142 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| Full Idea: Anaximander was the first to produce a philosophical book (later conventionally titled 'On Nature'), if not the first to produce a book at all. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by István Bodnár - Anaximander | |
| A reaction: Wow! Presumably there were Egyptian 'books', but this still sounds like a stupendous claim to fame. |
| 5361 | Philosophers must get used to absurdities [Russell] |
| Full Idea: Whoever wishes to become a philosopher must learn not to be frightened by absurdities. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: He says this jokingly, but it is obviously true. Philosophy requires extreme imagination, and it also requires taking seriously possibilities that are dismissed by others. It would be a catastrophe if we all dismissed the truth as self-evidently false. |
| 5368 | Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell] |
| Full Idea: Philosophy should show us the hierarchy of our instinctive beliefs, ..and show that they do not clash, but form a harmonious system. There is no reason to reject an instinctive belief, except that it clashes with others. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This is open to the standard objections to the coherence theory of truth (as explained by Russell!), but I like this view of philosophy. Somewhere behind it is the rationalist dream that the final set of totally consistent beliefs will have to be true. |
| 5432 | Metaphysics cannot give knowledge of the universe as a whole [Russell] |
| Full Idea: It would seem that knowledge concerning the universe as a whole is not to be obtained by metaphysics. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.14) | |
| A reaction: Although Russell is strongly attracted to rationalism and platonism, this remark puts him firmly in the camp of Hume, and makes him godfather to the logical positivists. I regard metaphysics as extremely speculative attempts at explanation. |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| Full Idea: For me, although the enterprise of philosophical analysis is driven by natural language, its goal is not a linguistic analysis of English but rather an expressively strong framework that may at best be seen as a revision of English. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 12) | |
| A reaction: I agree, but the problem is that there are different ideals for the revision, which may be in conflict. Logicians, mathematicians, metaphysicians, scientists, moralists and aestheticians are queueing up to improve in their own way. |
| 5434 | Philosophy is similar to science, and has no special source of wisdom [Russell] |
| Full Idea: Philosophical knowledge does not differ essentially from scientific knowledge; there is no special source of wisdom which is open to philosophy but not to science. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.14) | |
| A reaction: I agree. I take Plato's Theory of Forms, for example, to be a scientific theory, for which no one can devise an empirical test (just like string theory). Personally I consider philosophy to be the senior partner, and regard scientists as servants. |
| 5396 | Three Laws of Thought: identity, contradiction, and excluded middle [Russell] |
| Full Idea: For no very good reason, three principles have been singled out by tradition under the name of 'Laws of Thought': the laws of identity ('what is, is'), contradiction ('never be and not be'), and excluded middle ('always be or not be'). | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: 'For no very good reason' seems a bit unfair, probably to medieval logicians, who deserve more respect. Russell suggests that the concept of implication deserves to be on the list. Presumably optimism about thinking is a presupposition of thought. |
| 5405 | The law of contradiction is not a 'law of thought', but a belief about things [Russell] |
| Full Idea: The law of contradiction is not a 'law of thought' ..because it is a belief about things, not only about thoughts. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: The principle is a commitment about things, but it is inconceivable that any experience, no matter how weird, could ever contradict it. It would be better to assume that we had gone insane, than that a contradiction had occurred in the world. |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| Full Idea: Something which is established in the centre and has equality in relation to the extremes has no more reason to move up than it has down or to the sides (so the earth is stationary) | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A26) by Aristotle - On the Heavens 295b11 |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| Full Idea: Explicit definitions allow for a complete elimination of the defined notion (at least in extensional contexts). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: If the context isn't extensional (concerning the things themselves) then we could define one description of it, but be unable to eliminate it under another description. Elimination is no the aim of an Aristotelian definition. Halbach refers to truth. |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| Full Idea: Arguments from analogy are to be distrusted: at best they can serve as heuristics. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) |
| 5420 | Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell] |
| Full Idea: Although truth and falsehood are properties of beliefs, they are properties dependent upon the relations of the beliefs to other things, not upon any internal quality of the beliefs. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Beliefs can have an intrinsic property of subjective certainty, but Russell is right that that is not enough. So is truth a property or a relation? |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| Full Idea: Truth-value 'gluts' correspond to a so-called dialethic conception of truth; excluding gluts and admitting only 'gaps' leads to a conception of what is usually called 'partial' truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.2) | |
| A reaction: Talk of 'gaps' and 'gluts' seem to be the neatest way of categorising views of truth. I want a theory with no gaps or gluts. |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| Full Idea: Two typed disquotation sentences, truth axioms of TB, suffice for proving that there at least two objects. Hence truth is not a logical notion if one expects logical notions to be ontologically neutral. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) |
| 16324 | Any definition of truth requires a metalanguage [Halbach] |
| Full Idea: It is plain that the distinction between object and metalanguage is required for the definability of truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 11) | |
| A reaction: Halbach's axiomatic approach has given up on definability, and therefore it can seek to abandon the metalanguage and examine 'type-free' theories. |
| 16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
| Full Idea: A common complaint against traditional definitional theories of truth is that it is far from clear that the definiens is not more in need of clarification than the definiendum (that is, the notion of truth). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: He refers to concepts like 'correspondence', 'facts', 'coherence' or 'utility', which are said to be trickier to understand than 'true'. I suspect that philosophers like Halbach confuse 'clear' with 'precise'. Coherence is quite clear, but imprecise. |
| 16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
| Full Idea: If one were wondering whether truth should be considered a legitimate notion at all, a definition might be useful in dispersing doubts about its legitimacy. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
| A reaction: Halbach is proposing to skip definitions, and try to give rules for using 'true' instead, but he doesn't rule out definitions. A definition of 'knowledge' or 'virtue' or 'democracy' might equally give those credibility. |
| 5419 | Truth and falsehood are properties of beliefs and statements [Russell] |
| Full Idea: Truth and falsehood are properties of beliefs and statements, so a world of mere matter would contain no truth or falsehood. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Can it be beliefs AND statements? What about propositions? All that matters here is to establish that truth is a feature of certain mental states. This makes possible my slogan that "the brain is a truth-machine". Out there are the 'facts'. |
| 5417 | A good theory of truth must make falsehood possible [Russell] |
| Full Idea: A good theory of truth must be such as to admit of its opposite, falsehood. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) |
| 7395 | Truth as congruence may work for complex beliefs, but not for simple beliefs about existence [Joslin on Russell] |
