230 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] |
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] |
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] |
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] |
13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
13643 | Aristotelian logic is complete [Shapiro] |
13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
13627 | There is no 'correct' logic for natural languages [Shapiro] |
13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
20309 | If our ideas are adequate, what follows from them is also adequate [Spinoza] |
13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
13644 | Semantics for models uses set-theory [Shapiro] |
13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
13670 | Categoricity can't be reached in a first-order language [Shapiro] |
13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
13628 | We can live well without completeness in logic [Shapiro] |
13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
13646 | Compactness is derived from soundness and completeness [Shapiro] |
13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
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] |
13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
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] |
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] |
13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
17195 | Things persevere through a force which derives from God [Spinoza] |
17206 | The essence of a thing is its effort to persevere [Spinoza] |
17192 | The 'universal' term 'man' is just imagining whatever is the same in a multitude of men [Spinoza] |
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] |
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] |
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] |
12314 | Audience-relative explanation, or metaphysical explanation based on information? [Stanford] |
12313 | Explanation is for curiosity, control, understanding, to make meaningful, or to give authority [Stanford] |
4312 | To understand a phenomenon, we must understand why it is necessary, not merely contingent [Spinoza, by Cottingham] |
12315 | We can explain by showing constitution, as well as showing causes [Stanford] |
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] |
17196 | The will is not a desire, but the faculty of affirming what is true or false [Spinoza] |
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] |
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] |
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] |
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] |
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] |
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] |
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] |
17221 | A man ignorant of himself is ignorant of all of the virtues [Spinoza] |
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] |
21874 | The ideal for human preservation is unanimity among people [Spinoza] |
8020 | Only self-knowledge can liberate us [Spinoza, by MacIntyre] |
7412 | Spinoza extended Hobbes's natural rights to cover all possible desires and actions [Spinoza, by Tuck] |
17227 | Slavery is a disgraceful crime [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] |
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] |
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] |
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] |
4823 | God does not act according to the freedom of the will [Spinoza] |
21859 | God has no purpose, because God lacks nothing [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] |
4827 | Priests reject as heretics anyone who tries to understand miracles in a natural way [Spinoza] |
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] |
7836 | In Spinoza, one could substitute 'nature' or 'substance' for the word 'God' throughout [Spinoza, by Stewart,M] |
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] |