250 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] |
| 13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
| 13421 | 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock] |
| 13422 | 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock] |
| 13355 | 'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock] |
| 13350 | 'Assumptions' says that a formula entails itself (φ|=φ) [Bostock] |
| 13351 | 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock] |
| 13356 | The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock] |
| 13352 | 'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock] |
| 13353 | 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock] |
| 13354 | 'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock] |
| 13610 | A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock] |
| 13846 | A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock] |
| 13346 | Truth is the basic notion in classical logic [Bostock] |
| 13545 | Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock] |
| 13822 | Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock] |
| 13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
| 13347 | Validity is a conclusion following for premises, even if there is no proof [Bostock] |
| 13348 | It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock] |
| 13349 | Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock] |
| 20309 | If our ideas are adequate, what follows from them is also adequate [Spinoza] |
| 13614 | MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock] |
| 13617 | MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock] |
| 13800 | |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock] |
| 13803 | If we are to express that there at least two things, we need identity [Bostock] |
| 13799 | The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock] |
| 13357 | Truth-functors are usually held to be defined by their truth-tables [Bostock] |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| 13360 | In logic, a name is just any expression which refers to a particular single object [Bostock] |
| 13361 | An expression is only a name if it succeeds in referring to a real object [Bostock] |
| 13813 | Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock] |
| 13814 | Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock] |
| 13816 | Because of scope problems, definite descriptions are best treated as quantifiers [Bostock] |
| 13817 | Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock] |
| 13848 | We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock] |
| 13815 | Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock] |
| 13438 | 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock] |
| 13818 | If we allow empty domains, we must allow empty names [Bostock] |
| 13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
| 13619 | Quantification adds two axiom-schemas and a new rule [Bostock] |
| 13622 | Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock] |
| 13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
| 13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
| 13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
| 13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
| 13753 | Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock] |
| 13755 | Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock] |
| 13758 | In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock] |
| 13754 | Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock] |
| 13757 | Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock] |
| 13611 | Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock] |
| 13613 | A completed open branch gives an interpretation which verifies those formulae [Bostock] |
| 13612 | Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock] |
| 13761 | In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock] |
| 13756 | A tree proof becomes too broad if its only rule is Modus Ponens [Bostock] |
| 13762 | Tableau rules are all elimination rules, gradually shortening formulae [Bostock] |
| 13759 | Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock] |
| 13760 | A sequent calculus is good for comparing proof systems [Bostock] |
| 13364 | Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG] |
| 13821 | Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock] |
| 13362 | If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock] |
| 13541 | For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock] |
| 13542 | A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock] |
| 13540 | A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock] |
| 13544 | Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock] |
| 13618 | Compactness means an infinity of sequents on the left will add nothing new [Bostock] |
| 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] |
| 13358 | Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock] |
| 13359 | Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock] |
| 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] |
| 13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
| 13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
| 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] |
| 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] |
| 13847 | If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock] |
| 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] |
| 13820 | The idea that anything which can be proved is necessary has a problem with empty names [Bostock] |
| 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] |
| 4312 | To understand a phenomenon, we must understand why it is necessary, not merely contingent [Spinoza, by Cottingham] |
| 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] |
| 7535 | If all beliefs are propositional, then belief and judgement are the same thing [Monk] |
| 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] |
| 13363 | A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock] |
| 4838 | Claiming that actions depend on the will is meaningless; no one knows what the will is [Spinoza] |
| 4309 | Spinoza argues that in reality the will and the intellect are 'one and the same' [Spinoza, by Cottingham] |
| 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] |
| 4823 | God does not act according to the freedom of the will [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] |
| 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] |