| Full Idea: If truth is congruence between a complex belief and a complex relation between objects in the world, this may work for Othello's belief about Desdemona, but it doesn't seem to work for the simple belief that an object exists. | |
| From: comment on Bertrand Russell (Problems of Philosophy [1912], Ch.12) by Jack Joslin - talk | |
| A reaction: Though Russell has an interesting and persuasive theory, this seems like a big problem. To have a complex belief about a complex of objects, you must first have beliefs about the objects (and that can't be acquaintance, because error is possible). |
| 5428 | Beliefs are true if they have corresponding facts, and false if they don't [Russell] |
| Full Idea: A belief is true when there is a corresponding fact, and is false when there is no corresponding fact. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Russell tries to explain a 'fact' as a complex unity of constituents with a certain order among them. There is an obvious problem that some of the 'orders' in the world are imposed on it by the mind. But we don't invent 'D's love for C'. |
| 5421 | The coherence theory says falsehood is failure to cohere, and truth is fitting into a complete system of Truth [Russell] |
| Full Idea: The coherence theory of truth says falsehood is a failure to cohere in the body of our beliefs, and that it is the essence of a truth to form part of the completely rounded system which is The Truth. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: One could embrace the idea of coherence without accepting the extravagant ninenteenth century Idealists' dream of an ultimate complete Truth (or Absolute). The theory needs a decent account of coherence to get off the ground. |
| 5422 | More than one coherent body of beliefs seems possible [Russell] |
| Full Idea: There is no reason to suppose that only one coherent body of beliefs is possible. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Presumably this possibility would not be accepted for the ultimate ideal body of beliefs, but it seems undeniable that limited humanity will be stuck with several coherent possibilities. Coherence, though, is within our grasp, unlike correspondence. |
| 5423 | If we suspend the law of contradiction, nothing will appear to be incoherent [Russell] |
| Full Idea: If the law of contradiction itself were subjected to the test of coherence, we should find that, if we choose to suppose it false, nothing will any longer be incoherent with anything else. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Russell is in error in treating coherence as if it was merely non-contradiction. If I see you as four feet tall today and six feet tall tomorrow, that is incoherent (to me) but not an actual contradiction. All accounts of truth need presuppositions. |
| 5424 | Coherence is not the meaning of truth, but an important test for truth [Russell] |
| Full Idea: Coherence cannot be accepted as the meaning of truth, though it is often a most important test of truth after a certain amount of truth has become known. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: The coherence theory is in fact a confusion of epistemology and ontology. Compare Idea 1364, where Reid charges Locke with confusing the test for personal identity with the thing itself. I wonder if refusal to accept essences causes this problem? |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| Full Idea: In semantic theories (e.g.Tarski's or Kripke's), a definition evades Tarski's Theorem by restricting the possible instances in the schema T[φ]↔φ to sentences of a proper sublanguage of the language formulating the equivalences. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: The schema says if it's true it's affirmable, and if it's affirmable it's true. The Liar Paradox is a key reason for imposing this restriction. |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| Full Idea: The problem of restricted deductive power has haunted disquotational theories of truth (…because they can't prove generalisations). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.5) |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| Full Idea: Choosing an axiomatic approach to truth might well be compatible with the view that truth is definable; the definability of truth is just not presupposed at the outset. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: Is it possible that a successful axiomatisation is a successful definition? |
| 16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
| Full Idea: Revision semantics is arguably the main competitor of Kripke's theory of truth among semantic truth theories. …In the former one may hope through revision to arrive at better and better models, ..sorting out unsuitable extensions of the truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 14) | |
| A reaction: Halbach notes later that Kripke's theory (believe it or not) is considerably simpler than revision semantics. |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| Full Idea: If the clauses of Tarski's definition of truth are turned into axioms (as Davidson proposed) then a primitive binary predicate symbol for satisfaction is needed, as Tarski defined truth in terms of satisfaction. Standard language has a unary predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.2) |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
| Full Idea: In the typed Compositional Truth theory CT, it is compositional because the truth of a sentence depends on the semantic values of the constituents of that sentence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) | |
| A reaction: [axioms on p. 65 of Halbach] |
| 16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
| Full Idea: Often syntactic objects are identified with their numerical codes. …Expressions of a countable formal language can be coded in the natural numbers. This allows a theory of truth to use Peano Arithmetic (with its results) as a base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
| A reaction: The numbering system is the famous device invented by Gödel for his great proof of incompleteness. This idea is a key to understanding modern analytic philosophy. It is the bridge which means philosophical theories can be treated mathematically. |
| 16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
| Full Idea: Considering the truth axioms in the absence of a base theory is not very sensible because characteristically truth theoretic reasoning arises from the interplay of the truth axioms with the base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) | |
| A reaction: The base theory usually seems to be either Peano arithmetic or set theory. We might say that introverted thought (e.g. in infants) has little use for truth; it is when you think about the world that truth becomes a worry. |
| 16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
| Full Idea: In the light of incompleteness phenomena, one should not expect a categorical axiomatisation of truth to be feasible, but this should not keep one from studying axiomatic theories of truth (or of arithmetic). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
| A reaction: This, of course, is because of Gödel's famous results. It is important to be aware in this field that there cannot be a dream of a final theory, so we are just seeing what can be learned about truth. |
| 16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
| Full Idea: A truth theory is 'conservative' if the addition of the truth predicate does not add any new theorems to the base theory. | |
| From: report of Volker Halbach (Axiomatic Theories of Truth [2011], 6 Df 6.6) by PG - Db (ideas) | |
| A reaction: Halbach presents the definition more formally, and this is my attempt at getting it into plain English. Halbach uses Peano Arithmetic as his base theory, but set theory is also sometimes used. |
| 16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
| Full Idea: The truth theory TB (Tarski Biconditional) is all the axioms of Peano Arithmetic, including all instances of the induction schema with the truth predicate, plus all the sentences of the form T[φ] ↔ φ. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
| A reaction: The biconditional formula is the famous 'snow is white' iff snow is white. The truth of the named sentence is equivalent to asserting the sentence. This is a typed theory of truth, and it is conservative over PA. |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| Full Idea: I sort theories of truth into the large families of 'typed' and 'type-free'. Roughly, typed theories prohibit a truth predicate's application to sentences with occurrences of that predicate, and one cannot prove the truth of sentences containing 'true'. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], II Intro) | |
