to cause [Spinoza] |
4818 | People who are ignorant of true causes imagine anything can change into anything else [Spinoza] |
20310 | Error does not result from imagining, but from lacking the evidence of impossibility [Spinoza] |
17208 | A horse would be destroyed if it were changed into a man or an insect [Spinoza] |
17209 | A thing is contingent if nothing in its essence determines whether or not it exists [Spinoza] |
5640 | Spinoza's three levels of knowledge are perception/imagination, then principles, then intuitions [Spinoza, by Scruton] |
17211 | Understanding is the sole aim of reason, and the only profit for the mind [Spinoza] |
21801 | Unlike Descartes' atomism, Spinoza held a holistic view of belief [Spinoza, by Schmid] |
21863 | You only know you are certain of something when you actually are certain of it [Spinoza] |
17199 | A man who assents without doubt to a falsehood is not certain, but lacks a cause to make him waver [Spinoza] |
17193 | True ideas intrinsically involve the highest degree of certainty [Spinoza] |
5638 | 'I think' is useless, because it is contingent, and limited to the first person [Spinoza, by Scruton] |
4831 | If the body is affected by an external object, the mind can't help believing that the object exists [Spinoza] |
4865 | The eyes of the mind are proofs [Spinoza] |
20306 | Once we have experienced two feelings together, one will always give rise to the other [Spinoza] |
18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
4835 | Anyone who knows, must know that they know, and even know that they know that they know.. [Spinoza] |
20308 | Encounters with things confuse the mind, and internal comparisons bring clarity [Spinoza] |
4312 | To understand a phenomenon, we must understand why it is necessary, not merely contingent [Spinoza, by Cottingham] |
13073 | To understand the properties we must know the essence, as with a circle [Spinoza] |
4833 | The human mind is the very idea or knowledge of the human body [Spinoza] |
16198 | Knowledge is the essence of the mind [Spinoza] |
17198 | Will and intellect are the same thing [Spinoza] |
17201 | The will is finite, but the intellect is infinite [Spinoza] |
18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
17196 | The will is not a desire, but the faculty of affirming what is true or false [Spinoza] |
18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
21805 | Spinoza held that the mind is just a bundle of ideas [Spinoza, by Schmid] |
17204 | Animals are often observed to be wiser than people [Spinoza] |
17212 | To understand is the absolute virtue of the mind [Spinoza] |
21804 | Faculties are either fictions, or the abstract universals of ideas [Spinoza] |
4832 | If the body is affected by two things together, the imagining of one will conjure up the other [Spinoza] |
21869 | Our own force of persevering is nothing in comparison with external forces [Spinoza] |
20307 | As far as possible, everything tries to persevere [Spinoza] |
21803 | The conatus (striving) of mind and body together is appetite, which is the essence of man [Spinoza] |
4836 | The mind only knows itself by means of ideas of the modification of the body [Spinoza] |
21861 | Self-knowledge needs perception of the affections of the body [Spinoza] |
18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
17216 | The poet who forgot his own tragedies was no longer the same man [Spinoza] |
4814 | A thing is free if it acts by necessity of its own nature, and the act is determined by itself alone [Spinoza] |
19922 | People are only free if they are guided entirely by reason [Spinoza] |
4871 | A thing is free if it acts only by the necessity of its own nature [Spinoza] |
21802 | An act of will can only occur if it has been caused, which implies a regress of causes [Spinoza] |
4837 | 'Free will' is a misunderstanding arising from awareness of our actions, but ignorance of their causes [Spinoza] |
4843 | Would we die if we lacked free will, and were poised between equal foods? Yes! [Spinoza] |
4844 | The mind is not free to remember or forget anything [Spinoza] |
4311 | We think we are free because we don't know the causes of our desires and choices [Spinoza] |
