270 ideas
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
9218 | Maybe what distinguishes philosophy from science is its pursuit of necessary truths [Sider] |
14721 | Metaphysical enquiry can survive if its conclusions are tentative [Sider] |
15010 | Your metaphysics is 'cheating' if your ontology won't support the beliefs you accept [Sider] |
14977 | Metaphysics is not about what exists or is true or essential; it is about the structure of reality [Sider] |
14994 | Extreme doubts about metaphysics also threaten to undermine the science of unobservables [Sider] |
15003 | It seems unlikely that the way we speak will give insights into the universe [Sider] |
14986 | Conceptual analysts trust particular intuitions much more than general ones [Sider] |
13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
14981 | Philosophical concepts are rarely defined, and are not understood by means of definitions [Sider] |
15015 | It seems possible for a correct definition to be factually incorrect, as in defining 'contact' [Sider] |
14992 | We don't care about plain truth, but truth in joint-carving terms [Sider] |
15012 | Orthodox truthmaker theories make entities fundamental, but that is poor for explanation [Sider] |
13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
13711 | System B introduces iterated modalities [Sider] |
13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
13714 | We can treat modal worlds as different times [Sider] |
13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
13723 | System B is needed to prove the Barcan Formula [Sider] |
15023 | The Barcan schema implies if X might have fathered something, there is something X might have fathered [Sider] |
13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
8625 | What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill] |
15004 | 'Gunk' is an object in which proper parts all endlessly have further proper parts [Sider] |
14984 | Which should be primitive in mereology - part, or overlap? [Sider] |
14980 | There is a real issue over what is the 'correct' logic [Sider] |
15000 | 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider] |
15020 | Classical logic is good for mathematics and science, but less good for natural language [Sider] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13680 | Maybe logical consequence is a primitive notion [Sider] |
15029 | Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
15019 | Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider] |
17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill] |
13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
13700 | A 'total' function must always produce an output for a given domain [Sider] |
10427 | All names are names of something, real or imaginary [Mill] |
4944 | Mill says names have denotation but not connotation [Mill, by Kripke] |
7762 | Proper names are just labels for persons or objects, and the meaning is the object [Mill, by Lycan] |
9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
15001 | 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider] |
13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
8742 | The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro] |
17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill] |
13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
9798 | Different parcels made from three pebbles produce different actual sensations [Mill] |
9797 | '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill] |
9799 | 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill] |
9802 | Numbers denote physical properties of physical phenomena [Mill] |
9803 | We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious [Mill] |
9804 | Arithmetical results give a mode of formation of a given number [Mill] |
9805 | 12 is the cube of 1728 means pebbles can be aggregated a certain way [Mill] |
8741 | Numbers must be of something; they don't exist as abstractions [Mill] |
13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
5201 | Mill says logic and maths is induction based on a very large number of instances [Mill, by Ayer] |
9360 | If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI on Mill] |
9888 | Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett on Mill] |
9794 | There are no such things as numbers in the abstract [Mill] |
9796 | Things possess the properties of numbers, as quantity, and as countable parts [Mill] |
9795 | Numbers have generalised application to entities (such as bodies or sounds) [Mill] |
12411 | Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill] |
5656 | Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill] |
9624 | Numbers are a very general property of objects [Mill, by Brown,JR] |
13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
14760 | Four-dimensionalism sees things and processes as belonging in the same category [Sider] |
15017 | Supervenience is a modal connection [Sider] |
15008 | Is fundamentality in whole propositions (and holistic), or in concepts (and atomic)? [Sider] |
15013 | Tables and chairs have fundamental existence, but not fundamental natures [Sider] |
15014 | Unlike things, stuff obeys unrestricted composition and mereological essentialism [Sider] |
15009 | We must distinguish 'concrete' from 'abstract' and necessary states of affairs. [Sider] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
14983 | Accept the ontology of your best theory - and also that it carves nature at the joints [Sider] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
14978 | A property is intrinsic if an object alone in the world can instantiate it [Sider] |
14194 | Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider] |
14995 | Predicates can be 'sparse' if there is a universal, or if there is a natural property or relation [Sider] |
9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
14745 | If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider] |