| A reaction: The problem sentence the typed theories are terrified of is the Liar Sentence. Typing produces a hierarchy of languages, referring down to the languages below them. |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| Full Idea: Compositional Truth CT proves the consistency of Peano arithmetic, which is not provable in Peano arithmetic by Gödel's second incompleteness theorem. Hence the theory CT is not conservative over Peano arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.6) |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| Full Idea: The Friedman-Sheard truth system FS is based on compositional theory CT. The axioms of FS are obtained by relaxing the type restriction on the CT-axioms, and adding rules inferring sentences from their truth, and vice versa. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15) | |
| A reaction: The rules are called NEC and CONEC by Halbach. The system FSN is FS without the two rules. |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| Full Idea: The Kripke-Feferman theory KF is an axiomatisation of the fixed points of an operator, that is, of a Kripkean fixed-point semantics with the Strong Kleene evaluation schema with truth-value gluts. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.1) |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| Full Idea: The Kripke-Feferman theory is relatively deductively very strong. In particular, it is much stronger than its competitor FS, which is based on a completely classical notion of truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.3) |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| Full Idea: KF is useful for explicating Peano arithmetic, but it certainly does not come to close to being a theory that contains its own truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16) | |
| A reaction: Since it is a type-free theory, its main philosophical aspiration was to contain its own truth predicate, so that is bad news (for philosophers). |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| Full Idea: Some authors have tried to understand the deflationist claim that truth is not a substantial notion as the claim that a satisfactory axiomatisation of truth should be conservative over the base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| Full Idea: There are two doctrines at the core of deflationism. The first says truth is a device of disquotation used to express generalisations, and the second says truth is a thin notion that contributes nothing to our knowledge of the world | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21) |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| Full Idea: The main criticism that deflationist theories based on the disquotation sentences or similar axioms have to meet was raised by Tarski: the disquotation sentences do not allow one to prove generalisations. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| Full Idea: Deflationists do not hold that truth is completely dispensable. They claim that truth serves the purpose of expressing infinite conjunctions or generalisations. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
| A reaction: It is also of obvious value as a shorthand in ordinary conversation, but rigorous accounts can paraphrase that out. 'What he said is true'. 'Pick out the true sentences from p,q,r and s' seems to mean 'affirm some of them'. What does 'affirm' mean? |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| Full Idea: Compositional Truth CT and its variants has desirable generalisations among its logical consequences, so they seem to have ousted purely disquotational theories such as TB in the discussion on deflationism. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
| 5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
| Full Idea: We would do better to go straight from the evidence that some men have died to the mortality of Socrates, than to go via 'all men are mortal', for the probability that Socrates is mortal is greater than the probability that all men are mortal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Russell claims that deduction should stick to a priori truth, and induction is best for the real world. Interesting. To show that something is a member of a set (e.g. planets) you need an awful lot of knowledge of the set. |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| Full Idea: In Strong Kleene logic a disjunction of two sentences is true if at least one disjunct is true, even when the other disjunct lacks a truth value. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 18) | |
| A reaction: This sounds fine to me. 'Either I'm typing this or Homer had blue eyes' comes out true in any sensible system. |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
| Full Idea: In Weak Kleene Logic, with truth-value gaps, a sentence is neither true nor false if one of its components lacks a truth value. A line of the truth table shows a gap if there is a gap anywhere in the line, and the other lines are classical. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 18) | |
| A reaction: This will presumably apply even if the connective is 'or', so a disjunction won't be true, even if one disjunct is true, when the other disjunct is unknown. 'Either 2+2=4 or Lot's wife was left-handed' sounds true to me. Odd. |
| 16309 | Every attempt at formal rigour uses some set theory [Halbach] |
| Full Idea: Almost any subject with any formal rigour employs some set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4.1) | |
| A reaction: This is partly because mathematics is often seen as founded in set theory, and formal rigour tends to be mathematical in character. |
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| Full Idea: The costs of giving up classical logic are easily underestimated, …the price being paid in terms of mathematical reasoning. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16.2) | |
| A reaction: No one cares much about such costs, until you say they are 'mathematical'. Presumably this is a message to Graham Priest and his pals. |
| 5395 | Demonstration always relies on the rule that anything implied by a truth is true [Russell] |
| Full Idea: All demonstrations involve the principle that 'anything implied by a true proposition is true', or 'whatever follows from a true proposition is true'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: This is modus ponens, a broad principle of rationality, rather than of strict logicality, because it covers practical inferences and vague propositions. Presumably truth is a prior concept to implication, and therefore more metaphysically basic. |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| Full Idea: A theory is a set of formulae closed under first-order logical consequence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.1) |
| 5386 | Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell] |
| Full Idea: Common words, even proper names, are usually really descriptions; that is, the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This is open to challenge, and the modern idea is that they are more like baptisms, but it all comes down to the debate about internal and external content. Russell would appear to be voicing the internalist theory of names. |
| 5385 | The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell] |
| Full Idea: A phrase of the form 'a so-and-so' I shall call an 'ambiguous' description, and a phrase of the form 'the so-and-so' (in the singular) I shall call a 'definite' description. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This leaves the problem of those definite descriptions which succeed in referring ('the present Prime Minister'), those which haven't succeeded yet ('the person who will get the most votes'), and those which won't refer ('the present King of France'). |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| Full Idea: One cannot just accept that all the theorems of Peano arithmetic are true when one accepts Peano arithmetic as the notion of truth is not available in the language of arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: This is given as the reason why Kreisel and Levy (1968) introduced 'reflection principles', which allow you to assert whatever has been proved (with no mention of truth). (I think. The waters are closing over my head). |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| Full Idea: If one endorses a theory, so one might argue, one should also take it to be sound. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| Full Idea: Soundness seems to be a notion essentially involving truth. At least I do not know how to fully express the soundness of Peano arithmetic without invoking a truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: I suppose you could use some alternative locution such as 'assertible' or 'cuddly'. Intuitionists seem a bit vague about the truth end of things. |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| Full Idea: Paradoxes that arise from interaction of predicates such as truth, necessity, knowledge, future and past truths have receive little attention. There may be many unknown paradoxes lurking when we develop frameworks with these intensional notions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: Nice. This is a wonderful pointer to new research in the analytic tradition, in which formal problems will gradually iron out our metaphysical framework. |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| Full Idea: An essential feature of the liar paradox is the application of the truth predicate to a sentence with a negated occurrence of the truth predicate, though the negation can be avoided by using the conditional. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.3) |