7828 | The actual world is the only one God could have created [Spinoza] |
18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
21860 | Ideas and things have identical connections and order [Spinoza] |
4308 | Mind and body are one thing, seen sometimes as thought and sometimes as extension [Spinoza] |
4846 | We are incapable of formulating an idea which excludes the existence of our body [Spinoza] |
4834 | Mind and body are the same thing, sometimes seen as thought, and sometimes as extension [Spinoza] |
23951 | Emotion is a modification of bodily energy, controlling our actions [Spinoza] |
4849 | The three primary emotions are pleasure, pain and desire [Spinoza] |
23990 | The three primary emotions are pleasure, pain, and desire [Spinoza, by Goldie] |
17203 | Minds are subject to passions if they have inadequate ideas [Spinoza] |
4864 | An emotion is only bad if it hinders us from thinking [Spinoza] |
7832 | Stoics want to suppress emotions, but Spinoza overcomes them with higher emotions [Spinoza, by Stewart,M] |
4863 | An emotion comes more under our control in proportion to how well it is known to us [Spinoza] |
4841 | People make calculation mistakes by misjudging the figures, not calculating them wrongly [Spinoza] |
21807 | Ideas are powerful entities, which can produce further ideas [Spinoza, by Schmid] |
4830 | An 'idea' is a mental conception which is actively formed by the mind in thinking [Spinoza] |
4842 | Ideas are not images formed in the brain, but are the conceptions of thought [Spinoza] |
20311 | An idea involves affirmation or negation [Spinoza] |
4309 | Spinoza argues that in reality the will and the intellect are 'one and the same' [Spinoza, by Cottingham] |
4838 | Claiming that actions depend on the will is meaningless; no one knows what the will is [Spinoza] |
20305 | Whenever we act, then desire is our very essence [Spinoza] |
21868 | We love or hate people more strongly because we think they are free [Spinoza] |
17202 | We are the source of an action if only our nature can explain the action [Spinoza] |
21865 | We act when it follows from our nature, and is understood in that way [Spinoza] |
4870 | The most beautiful hand seen through the microscope will appear horrible [Spinoza] |
4867 | Whether nature is beautiful or orderly is entirely in relation to human imagination [Spinoza] |
21873 | Men only agree in nature if they are guided by reason [Spinoza] |
21872 | We seek our own advantage, and virtue is doing this rationally [Spinoza] |
18464 | Justice is each person fulfilling his function [Porphyry] |
17189 | The essence of man is modifications of the nature of God [Spinoza] |
17207 | By 'good' I mean what brings us ever closer to our model of human nature [Spinoza] |
8019 | Along with his pantheism, Spinoza equates ethics with the study of human nature [Spinoza, by MacIntyre] |
17229 | If infancy in humans was very rare, we would consider it a pitiful natural defect [Spinoza] |
4845 | We don't want things because they are good; we judge things to be good because we want them [Spinoza] |
17217 | Love is joy with an external cause [Spinoza] |
18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
4848 | Love is nothing else but pleasure accompanied by the idea of an external cause [Spinoza] |
7833 | Spinoza names self-interest as the sole source of value [Spinoza, by Stewart,M] |
17224 | If our ideas were wholly adequate, we would have no concept of evil [Spinoza] |
21870 | Music is good for a melancholic, bad for a mourner, and indifferent to the deaf [Spinoza] |
4860 | Man's highest happiness consists of perfecting his understanding, or reason [Spinoza] |
4847 | Pleasure is a passive state in which the mind increases in perfection [Spinoza] |
4859 | Pleasure is only bad in so far as it hinders a man's capability for action [Spinoza] |
4851 | Reason demands nothing contrary to nature, and so it demands self-love [Spinoza] |
17220 | Self-satisfaction is the highest thing for which we can hope [Spinoza] |
4852 | Both virtue and happiness are based on the preservation of one's own being [Spinoza] |
17214 | To act virtuously is to act rationally [Spinoza] |
21871 | The more we strive for our own advantage, the more virtuous we are [Spinoza] |