14740 | If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider] |
14752 | Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider] |
14743 | The stage view of objects is best for dealing with coincident entities [Sider] |
14747 | 'Composition as identity' says that an object just is the objects which compose it [Sider] |
9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
14757 | Mereological essentialism says an object's parts are necessary for its existence [Sider] |
15026 | Essence (even if nonmodal) is not fundamental in metaphysics [Sider] |
14727 | Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider] |
14738 | Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider] |
14726 | Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider] |
14728 | 4D says intrinsic change is difference between successive parts [Sider] |
14729 | 4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider] |
14730 | Temporal parts exist, but are not prior building blocks for objects [Sider] |
14731 | Temporal parts are instantaneous [Sider] |
14758 | How can an instantaneous stage believe anything, if beliefs take time? [Sider] |
14762 | Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider] |
14741 | The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
14754 | If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider] |
12190 | Necessity is what will be, despite any alternative suppositions whatever [Mill] |
22623 | Necessity can only mean what must be, without conditions of any kind [Mill] |
13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
13709 | Logical truths must be necessary if anything is [Sider] |
13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
15030 | Humeans say that we decide what is necessary [Sider] |
15031 | Modal terms in English are entirely contextual, with no modality outside the language [Sider] |
15027 | If truths are necessary 'by convention', that seems to make them contingent [Sider] |
15028 | Conventionalism doesn't seem to apply to examples of the necessary a posteriori [Sider] |
15033 | Humeans says mathematics and logic are necessary because that is how our concept of necessity works [Sider] |
15025 | The world does not contain necessity and possibility - merely how things are [Sider] |
13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
14763 | Counterparts rest on similarity, so there are many such relations in different contexts [Sider] |
13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
3583 | External objects are permanent possibilities of sensation [Mill] |
16859 | Most perception is one-tenth observation and nine-tenths inference [Mill] |
9082 | Clear concepts result from good observation, extensive experience, and accurate memory [Mill] |
16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill] |
14988 | A theory which doesn't fit nature is unexplanatory, even if it is true [Sider] |
14982 | If I used Ramsey sentences to eliminate fundamentality from my theory, that would be a real loss [Sider] |
16845 | The whole theory of induction rests on causes [Mill] |
16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
14989 | Problem predicates in induction don't reflect the structure of nature [Sider] |
14997 | Two applications of 'grue' do not guarantee a similarity between two things [Sider] |
14990 | Bayes produces weird results if the prior probabilities are bizarre [Sider] |
17086 | Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Mill, by Ruben] |
15005 | Explanations must cite generalisations [Sider] |
17091 | Explanation is fitting of facts into ever more general patterns of regularity [Mill, by Ruben] |
16805 | Causal inference is by spotting either Agreements or Differences [Mill, by Lipton] |
16835 | The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton] |
15011 | If the ultimate explanation is a list of entities, no laws, patterns or mechanisms can be cited [Sider] |
3537 | I judge others' feeling by analogy with my body and behaviour [Mill] |
15018 | Intentionality is too superficial to appear in the catalogue of ultimate physics [Sider] |
9079 | We can focus our minds on what is common to a whole class, neglecting other aspects [Mill] |
9081 | We don't recognise comparisons by something in our minds; the concepts result from the comparisons [Mill] |
13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
9080 | General conceptions are a necessary preliminary to Induction [Mill] |
9078 | The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill] |
13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
14999 | Prior to conventions, not all green things were green? [Sider] |
7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
14998 | Conventions are contingent and analytic truths are necessary, so that isn't their explanation [Sider] |
15016 | Analyticity has lost its traditional role, which relied on truth by convention [Sider] |
3772 | The will, in the beginning, is entirely produced by desire [Mill] |
7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
3769 | With early training, any absurdity or evil may be given the power of conscience [Mill] |
3767 | Motive shows the worth of the agent, but not of the action [Mill] |
7076 | Mill wondered if he would be happy if all his aims were realised, and answered no [Mill, by Critchley] |
3771 | Virtues only have value because they achieve some further end [Mill] |
3768 | Orthodox morality is the only one which feels obligatory [Mill] |
7214 | Ethics rests on utility, which is the permanent progressive interests of people [Mill] |
7202 | The English believe in the task of annihilating evil for the victory of good [Nietzsche on Mill] |
5935 | Mill's qualities of pleasure is an admission that there are other good states of mind than pleasure [Ross on Mill] |
3764 | Actions are right if they promote pleasure, wrong if they promote pain [Mill] |