| 16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
| Full Idea: Nonstandard models of Peano arithmetic are models of PA that are not isomorphic to the standard model. Their existence can be established with the compactness theorem or the adequacy theorem of first-order logic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.3) |
| 16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
| Full Idea: The global reflection principle ∀x(Sent(x) ∧ Bew[PA](x) → Tx) …seems to be the full statement of the soundness claim for Peano arithmetic, as it expresses that all theorems of Peano arithmetic are true. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: That is, an extra principle must be introduced to express the soundness. PA is, of course, not complete. |
| 16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
| Full Idea: For the reduction of Peano Arithmetic to ZF set theory, usually the set of finite von Neumann ordinals is used to represent the non-negative integers. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 6) | |
| A reaction: Halbach makes it clear that this is just one mode of reduction, relative interpretability. |
| 5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
| Full Idea: If induction was the source of our mathematical knowledge, we should proceed differently. In fact, a certain number of instances make us think of two abstractly, and we then see the general principle, and further instances become unnecessary. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: In practice, of course, we stop checking whether the sun has come up yet again this morning. Russell's point is better expressed as: if contradictory evidence were observed, we would believe the arithmetic and doubt the experience. |
| 16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
| Full Idea: While set theory was liberated much earlier from type restrictions, interest in type-free theories of truth only developed more recently. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) | |
| A reaction: Tarski's theory of truth involves types (or hierarchies). |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| Full Idea: Anaximander discovers the contradictory character of our world: it perishes from its own qualities. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Friedrich Nietzsche - Unpublished Notebooks 1872-74 19 [239] | |
| A reaction: A lovely gloss on Anaximander, though I am not sure that I understand what Nietzsche means. |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| Full Idea: The observation that Peano arithmetic is relatively interpretable in ZF set theory is taken by many philosophers to be a reduction of numbers to sets. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 23) | |
| A reaction: Nice! Being able to express something in a different language is not the same as a reduction. Back to the drawing board. What do you really mean by a reduction? If we model something, we don't 'reduce' it to the model. |
| 5370 | Space is neutral between touch and sight, so it cannot really be either of them [Russell] |
| Full Idea: The space of science is neutral as between touch and sight; thus it cannot be either the space of touch or the space of sight. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: I find this persuasive, although it is hardly a knock-down argument. It is a very simple problem for anti-realists, that if you say reality IS sensations (ŕ la Berkeley), then you have conflicting sensations of what seems to be one reality. |
| 5418 | In a world of mere matter there might be 'facts', but no truths [Russell] |
| Full Idea: If we imagine a world of mere matter, there would be no room for falsehood, and although it would contain what may be called 'facts', it would not contain any truths. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Only a realist will buy a concept of mind-independent 'facts', but I am with Russell all the way here. We should not say "the truth is out there", but "the facts are out there". Facts are the target of thought, and truth is a relationship to the facts. |
| 5371 | Because we depend on correspondence, we know relations better than we know the items that relate [Russell] |
| Full Idea: We can know the properties of the relations required to preserve the correspondence between sense-data and reality, but we cannot know the nature of the terms between which the relations hold. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: Thus Russell always puts great emphasis on relations in his metaphysics. I would say that he is right, and that what he calls the 'nature of the terms' are essences, and that these are knowable, by inference and explanation. |
| 5407 | That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell] |
| Full Idea: Nothing mental is presupposed in the fact that Edinburgh is north of London, but this involves the universal 'north of', so we must admit that relations are not dependent upon thought, but belong to the independent world which thought apprehends. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: We cannot deny that Edinburgh being north of London is independent of our minds, but we might deny that 'north of' is a universal. 'North' is clearly a human convention, but 'nearer a pole' isn't. Distances exist in space, rather than as relations. |
| 5383 | Every complete sentence must contain at least one word (a verb) which stands for a universal [Russell] |
| Full Idea: Every complete sentence must contain at least one word which stands for a universal, since all verbs have a meaning which is universal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Not all meaningful statements are sentences. One could try a programme of eliminating from discourse all words which imply universals. Daily physical life would survive all right, but universities would close down. |
| 4428 | Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives) [Russell] |
| Full Idea: In general, adjectives and nouns express properties of things, whereas prepositions and verbs express relations between things, so neglect of the latter led to the belief that every proposition attributes properties rather than relations. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: A simple point on which Russell was very keen to insist, and which seems right. It invites the question whether there are further universals, beyond properties and relations. |
| 5406 | Confused views of reality result from thinking that only nouns and adjectives represent universals [Russell] |
| Full Idea: The monism of Spinoza and Bradley, and the monadism of Leibniz, result, in my opinion, from an undue attention to one sort of universals, namely the sort represented by adjectives and substantives rather than by verbs and prepositions. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: The 'linguistic turn' of 20th century philosophy, which should be treated with caution, but I agree that if we are going to accept universals, we need a wide vision of what categories they might fall into. I would prefer an ontology without 'relations'. |
| 4479 | All universals are like the relation "is north of", in having no physical location at all [Russell, by Loux] |
| Full Idea: Russell denies that universals have any location at all. ..He is generalising from the case of "is north of", which does not exist any more in Edinburgh than in London. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch. 9) by Michael J. Loux - Metaphysics: contemporary introduction p.55 | |
| A reaction: Russell may claim that the relation "is north of" is natural, but I suspect that it is a convention, mapped onto a physical situation. Reifying relations invite charges of a regress (as Bradley noted). |
| 4427 | Every sentence contains at least one word denoting a universal, so we need universals to know truth [Russell] |
| Full Idea: No sentence can be made up without at least one word which denotes a universal. ..Thus all truths involve universals, and all knowledge of truths involves acquaintance with universals. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Sounds right, and is a beautifully neat way of showing the connection between metaphysics and life. |
| 4030 | Russell claims that universals are needed to explain a priori knowledge (as their relations) [Russell, by Mellor/Oliver] |