17210 | All virtue is founded on self-preservation [Spinoza] |
4856 | To live according to reason is to live according to the laws of human nature [Spinoza] |
18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
17221 | A man ignorant of himself is ignorant of all of the virtues [Spinoza] |
18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
17225 | In a free man, choosing flight can show as much strength of mind as fighting [Spinoza] |
17219 | A person unmoved by either reason or pity to help others is rightly called 'inhuman' [Spinoza] |
4857 | Pity is a bad and useless thing, as it is a pain, and rational people perform good deeds without it [Spinoza] |
17223 | Pity is not a virtue, but at least it shows a desire to live uprightly [Spinoza] |
17218 | People who live according to reason should avoid pity [Spinoza] |
17228 | Rational people judge money by needs, and live contented with very little [Spinoza] |
4853 | Rational people are self-interested, but also desire the same goods for other people [Spinoza] |
4858 | A rational person will want others to have the goods he seeks for himself [Spinoza] |
4855 | If people are obedient to reason, they will live in harmony [Spinoza] |
19935 | Peoples are created by individuals, not by nature, and only distinguished by language and law [Spinoza] |
21874 | The ideal for human preservation is unanimity among people [Spinoza] |
8020 | Only self-knowledge can liberate us [Spinoza, by MacIntyre] |
19914 | In nature everything has an absolute right to do anything it is capable of doing [Spinoza] |
19915 | Natural rights are determined by desire and power, not by reason [Spinoza] |
7412 | Spinoza extended Hobbes's natural rights to cover all possible desires and actions [Spinoza, by Tuck] |
7487 | Society exists to extend human awareness [Spinoza, by Watson] |
19943 | The state aims to allow personal development, so its main purpose is freedom [Spinoza] |
19930 | Sovereignty must include the power to make people submit to it [Spinoza] |
19936 | Kings tend to fight wars for glory, rather than for peace and liberty [Spinoza] |
19937 | Monarchs are always proud, and can't back down [Spinoza] |
19940 | Deposing a monarch is dangerous, because the people are used to royal authority [Spinoza] |
19931 | Every state is more frightened of its own citizens than of external enemies [Spinoza] |
19920 | Democracy is a legitimate gathering of people who do whatever they can do [Spinoza] |
19933 | If religion is law, then piety is justice, impiety is crime, and non-believers must leave [Spinoza] |
19938 | Allowing religious ministers any control of the state is bad for both parties [Spinoza] |
17227 | Slavery is a disgraceful crime [Spinoza] |
19923 | Slavery is not just obedience, but acting only in the interests of the master [Spinoza] |
19939 | Government is oppressive if opinions can be crimes, because people can't give them up [Spinoza] |
19944 | Without liberty of thought there is no trust in the state, and corruption follows [Spinoza] |
19942 | Treason may be committed as much by words as by deeds [Spinoza] |
19924 | The freest state is a rational one, where people can submit themselves to reason [Spinoza] |
7827 | Spinoza wanted democracy based on individual rights, and is thus the first modern political philosopher [Stewart,M on Spinoza] |
19926 | The sovereignty has absolute power over citizens [Spinoza] |
19918 | Forming a society meant following reason, and giving up dangerous appetites and mutual harm [Spinoza] |
19919 | People only give up their rights, and keep promises, if they hope for some greater good [Spinoza] |
19921 | Once you have given up your rights, there is no going back [Spinoza] |
19925 | In democracy we don't abandon our rights, but transfer them to the majority of us [Spinoza] |
19928 | No one, in giving up their power and right, ceases to be a human being [Spinoza] |
19929 | Everyone who gives up their rights must fear the recipients of them [Spinoza] |
19932 | The early Hebrews, following Moses, gave up their rights to God alone [Spinoza] |
19916 | The order of nature does not prohibit anything, and allows whatever appetite produces [Spinoza] |
19927 | State and religious law can clash, so the state must make decisions about religion [Spinoza] |