3776 | Utilitarianism only works if everybody has a totally equal right to happiness [Mill] |
3765 | Only pleasure and freedom from pain are desirable as ends [Mill] |
3763 | Ultimate goods such as pleasure can never be proved to be good [Mill] |
3766 | Better to be Socrates dissatisfied than a fool satisfied [Mill] |
3770 | General happiness is only desirable because individuals desire their own happiness [Mill] |
6697 | Moral rules protecting human welfare are more vital than local maxims [Mill] |
7212 | Individuals have sovereignty over their own bodies and minds [Mill] |
3773 | No individual has the right to receive our benevolence [Mill] |
3774 | Rights are a matter of justice, not of benevolence [Mill] |
7210 | The will of the people is that of the largest or most active part of the people [Mill] |
7227 | It is evil to give a government any more power than is necessary [Mill] |
7228 | Individuals often do things better than governments [Mill] |
7230 | Aim for the maximum dissemination of power consistent with efficiency [Mill] |
20515 | Maximise happiness by an area of strict privacy, and an area of utilitarian interventions [Mill, by Wolff,J] |
7229 | People who transact their own business will also have the initiative to control their government [Mill] |
20508 | How people vote should be on public record, so they can be held accountable [Mill, by Wolff,J] |
20507 | Voting is a strict duty, like jury service, and must only be aimed at the public good [Mill] |
20505 | Direct democracy is inexperience judging experience, and ignorance judging knowledge [Mill] |
20504 | People can only participate in decisions in small communities, so representatives are needed [Mill] |
7211 | Prevention of harm to others is the only justification for exercising power over people [Mill] |
7231 | The worth of a State, in the long run, is the worth of the individuals composing it [Mill] |
7217 | The main argument for freedom is that interference with it is usually misguided [Mill] |
7213 | Liberty arises at the point where people can freely and equally discuss things [Mill] |
20517 | Utilitarianism values liberty, but guides us on which ones we should have or not have [Mill, by Wolff,J] |
20516 | Mill defends freedom as increasing happiness, but maybe it is an intrinsic good [Wolff,J on Mill] |
7215 | True freedom is pursuing our own good, while not impeding others [Mill] |
7218 | Individuals are not accountable for actions which only concern themselves [Mill] |
7221 | Blocking entry to an unsafe bridge does not infringe liberty, since no one wants unsafe bridges [Mill] |
7223 | Pimping and running a gambling-house are on the border between toleration and restraint [Mill] |
7220 | Restraint for its own sake is an evil [Mill] |
3775 | A right is a valid claim to society's protection [Mill] |
7219 | Society can punish actions which it believes to be prejudicial to others [Mill] |
7226 | Benefits performed by individuals, not by government, help also to educate them [Mill] |
7224 | We need individual opinions and conduct, and State education is a means to prevent that [Mill] |
7225 | It is a crime to create a being who lacks the ordinary chances of a desirable existence [Mill] |
8345 | A cause is the total of all the conditions which inevitably produce the result [Mill] |
10391 | Causes and conditions are not distinct, because we select capriciously from among them [Mill] |
14547 | The strict cause is the total positive and negative conditions which ensure the consequent [Mill] |
8377 | Causation is just invariability of succession between every natural fact and a preceding fact [Mill] |
14545 | A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill] |
4773 | Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos] |
4775 | In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Mill, by Psillos] |
4776 | In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Mill, by Psillos] |
9417 | What are the fewest propositions from which all natural uniformities could be inferred? [Mill] |
14987 | Many of the key theories of modern physics do not appear to be 'laws' [Sider] |
14985 | The notion of law doesn't seem to enhance physical theories [Sider] |
14725 | Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider] |
14991 | Space has real betweenness and congruence structure (though it is not the Euclidean concepts) [Sider] |
14735 | Space is 3D and lacks a direction; time seems connected to causation [Sider] |
15021 | The central question in the philosophy of time is: How alike are time and space? [Sider] |
15024 | The spotlight theorists accepts eternal time, but with a spotlight of the present moving across it [Sider] |
14722 | Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider] |
14756 | For Presentists there must always be a temporal vantage point for any description [Sider] |
14724 | Presentists must deny truths about multiple times [Sider] |
14723 | Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider] |
14736 | The B-theory is adequate, except that it omits to say which time is present [Sider] |
14734 | The B-series involves eternalism, and the reduction of tense [Sider] |
21332 | We don't get a love of 'order' from nature - which is thoroughly chaotic [Mill] |
7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |
21333 | Evil comes from good just as often as good comes from evil [Mill] |
21335 | Belief that an afterlife is required for justice is an admission that this life is very unjust [Mill] |
21334 | No necessity ties an omnipotent Creator, so he evidently wills human misery [Mill] |
21329 | Nature dispenses cruelty with no concern for either mercy or justice [Mill] |
21328 | Killing is a human crime, but nature kills everyone, and often with great tortures [Mill] |
21330 | Nature makes childbirth a miserable experience, often leading to the death of the mother [Mill] |
21331 | Hurricanes, locusts, floods and blight can starve a million people to death [Mill] |