| Full Idea: Russell's positive argument for universals is that they explain how we can have a priori knowledge, which 'deals exclusively with the relations of universals'. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch. 9) by DH Mellor / A Oliver - Introduction to 'Properties' §3 | |
| A reaction: Unfortunately we can invent the universals, and then delude ourselves that we have a priori knowledge |
| 5409 | Normal existence is in time, so we must say that universals 'subsist' [Russell] |
| Full Idea: We think of things existing when they are in time (though possibly at all times), but universals do not exist in this sense, so we shall say that they 'subsist' or 'have being'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Russell picked up the word 'subsist' from medieval philosophy. This idea brings the full Platonic metaphysics with it, which is tricky, to say the least. But what can you do? Admitting the content of thought brings baggage with it. |
| 5408 | If we identify whiteness with a thought, we can never think of it twice; whiteness is the object of a thought [Russell] |
| Full Idea: If whiteness were the thought as opposed to its object no two different men could think of it, and no one man could think of it twice. What many different thoughts of whiteness have in common is their object, and this object is different from all of them. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: This seems to me a powerful argument in favour of thinking of universals as in some sense real - but in what sense? The crux is that Russell shows that we must find a place in our ontology for the content of thoughts, as well as of thoughts. |
| 4441 | 'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal [Russell] |
| Full Idea: To be a universal, a resemblance must hold between many pairs of white things. We can't say there is a different resemblance between each pair, since the resemblances must resemble each other, so we are forced to admit that resemblance is a universal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Apparently this objection is much discussed and controversial. It looks like a threat to any theory of universals (involving 'sets', or 'concepts', or 'predicates'). We seem to need 'basic' and 'derivative' universals. Cf Idea 7956. |
| 4429 | If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell] |
| Full Idea: If we come to regard an 'idea' like whiteness as an act of thought, then we come to think of whiteness as mental, but in doing so we rob it of its essential quality of universality. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: Presumably we need an ontological commitment to the existence of universals, which is very Platonic. Fatherhood might be a better example, since whiteness is a quale. |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| Full Idea: Should necessity be treated as a predicate rather than (as in modal logic) as a sentential operator? It is odd to assign different status to necessity and truth, hampering their interaction. That all necessities are true can't be expressed by an operator. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: [compressed] Halbach and Horsten consistently treat truth as a predicate, but maybe truth is an operator. Making necessity a predicate and not an operator would be a huge upheaval in the world of modal logic. Nice move! |
| 5400 | In any possible world we feel that two and two would be four [Russell] |
| Full Idea: In any possible world we feel that two and two would be four. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Thinking of necessity in terms of possible worlds is not a new invention, but then Russell was a keen fan of Leibniz. Suppose there were no world at all, and only one truth, namely that two and two make five? (No, I can't make sense of that!) |
| 5431 | Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell] |
| Full Idea: 'Knowledge' is not a precise conception: it merges into 'probable opinion', and so a very precise definition should not be sought. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.13) | |
| A reaction: This announcement comes as a relief, after endless attempts (mainly by American academics) to give watertight, carefully worded definitions. It seems to me undeniable that what we will accept as knowledge is partly a matter of social negotiation. |
| 5426 | Belief relates a mind to several things other than itself [Russell] |
| Full Idea: A belief or judgement relates a mind to several things other than itself. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: Presumably we must say that if I believe that (say) 'x exists', this is relating x to the universal 'exists'. If so, Russell's point becomes a bit of a tautology. We believe propositions, which are combinations of concepts, so are multiple. |
| 5366 | We have an 'instinctive' belief in the external world, prior to all reflection [Russell] |
| Full Idea: We find a belief in an independent external world ready in ourselves as soon as we begin to reflect: it is what may be called an 'instinctive' belief. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: Somewhere Hume calls this a 'natural belief', and it is fairly central to his idea that most of our beliefs are built up fairly mechanically by associations. I am tempted to ask whether such things even count as beliefs, if they are so uncritical. |
| 5359 | Descartes showed that subjective things are the most certain [Russell] |
| Full Idea: By showing that subjective things are the most certain, Descartes performed a great service to philosophy. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This praise comes from an empiricist, who has just said that 'sense-data' are the most certain things. I presume that animals are more certain of the world than they are of subjective things. In fact, probably on philosophers agree with Russell. |
| 5377 | 'Acquaintance' is direct awareness, without inferences or judgements [Russell] |
| Full Idea: We shall say we have 'acquaintance' with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Although Russell understands the difficulty of precise distinctions here, he implies that some knowledge is directly knowable, although truth only enters at the stage of judgement. Personally I would suggest that pure acquaintance is not knowledge. |
| 6510 | Russell (1912) said phenomena only resemble reality in abstract structure [Russell, by Robinson,H] |
| Full Idea: Russell held in 'Problems of Philosophy' that the physical world resembles the phenomenal only in abstract structure. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by Howard Robinson - Perception VII.5 | |
| A reaction: Russell's problem is that he then requires full-blown and elaborate 'inferences' to get from the abstract structure to some sort of 'theory' of reality, but our experience seems much more direct, even if it isn't actually 'naďve'. |
| 5372 | There is no reason to think that objects have colours [Russell] |
| Full Idea: It is quite gratuitous to suppose that physical objects have colours. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: This has always seemed to me self-evident, from the day I started to study philosophy. I cannot make sense of serious attempts to defend direct (naďve) realism. Colour is a brilliant trick of natural selection for extracting environmental information. |
| 5373 | 'Idealism' says that everything which exists is in some sense mental [Russell] |
| Full Idea: We shall understand 'idealism' to be the doctrine that whatever exists, or at any rate whatever can be known to exist, must be in some sense mental. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 4) | |
| A reaction: The interesting thing here is the phrase 'in some sense', which takes on a new light when we begin once against to take seriously ideas such as panpsychism. If the boundary between mind and brain is blurred, so is that between realism and idealism. |
| 5362 | It is not illogical to think that only myself and my mental events exist [Russell] |
| Full Idea: No logical absurdity results from the hypothesis that the world consists of myself and my thoughts and feelings and sensations, and that everything else is mere fancy. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: The only real attempt to meet this challenge is Wittgenstein's Private Language Argument, which tried to show that it would be a logical impossibility to speak a language if there were no other minds. Personally, I am with Russell. |
| 5412 | Some propositions are self-evident, but their implications may also be self-evident [Russell] |
| Full Idea: When a certain number of logical principles have been admitted as self-evident, the rest can be deduced from them; but the propositions deduced are often just as self-evident as those that were assumed without proof. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This seems an important corrective to the traditional rationalist dream, based on Euclid, that all knowledge is self-evident axioms followed by proofs of the rest. But Russell here endorses a more sensible sort of rationalism. |
| 5413 | Particular instances are more clearly self-evident than any general principles [Russell] |
| Full Idea: Particular instances are more self-evident than general principles; for example, the law of contradiction is evident as soon as it is understood, but it is not as evident as that a particular rose cannot be both red and not red. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This seems to true about nearly all reasoning, because whenever we are faced with a general principle for assessment, we check it by testing it against a series of particular instances, and try to think of contradictory particular counterexamples. |
| 5415 | As shown by memory, self-evidence comes in degrees [Russell] |
| Full Idea: It is clear from the case of memory that self-evidence has degrees, and is present in gradations ranging from absolute certainty down to an almost imperceptible faintness. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: I am beginning to see Russell as the 'father of modern rationalism'. His relaxation of notions of an all-or-nothing a priori, and of a sharp distinction between axioms and proofs, lead to a sensible rationalism which even a Humean sceptic might buy. |
| 5416 | If self-evidence has degrees, we should accept the more self-evident as correct [Russell] |
| Full Idea: If propositions can have some degree of self-evidence without being true, we must say, where there is a conflict, that the more self-evident proposition is to be retained and the less self-evident rejected. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This is a key part of Russell's 'moderate rationalism'. Presumably the rejected propositions were therefore not self-evident, and can be used as training for intuitions, by seeing why we got it wrong. Fools find absurd falsehoods self-evidently true. |
| 5397 | The rationalists were right, because we know logical principles without experience [Russell] |
| Full Idea: In the most important point of the controversy between empiricists and rationalist, the rationalists were right, since logical principles are known to us, but cannot be proved by experience, since all proof presupposes them | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Russell initially presents this as the answer to 'innate ideas'. I would prefer to say, in the style of Descartes, that logic is self-evident to the natural light of reason. The debate isn't over. A Turing machine may be able to do logic. |
| 4430 | All a priori knowledge deals with the relations of universals [Russell] |
| Full Idea: All a priori knowledge deals with the relations of universals. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.10) | |
| A reaction: A nice bold proposition, and remarkably Platonic for a famous empiricist. But then a priori knowledge of particulars sounds unlikely. |
| 5411 | We can know some general propositions by universals, when no instance can be given [Russell] |
| Full Idea: The general proposition 'All products of two integers, which never have been and never will be thought of by any human being, are over 100' is undeniably true, and yet we can never give an instance of it; ..only a knowledge of the universals is required. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.10) | |
| A reaction: A nice example which it seems to be impossible to contradict. But maybe we can explain our knowledge of it in terms of rules, instead of mentioning universals. Can a rule be stated without recourse to universals? Sounds unlikely. |
| 6514 | Russell's representationalism says primary qualities only show the structure of reality [Russell, by Robinson,H] |
| Full Idea: The weakest version of representationalism, found in Russell, asserts that there is no resemblance to reality on the level of secondary qualities, and also that primary qualities exhibit only a structural isomorphism. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by Howard Robinson - Perception IX.2 | |
| A reaction: This seems a plausible thing to say about, say, shape, but it is not clear how the idea works for hardness or mass. The sense of touch seems to be much more directly in contact with actual primary qualities than visions does (let alone smell or hearing). |
| 6415 | After 1912, Russell said sense-data are last in analysis, not first in experience [Russell, by Grayling] |
| Full Idea: During the decade after 'Problems of Philosophy' Russell points our repeatedly that specifications of sense-data come last in analysis, not first in experience. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: This was a symptom of Russell losing faith in sense-data, and he eventually abandoned them. There is a possible position where we deny any such item as sense-data in a scientific account, but allow them in our metaphysics. |
| 5358 | 'Sense-data' are what are immediately known in sensation, such as colours or roughnesses [Russell] |
| Full Idea: Let us give the name 'sense-data' to the things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 1) | |
| A reaction: This idea gradually became notorious, because it seems to create a new ontological category unnecessarily, and it creates problems, such as how the intermediary interacts with us and with things. Are sense-data totally non-conceptual? |
| 7290 | If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Russell, by Thompson] |
| Full Idea: If Russell rejects innate ideas, and he even thinks the laws of thought must by triggered by experiences (e.g. of a beech tree), and he doesn't embrace associations, this implies that he thinks the mind begins as a tabula rasa. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by George Thompson - talk | |
| A reaction: This nice observation places Russell as (in my view) a rather old-fashioned empiricist, who ignores Hume and Kant, and is not willing to speculate about how the mind can turn acquaintances with sense-data into knowledge |
| 5357 | It is natural to begin from experience, and presumably that is the basis of knowledge [Russell] |
| Full Idea: In the search for certainty, it is natural to begin with our present experiences, and in some sense, no doubt, knowledge is to be derived from them. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 1) | |
| A reaction: Is experience the 'natural' place to begin? It didn't seem to strike Descartes that way. It seems better to say that philosophy begins when we are not quite satisfied with experience, and the natural place to begin is 'dissatisfaction'. |
| 5382 | We are acquainted with outer and inner sensation, memory, Self, and universals [Russell, by PG] |
| Full Idea: We have acquaintance with outer senses, with inner sense (by introspection), with memory (of outer or inner sensations), with a Self (probably), and also with universals (general ideas). | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch. 5) by PG - Db (ideas) | |
| A reaction: The spectacular odd one out in a basic empiricist theory is, of course, universals, when one expects some sort of nominalist reduction of those into sense-data. I am very sympathetic to the Russell line, though it spells big ontological trouble. |
| 5389 | Knowledge by descriptions enables us to transcend private experience [Russell] |
| Full Idea: The chief importance of knowledge by descriptions is that it enables us to pass beyond the limits of our private experience. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: The most basic question for empiricism concerns how we can know things beyond immediate experience. Russell is right, though this doesn't tell us much. We need to know the rules for valid descriptions, explanation, speculations etc. |
| 5376 | I can know the existence of something with which nobody is acquainted [Russell] |
| Full Idea: There is no reason why I should not know of the existence of something with which nobody is acquainted. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 4) | |
| A reaction: This sort of realist claim (which he goes on to say results from inferences from descriptions) is needed to save empiricism from the absurdities of Berkeley and (dare I say it?) Quine. The Kantian Ego is a candidate. |
| 5414 | Images are not memory, because they are present, and memories are of the past [Russell] |
| Full Idea: An image cannot constitute a memory, because we notice that the image is in the present, whereas what is remembered is known to be in the past. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.11) | |
| A reaction: This sounds a bit glib, and maybe makes the mistake for which he criticises Berkeley, of confusing a thought and its content. The puzzle is how we know that some images represent the past, others the present, others predictions, and others fantasy. |
| 5430 | A true belief is not knowledge if it is reached by bad reasoning [Russell] |
| Full Idea: A true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning. If I know all Greeks are men, and Socrates was a man, I cannot know that Socrates was a Greek, even if I falsely infer it. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.13) | |
| A reaction: Another very nice 'Gettier' example, fifty years before Gettier. There is a danger of circularity here, between knowledge, fallacy and truth. Giving them three independent definitions does not look promising. |
| 5429 | True belief is not knowledge when it is deduced from false belief [Russell] |
| Full Idea: A true belief is not knowledge when it is deduced from a false belief (as when deducing that the late Prime Minister's name began with B, believing it was Balfour, when actually it was Bannerman). | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.13) | |
| A reaction: Correct me if I am wrong, but isn't this the 'Gettier Problem'? It raises the central question of modern epistemology, which is what will be counted as adequate justification to make a true belief qualify as knowledge. How high do we set the bar? |
| 5378 | All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell] |
| Full Idea: All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundations. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Russell here allies himself with Hume, and with the empiricist version of foundationalism. 'Acquaintance' plays the role which 'impressions' played for Hume. He is eliminating any possible cognitive content from the Hume idea, implying pure sense-data. |
| 5365 | Dreams can be explained fairly scientifically if we assume a physical world [Russell] |
| Full Idea: Dreams are more or less suggested by what we call waking life, and are capable of being more or less accounted for on scientific principles if we assume that there really is a physical world. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This sounds a bit circular, since scientific principles depend entirely on the assumption that there is a physical world. No doubt if we assume fairies, 'fairy lore' will explain everything. 'Explanation' is the basic concept here. |
| 5391 | Science aims to find uniformities to which (within the limits of experience) there are no exceptions [Russell] |
| Full Idea: The business of science is to find uniformities, such as the laws of motion and the law of gravitation, to which, so far as our experience extends, there are no exceptions. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This seems nicely stated, based on the Humean 'regularity' view of scientific laws. When we discover such uniformities (such as the gravitational equation), we are still faced with the metaphysical question of their status. Necessity, or pattern? |
| 5394 | We can't prove induction from experience without begging the question [Russell] |
| Full Idea: We can never use experience to prove the inductive principle without begging the question. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This highlights why induction is such a big problem for hard-line empiricists, who are reduced to saying that it is a 'dogma', or an unsupported 'natural belief'. And that seems right. All creatures which evolve in a stable universe will do induction. |
| 5390 | Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell] |
| Full Idea: The man who has fed his chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: A justly famous illustration of Hume's problem of induction, that a vast amount of evidence could still support a false conclusion. If we say 'the future will be like the past', this depends on understanding what was happening in the past. |
| 5392 | It doesn't follow that because the future has always resembled the past, that it always will [Russell] |
| Full Idea: We have experience of past futures, but not of future futures, and the question is: Will future futures resemble past futures? This question is not to be answered by an argument which starts from past futures alone. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This nicely makes the problem of induction unavoidable, for anyone who preferred not to face the problem. The simple solution is to recognise that the future may NOT resemble the past, for all we know. Actually I think it will, but what was the past like? |
| 5363 | If the cat reappears in a new position, presumably it has passed through the intermediate positions [Russell] |
| Full Idea: If the cat appears at one moment in one part of the room, and at another in another part, it is natural to suppose that it has moved from the one to the other, passing over a series of intermediate positions. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This example seems perfect as an illustration of inference to the best explanation (now called 'abduction'), and that seems to me the absolute key to human knowledge. The cat example is what made me a devotee of Bertrand Russell. |
| 5367 | Belief in real objects makes our account of experience simpler and more systematic [Russell] |
| Full Idea: The belief that there are objects corresponding to our sense-data tends to simplify and systematize our account of our experiences, so there seems no good reason for rejecting it. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This hardly counts as a good argument against the logical possibility of global scepticism, but it is a nice statement of the concept of 'best explanation', which obviously requires some sort of rational criteria if it is to provide a theory of knowledge. |
| 5364 | It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves [Russell] |
| Full Idea: When human beings speak, it is very difficult to suppose that what we hear is not the expression of a thought, as we know it would be if we emitted the same sounds. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 2) | |
| A reaction: This is partly the 'argument from analogy', which seems a bit suspect (induction from a single instance), but it is also the rather undeniable Humean idea that we have a 'natural belief' in other minds, which we could never disbelieve. |
| 5379 | If we didn't know our own minds by introspection, we couldn't know that other people have minds [Russell] |
| Full Idea: But for our acquaintance with the contents of our own minds, we should be unable to imagine the minds of others, and therefore we could never arrive at the knowledge that they have minds. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: Not only does this depend on the notorious 'argument from analogy', but it actually strikes me as false. If a robot observed a human to be writhing in pain, it would be mystified, until it inferred that we have minds in which we actually 'feel' damage. |
| 5410 | I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red [Russell] |
| Full Idea: If I see simultaneously two shades of green, I can see that they resemble each other, and I see that they resemble each other more than they resemble a shade of red; in this way I become acquainted with the universal 'resemblance'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.10) | |
| A reaction: This is strikingly different from the account of Hume, who seemed to regard resemblance as a fairly mechanical, computer-like activity of the brain, whereas Russell (an empiricist) responds by inclining towards Platonism. Hume sounds better here. |
| 5381 | In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell] |
| Full Idea: When I see the sun, it does not seem necessary to suppose that we are acquainted with a more or less permanent person, but we must be acquainted with that thing which sees the sun and has acquaintance with sense-data. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: I think this is exactly right. I personally believe that I have a very clear personal identity as I write this, but I do not believe that there is a strict identity with the person who wrote similar comments three years ago. So how do I change 'my' mind? |
| 5380 | In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell] |
| Full Idea: When I am acquainted with 'my seeing the sun', it seems plain that on the one hand there is the sense-datum which represents the sun to me, on the other hand there is that which sees this sense-datum. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This appears to flatly contradict Hume's scepticism about seeing his 'self', but maybe Russell is only aware of his body, and then fictionalises a 'self' as the controller of this body. But I agree with Russell. I am the thing that cares about the sun. |
| 5369 | It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell] |
| Full Idea: In the preceding chapter we agreed, though without being able to find demonstrative reasons, that it is rational to believe that our sense-data are signs of an independent reality. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: I wonder if Russell was the first to grasp this essential distinction. I suspect that three hundred years (1600-1900) were wasted in philosophy because they thought that everything rational had to be demonstrable. E.g. Hume on induction. |
| 5375 | Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things [Russell] |
| Full Idea: The word 'know' has two senses: the first is 'knowledge of truths', which is opposed to error, applies to judgements, and is knowing that something; the second is 'acquaintance', and is knowledge of things, particularly of sense-data. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 4) | |
| A reaction: We can also add procedural knowledge ('knowing how'). The question for Russell is whether his 'knowledge by acquaintance' can ever qualify as knowledge on its own, without the intrusion of judgements. Does perception necessarily have content? |
| 21711 | Russell's 'multiple relations' theory says beliefs attach to ingredients, not to propositions [Russell, by Linsky,B] |
| Full Idea: The basic idea of Russell's new 'multiple relations' theory of belief was that belief does not relate an individual to a proposition composed of various individuals and universals, but rather relates the believer directly to those constituents. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912], Ch.12) by Bernard Linsky - Russell's Metaphysical Logic 3.1 | |
| A reaction: Russell abandoned his commitment to propositions in 1908, and retained this new view until 1918. Wittgenstein gave Russell hell over this theory. This view made his 'congruence' account of the correspondence theory of truth possible. |
| 5427 | Truth is when a mental state corresponds to a complex unity of external constituents [Russell] |
| Full Idea: Judging or believing is a certain complex unity of which a mind is a constituent; if the remaining constituents, taken in the order which they have in the belief, form a complex unity, then the belief is true. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: The modern label of 'congruence' for this view of truth makes it clearer. We aim to get a complex unity of constituents in our minds which are in the same 'order' as the constituents in the world. It is a good proposal, but leaves 'facts' as a problem. |
| 5425 | In order to explain falsehood, a belief must involve several terms, not two [Russell] |
| Full Idea: The relation involved in judging or believing must, if falsehood is to be duly allowed for, be taken to be a relation between several terms, not between two. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch.12) | |
| A reaction: His point is that if a belief relates to one object ('D's love for C') it will always be true. Russell is trying to explain what goes wrong when we believe a falsehood. It is not clear how the judgement 'x exists' involves several terms. |
| 5384 | A universal of which we are aware is called a 'concept' [Russell] |
| Full Idea: A universal of which we are aware is called a 'concept'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: I am doubtful about this. Do children, and even animals, have a concept of 'my mother', without ever grasping the generalisation to 'his mother'? Is the word 'this' a non-universal concept? |
| 13468 | Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Russell, by Hart,WD] |
| Full Idea: Russell inadvertently started the philosophy of language by declaring that some sentences (like "Everything is identical with itself") that seem utterly in order are meaningless and express no proposition. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: The normal candidate for this honour would be Frege, with the sense/reference distinction, but this idea sounds right to me. Declaring that some sentences are 'meaningless' really gets people excited and interested. I like the example! |
| 5388 | Every understood proposition is composed of constituents with which we are acquainted [Russell] |
| Full Idea: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: This is somewhere between Hume and logical positivism, but it concerns understanding (not meaning) of propositions (not sentences), and its acquaintance can be of universals as well as of sense experience. I like Russell's version more than Ayer's. |
| 5387 | It is pure chance which descriptions in a person's mind make a name apply to an individual [Russell] |
| Full Idea: It is a matter of chance which characteristics of a man's appearance will come into a friend's mind when he thinks of Bismarck; thus the description in the friend's mind is accidental; he knows the various descriptions all apply to the same entity. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 5) | |
| A reaction: This seems to be an internalist account of reference, later called the 'bundle' theory of reference and associated with John Searle. It was attacked by Kripke. Personally I side, unfashionably, with Russell. |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| Full Idea: Being able to ascribe the same proposition as a belief to persons who do not have a common language seems to be one of the main reasons to employ propositions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
| A reaction: Propositions concern beliefs, as well as sentence meanings. I would want to say that a dog and I could believe the same thing, and that is a non-linguistic reason to believe in propositions. Maybe 'translation' cuts out the proposition middleman? |
| 21724 | The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B] |
| Full Idea: While the multiple relation theory (of belief, or of judgement) is nominally an account of belief and judgement, the emphasis in the account is on eliminating the need for propositions as objects of rational belief or judgement. | |
| From: report of Bertrand Russell (Problems of Philosophy [1912]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: The idea is that the mind relates directly with the ingredients of the proposition, and with the universals (such as relations) which connect them. He cuts out the middle man, just as he cut out sense-data, for similar reasons of economy. |
| 5398 | Judgements of usefulness depend on judgements of value [Russell] |
| Full Idea: All judgements as to what is useful depend upon some judgement as to what has value on its own account. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: This is a beautifully simple point to be made about utilitarianism. The notion that pleasure is the sole good is prior, and the first two sentences in Bentham totally beg that question. What is the value of pleasure? Is it wicked to turn down a pleasure? |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| Full Idea: The essential nature, whatever it is, of the non-limited is everlasting and ageless. | |
| From: Anaximander (fragments/reports [c.570 BCE], B2), quoted by (who?) - where? |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| Full Idea: Those thinkers are in error who postulate ...a single matter, for this cannot exist without some 'perceptible contrariety': this Boundless, which they identify with the 'original real', must be either light or heavy, either hot or cold. | |
| From: comment on Anaximander (fragments/reports [c.570 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 329a10 | |
| A reaction: A dubious objection, I would say. If there has to be a contrasting cold thing to any hot thing, what happens when the cold thing is removed? |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| Full Idea: The non-limited is the original material of existing things; their source is also that to which they return after destruction, according to necessity; they give justice and make reparation to each other for injustice, according to the arrangement of Time. | |
| From: Anaximander (fragments/reports [c.570 BCE], B1), quoted by Simplicius - On Aristotle's 'Physics' 24.13- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| Full Idea: Anaximander said that the first principle and element of existing things was the boundless; it was he who originally introduced this name for the first principle. | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A09) by Simplicius - On Aristotle's 'Physics' 9.24.14- | |
| A reaction: Simplicius is quoting Theophrastus |
| 5393 | We can't know that our laws are exceptionless, or even that there are any laws [Russell] |
| Full Idea: If some law which has no exceptions applies to a case, we can never be sure that we have discovered that law and not one to which there are exceptions; also the reign of law would seem to be itself only probable. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6) | |
| A reaction: None of this can be denied. In modern physics, several supposed laws have come up for question. Is the proton stable? Are the gravitational constant or the speed of light necessarily fixed? Russell is doing epistemology. How do we conceive the laws? |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |
| Full Idea: The parts of all things are susceptible to change, but the whole is unchangeable. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.An.2 |