17226 | The best use of talent is to teach other people to live rationally [Spinoza] |
4854 | It is impossible that the necessity of a person's nature should produce a desire for non-existence [Spinoza] |
17215 | Animals feel, but that doesn't mean we can't use them for our pleasure and profit [Spinoza] |
18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
17190 | We can easily think of nature as one individual [Spinoza] |
4826 | Nature has no particular goal in view, and final causes are mere human figments [Spinoza] |
1587 | Spinoza strongly attacked teleology, which is the lifeblood of classical logos [Roochnik on Spinoza] |
1588 | For Spinoza eyes don't act for purposes, but follow mechanical necessity [Roochnik on Spinoza] |
12731 | Final causes are figments of human imagination [Spinoza] |
4821 | An infinite line can be marked in feet or inches, so one infinity is twelve times the other [Spinoza] |
17177 | In nature there is just one infinite substance [Spinoza] |
4850 | A final cause is simply a human desire [Spinoza] |
4815 | From a definite cause an effect necessarily follows [Spinoza] |
18454 | Time is the circular movement of the soul [Porphyry] |
18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
7835 | The key question for Spinoza is: is his God really a God? [Stewart,M on Spinoza] |
17231 | God feels no emotions, of joy or sorrow [Spinoza] |
21859 | God has no purpose, because God lacks nothing [Spinoza] |
4823 | God does not act according to the freedom of the will [Spinoza] |
18460 | God is nowhere, and hence everywhere [Porphyry] |
17172 | God is a substance with infinite attributes [Spinoza] |
12928 | Spinoza's God is just power and necessity, without perfection or wisdom [Leibniz on Spinoza] |
7571 | Spinoza's God is not a person [Spinoza, by Jolley] |
4314 | God is wholly without passions, and strictly speaking does not love anyone [Spinoza, by Cottingham] |
7609 | God is the sum and principle of all eternal laws [Spinoza, by Armstrong,K] |
19435 | God is not loveable for producing without choice and by necessity; God is loveable for his goodness [Leibniz on Spinoza] |
4866 | God is a being with infinite attributes, each of them infinite or perfect [Spinoza] |
7829 | God no more has human perfections than we have animal perfections [Spinoza] |
4825 | To say that God promotes what is good is false, as it sets up a goal beyond God [Spinoza] |
21856 | Spinoza says a substance of infinite attributes cannot fail to exist [Spinoza, by Lord] |
17178 | Denial of God is denial that his essence involves existence, which is absurd [Spinoza] |
21858 | God is being as such, and you cannot conceive of the non-existence of being [Spinoza, by Lord] |
4820 | God must necessarily exist, because no reason can be given for his non-existence [Spinoza] |
17169 | Some things makes me conceive of it as a thing whose essence requires its existence [Spinoza] |
4817 | If a thing can be conceived as non-existing, its essence does not involve existence [Spinoza] |
4868 | Trying to prove God's existence through miracles is proving the obscure by the more obscure [Spinoza] |
4827 | Priests reject as heretics anyone who tries to understand miracles in a natural way [Spinoza] |
18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
12757 | That God is the substance of all things is an ill-reputed doctrine [Leibniz on Spinoza] |
4829 | The human mind is part of the infinite intellect of God [Spinoza] |
17181 | God is the efficient cause of essences, as well as of existences [Spinoza] |
17180 | Everything is in God, and nothing exists or is thinkable without God [Spinoza] |
7830 | A talking triangle would say God is triangular [Spinoza] |
7836 | In Spinoza, one could substitute 'nature' or 'substance' for the word 'God' throughout [Spinoza, by Stewart,M] |
19934 | Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza] |
4300 | The Bible has nothing in common with reasoning and philosophy [Spinoza] |
7831 | Spinoza's theory of mind implies that there is no immortality [Spinoza, by Stewart,M] |
21876 | After death, something eternal remains of the mind [Spinoza] |
18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |