71 ideas
| 6095 | The business of metaphysics is to describe the world [Russell] |
| Full Idea: It seems to me that the business of metaphysics is to describe the world. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §III) | |
| A reaction: At least he believed in metaphysics. Presumably he intends to describe the world in terms of its categories, rather than cataloguing every blade of grass. |
| 6106 | Reducing entities and premisses makes error less likely [Russell] |
| Full Idea: You diminish the risk of error with every diminution of entities and premisses. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VIII) | |
| A reaction: If there are actually lots of entities, you would increase error if you reduced them too much. Ockham's Razor seems more to do with the limited capacity of the human mind than with the simplicity or complexity of reality. See Idea 4456. |
| 16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
| Full Idea: Tarski's Theorem states that under fairly generally applicable conditions, the assumption that there is a definition of truth within a given theory for the language of that same theory leads to a contradiction. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1 | |
| A reaction: That might leave room for a definition outside the given theory. I take the main motivation for the axiomatic approach to be a desire to get a theory of truth within the given theory, where Tarski's Theorem says traditional approaches are just wrong. |
| 15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten] |
| Full Idea: Tarski's Theorem on the undefinability of truth says in a language sufficiently rich to talk about itself (which Gödel proved possible, via coding) the liar paradox can be carried out. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2 | |
| A reaction: The point is that truth is formally indefinable if it leads inescapably to contradiction, which the liar paradox does. This theorem is the motivation for all modern attempts to give a rigorous account of truth. |
| 19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski] |
| Full Idea: The possibility of a consistent use of 'true sentence' which is in harmony with the laws of logic and the spirit of everyday language seems to be very questionable, so the same doubt attaches to the possibility of constructing a correct definition. | |
| From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], §1) | |
| A reaction: This is often cited as Tarski having conclusively proved that 'true' cannot be defined from within a language, but his language here is much more circumspect. Modern critics say the claim depends entirely on classical logic. |
| 6090 | Facts make propositions true or false, and are expressed by whole sentences [Russell] |
| Full Idea: A fact is the kind of thing that makes a proposition true or false, …and it is the sort of thing that is expressed by a whole sentence, not by a single name like 'Socrates'. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §I) | |
| A reaction: It is important to note a point here which I consider vital - that Russell keeps the idea of a fact quite distinct from the language in which it is expressed. Facts are a 'sort of thing', of the kind which are now referred to as 'truth-makers'. |
| 18348 | Not only atomic truths, but also general and negative truths, have truth-makers [Russell, by Rami] |
| Full Idea: In 1918 Russell held that beside atomic truths, also general and negative truths have truth-makers. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Adolph Rami - Introduction: Truth and Truth-Making note 04 |
| 16296 | Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach] |
| Full Idea: Tarski's Theorem applies to any sufficient precise version of the correspondence theory of truth, and all the other traditional theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1 | |
| A reaction: This is the key reason why modern thinkers have largely dropped talk of the correspondence theory. See Idea 16295. |
| 10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack] |
| Full Idea: Tarskian semantics says that a sentence is true iff it is satisfied by every sequence, where a sequence is a set-theoretic individual, a set of ordered pairs each with a natural number as its first element and an object from the domain for its second. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Keith Hossack - Plurals and Complexes 3 |
| 15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten] |
| Full Idea: Tarski emancipated truth theory from traditional philosophy, by no longer posing Pilate's question (what is truth? or what is the essence of truth?) but instead 'how is truth used?', 'how does truth function?' and 'how can its functioning be described?'. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2 | |
| A reaction: Horsten, later in the book, does not give up on the essence of truth, and modern theorists are trying to get back to that question by following Tarski's formal route. Modern analytic philosophy at its best, it seems to me. |
| 16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach] |
| Full Idea: Tarski did not settle for a definition of truth, taking its adequacy for granted. Rather he proposed an adequacy criterion for evaluating the adequacy of definitions of truth. The criterion is his famous Convention T. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 | |
| A reaction: Convention T famously says the sentence is true if and only if a description of the sentence is equivalent to affirming the sentence. 'Snow is white' iff snow is white. |
| 19135 | Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski] |
| Full Idea: Tarski does not tell us how to apply his concept of truth to a new case, whether the new case is a new language or a word newly added to a language. This is because enumerating cases gives no clue for the next or general case. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: His account has been compared to a telephone directory. We aim to understand the essence of anything, so that we can fully know it, and explain and predict how it will behave. Either truth is primitive, or I demand to know its essence. |
| 19138 | Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski] |
| Full Idea: Tarski defined the class of true sentences by giving the extension of the truth predicate, but he did not give the meaning. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: This is analogous to giving an account of the predicate 'red' as the set of red objects. Since I regard that as a hopeless definition of 'red', I am inclined to think the same of Tarski's account of truth. It works in the logic, but so what? |
| 4699 | Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady] |
| Full Idea: Tarski's account doesn't hold for natural languages. The general notion of truth is replaced by "true-in-L", where L is a formal language. Hence truth is relativized to each artificial language. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Paul O'Grady - Relativism Ch.2 | |
| A reaction: This is a pretty good indication that Tarski's theory is NOT a correspondence theory, even if its structure may sometimes give that impression. |
| 19324 | Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski] |
| Full Idea: Tarski has to define truths so as not to make explicit the relation between a true sentence and an obtaining state of affairs. ...He has to list each sentence separately, and simply assign it a state of affairs. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.8 | |
| A reaction: He has to avoid semantic concepts like 'reference', because he wants a physicalist theory, according to Kirkham. Thus the hot interest in theories of reference in the 1970s/80s. And also attempts to give a physicalist account of meaning. |
| 15410 | Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski] |
| Full Idea: In Tarski's theory of truth, although the notion of truth is applicable only to closed formulas, to define it we must define a more general notion of satisfaction applicable to open formulas. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by John P. Burgess - Philosophical Logic 1.8 | |
| A reaction: This is a helpful pointer to what is going on in the Tarski definition. It culminates in the 'satisfaction of all sequences', which presumable delivers the required closed formula. |
| 18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt] |
| Full Idea: Tarski invoked the notion of a sentential function, where components are replaced by appropriate variables. A function is then satisfied by assigning objects to variables. An assignment satisfies if the function is true of the things assigned. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [very compressed] This use of sentential functions, rather than sentences, looks like the key to Tarski's definition of truth. |
| 15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten] |
| Full Idea: The truth predicate, says Tarski, should be defined in terms of the more primitive satisfaction relation: the relation of being 'true of'. The fundamental notion is a formula (containing the free variables) being true of a sequence of objects as values. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 06.3 |
| 19314 | For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham] |
| Full Idea: Tarski, a physicalist, reduced semantics to physical and/or logicomathematical concepts. He defined all semantic concepts, save satisfaction, in terms of truth. Then truth is defined in terms of satisfaction, and satisfaction is given non-semantically. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1 | |
| A reaction: The term 'logicomathematical' is intended to cover set theory. Kirkham says you can remove these restrictions from Tarski's theory, and the result is a version of the correspondence theory. |
| 19316 | Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham] |
| Full Idea: Tarski's great insight is find another property, since open sentences are not truth. It must be had by open and genuine sentences. Clauses having it must generate it for the whole sentence. Truth can be defined for sentences by using it. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.4 | |
| A reaction: The proposed property is 'satisfaction', which can (unlike truth) be a feature open sentences (such as 'x is green', which is satisfied by x='grass'), |
| 19175 | Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson] |
| Full Idea: Tarski turned his axiomatic characterisation of satisfaction into an explicit definition of the satisfaction-predicate using some fancy set theoretical apparatus, and this in turn leads to the explicit definition of the truth predicate. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 7 |
| 16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
| Full Idea: Tarski's proof of the definability of truth allowed him to establish truth as a respectable notion by his standards. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
| Full Idea: Tarski defined various predicates of the form 's is true in L', each applicable to a single language, but he failed to define a predicate of the form 's is true in L' for variable 'L'. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: You might say that no one defines 'tree' to be just 'in English', but we might define 'multiplies' to be in Peano Arithmetic. This indicates the limited and formal nature of what Tarski was trying to achieve. |
| 16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
| Full Idea: Every really adequate theory of truth should also prove the law of non-contradiction. Therefore Tarski's notion of adequacy in Convention T fails to capture the intuitive notion of adequacy he is after. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 | |
| A reaction: Tarski points out this weakness, in a passage quoted by Halbach. This obviously raises the question of what truth theories should prove, and this is explored by Halbach. If they start to prove arithmetic, we get nervous. Non-contradiction and x-middle? |
| 2571 | Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack] |
| Full Idea: Tarski says "we may remain naïve realists or idealists, empiricists or metaphysicians… The semantic conception is completely neutral toward all these issues." | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Susan Haack - Philosophy of Logics 7.5 |
| 10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H] |
| Full Idea: Tarski work was to persuade physicalist that eliminating semantics was on the wrong track, and that we should explicate notions in the theory of reference nonsemantically rather than simply get rid of them. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Hartry Field - Tarski's Theory of Truth §3 |
| 10822 | A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski] |
| Full Idea: We need to add theories of primitive reference to Tarski's account if we are to establish the notion of truth as a physicalistically acceptable notion. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Hartry Field - Tarski's Theory of Truth §4 | |
| A reaction: This is the main point of Field's paper, and sounds very plausible to me. There is something major missing from Tarski, and at some point there needs to be a 'primitive' notion of thought and language making contact with the world, as it can't be proved. |
| 10969 | Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read] |
| Full Idea: Besides a theory of truth of his own, Tarski developed a theory of theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Stephen Read - Thinking About Logic Ch.1 | |
| A reaction: The famous snow biconditional is the latter, and the recursive account based on satisfaction is the former. |
| 17746 | Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki] |
| Full Idea: Tarski's analysis of the concept of 'truth' ...is given a precise treatment as a particular relation between syntax (language) and semantics (the world). | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Michal Walicki - Introduction to Mathematical Logic History E.1 | |
| A reaction: My problem is that the concept of truth seems to apply to animal minds, which are capable of making right or wrong judgements, and of realising their errors. Tarski didn't make universal claims for his account. |
| 10904 | Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski] |
| Full Idea: The Tarskian account of truth neglects the atomic sentences. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Mulligan/Simons/Smith - Truth-makers §1 | |
| A reaction: Yes! The whole Tarskian edifice is built on a foundation which it is taboo even to mention. If truth is just the assignment of 'T' and 'F', that isn't even the beginnings of a theory of 'truth'. |
| 15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten] |
| Full Idea: Tarski's work is the earliest axiomatic theory of truth that meets minimal adequacy conditions. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 01.1 | |
| A reaction: This shows a way in which Tarski gave a new direction to the study of truth. Subsequent theories have been 'stronger'. |
| 16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
| Full Idea: Tarski preferred a definition of truth, but from that an axiomatisation can be extracted. His induction clauses can be turned into axioms. Hence he opened the way to axiomatic theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 6103 | Normally a class with only one member is a problem, because the class and the member are identical [Russell] |
| Full Idea: With the ordinary view of classes you would say that a class that has only one member was the same as that one member; that will land you in terrible difficulties, because in that case that one member is a member of that class, namely, itself. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VII) | |
| A reaction: The problem (I think) is that classes (sets) were defined by Frege as being identical with their members (their extension). With hindsight this may have been a mistake. The question is always 'why is that particular a member of that set?' |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| Full Idea: Tarski showed that the only binary relations invariant under arbitrary permutations are the universal relation, the empty relation, identity and non-identity, thus giving us a reason to include '=' among the logical terms. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 6 | |
| A reaction: Tarski was looking for a criterion to distinguish logical from non-logical terms, since his account of logical validity depended on it. This idea lies behind whether a logic is or is not specified to be 'with identity' (i.e. using '='). |
| 6092 | In a logically perfect language, there will be just one word for every simple object [Russell] |
| Full Idea: In a logically perfect language, there will be one word and no more for every simple object. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §II) | |
| A reaction: In other words, there would be no universals, only names? All that matters is that a language can successfully refer (unambiguously) to anything it wishes to. There must be better ways than Russell's lexical explosion. |
| 6101 | Romulus does not occur in the proposition 'Romulus did not exist' [Russell] |
| Full Idea: Romulus does not occur in the proposition 'Romulus did not exist'. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VI) | |
| A reaction: A very nice paradoxical assertion, which captures the problem of finding the logical form for negative existential statements. Presumably the proposition refers to the mythical founder of Rome, though. He is not, I suppose, rigidly designated. |
| 6102 | You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to [Russell] |
| Full Idea: If you understand English you would understand the phrase 'the author of Waverley' if you had not heard it before, whereas you would not understand the meaning of 'Scott', because to know the meaning of a name is to know who it is applied to. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VI) | |
| A reaction: Actually, you would find 'Waverley' a bit baffling too. Would you understand "he was the author of his own destruction"? You can understand "Homer was the author of this" without knowing quite who 'Homer' applies to. All very tricky. |
| 10423 | There are a set of criteria for pinning down a logically proper name [Russell, by Sainsbury] |
| Full Idea: A logically proper name must be semantically simple, have just one referent, be understood by the user, be scopeless, is not a definite description, and rigidly designates. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918], 24th pg) by Mark Sainsbury - The Essence of Reference Intro | |
| A reaction: Famously, Russell's hopes of achieving this logically desirable end got narrower and narrower, and ended with 'this' or 'that'. Maybe pure language can't do the job. |
| 7744 | Treat description using quantifiers, and treat proper names as descriptions [Russell, by McCullogh] |
| Full Idea: Having proposed that descriptions should be treated in quantificational terms, Russell then went on to introduce the subsidiary injunction that proper names should be treated as descriptions. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Gregory McCullogh - The Game of the Name 2.18 | |
| A reaction: McCulloch says Russell 'has a lot to answer for' here. It became a hot topic with Kripke. Personally I find Lewis's notion of counterparts the most promising line of enquiry. |
| 10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
| Full Idea: To say that the name x denotes a given object a is the same as to stipulate that the object a ... satisfies a sentential function of a particular type. | |
| From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], p.194) |
| 10426 | A name has got to name something or it is not a name [Russell] |
| Full Idea: A name has got to name something or it is not a name. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], 66th pg), quoted by Mark Sainsbury - The Essence of Reference 18.2 | |
| A reaction: This seems to be stipulative, since most people would say that a list of potential names for a baby counted as names. It may be wrong. There are fictional names, or mistakes. |
| 18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee] |
| Full Idea: Tarski discovered how to give a compositional semantics for predicate calculus, defining truth in terms of satisfaction, and showing how satisfaction for a complicated formula depends on satisfaction of the simple subformulas. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 4 | |
| A reaction: The problem was that the subformulas may contain free variables, and thus not be sentences with truth values. 'Satisfaction' can handle this, where 'truth' cannot (I think). |
| 19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham] |
| Full Idea: Tarski invented a formal semantics for quantified predicate logic, the logic of reasoning about mathematics. The heart of this great accomplishment is his theory of truth. It has been called semantic 'theory' of truth, but Tarski preferred 'conception'. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1 |
| 16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
| Full Idea: Tarski's distinction between object and metalanguage forms the basis of model theory. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 11 |
| 8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
| Full Idea: In Tarski's account of truth, self-reference (as found in the Liar Paradox) is prevented because the truth predicate for any given object language is never a part of that object language, and so a sentence can never predicate truth of itself. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Jennifer Fisher - On the Philosophy of Logic 03.I | |
| A reaction: Thus we solve the Liar Paradox by ruling that 'you are not allowed to say that'. Hm. The slightly odd result is that in any conversation about whether p is true, we end up using (logically speaking) two different languages simultaneously. Hm. |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| Full Idea: Tarski's theory of truth has been most influential in eventually creating a shift from the entirely syntactic way of doing things in metamathematics (promoted by Hilbert in the 1920s, in his theory of proofs), towards a set-theoretical, semantic approach. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Feferman / Feferman - Alfred Tarski: life and logic Int III |
| 6104 | Numbers are classes of classes, and hence fictions of fictions [Russell] |
| Full Idea: Numbers are classes of classes, and classes are logical fictions, so that numbers are, as it were, fictions at two removes, fictions of fictions. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VIII) | |
| A reaction: This summarises the findings of Russell and Whitehead's researches into logicism. Gödel may have proved that project impossible, but there is now debate about that. Personally I think of numbers as names of patterns. |
| 21708 | Russell's new logical atomist was of particulars, universals and facts (not platonic propositions) [Russell, by Linsky,B] |
| Full Idea: Russell's new logical atomist ontology was of particulars, universals and facts, replacing the ontology of 'platonic atomism' consisting just of propositions. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: Linsky cites Peter Hylton as saying that the earlier view was never replaced. The earlier view required propositions to be 'unified'. I surmise that the formula 'Fa' combines a universal and a particular, to form an atomic fact. [...but Idea 6111!] |
| 19051 | Russell's atomic facts are actually compounds, and his true logical atoms are sense data [Russell, by Quine] |
| Full Idea: In 1918 Russell does not admit facts as fundamental; atomic facts are atomic as facts go, but they are compound objects. The atoms of Russell's logical atomism are not atomic facts but sense data. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Willard Quine - Russell's Ontological Development p.83 | |
| A reaction: By about 1921 Russell had totally given up sense-data, because he had been reading behaviourist psychology. |
| 6089 | Logical atomism aims at logical atoms as the last residue of analysis [Russell] |
| Full Idea: I call my doctrine logical atomism because, as the last residue of analysis, I wish to arrive at logical atoms and not physical atoms; some of them will be particulars, and others will be predicates and relations and so on. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §I) | |
| A reaction: However we judge it, logical atomism is a vital landmark in the history of 'analytical' philosophy, because it lays out the ideal for our assessment. It is fashionable to denigrate analysis, but I think it is simply the nearest to wisdom we will ever get. |
| 6100 | Once you have enumerated all the atomic facts, there is a further fact that those are all the facts [Russell] |
| Full Idea: When you have enumerated all the atomic facts in the world, it is a further fact about the world that those are all the atomic facts there are about the world. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §V) | |
| A reaction: There is obviously a potential regress of facts about facts here. This looks like one of the reasons why the original logical atomism had a short shelf-life. Personally I see this as an argument in favour of rationalism, in the way Bonjour argues for it. |
| 6105 | Logical atoms aims to get down to ultimate simples, with their own unique reality [Russell] |
| Full Idea: Logical atomism is the view that you can get down in theory, if not in practice, to ultimate simples, out of which the world is built, and that those simples have a kind of reality not belonging to anything else. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VIII) | |
| A reaction: This dream is to empiricists what the Absolute is to rationalists - a bit silly, but an embodiment of the motivating dream. |
| 21709 | You can't name all the facts, so they are not real, but are what propositions assert [Russell] |
| Full Idea: Facts are the sort of things that are asserted or denied by propositions, and are not properly entities at all in the same sense in which their constituents are. That is shown by the fact that you cannot name them. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], p.235), quoted by Bernard Linsky - Russell's Metaphysical Logic 2.2 | |
| A reaction: [ref to Papers vol.8] It is customary to specify a proposition by its capacity for T and F. So is a fact just 'a truth'? This contains the Fregean idea that things are only real if they can be picked out. I think of facts as independent of minds. |
| 18376 | Russell asserts atomic, existential, negative and general facts [Russell, by Armstrong] |
| Full Idea: Russell argues for atomic facts, and also for existential facts, negative facts and general facts. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by David M. Armstrong - Truth and Truthmakers 05.1 | |
| A reaction: Armstrong says he overdoes it. I would even add disjunctive facts, which Russell rejects. 'Rain or snow will ruin the cricket match'. Rain can make that true, but it is a disjunctive fact about the match. |
| 5465 | Modern trope theory tries, like logical atomism, to reduce things to elementary states [Russell, by Ellis] |
| Full Idea: Russell and Wittgenstein sought to reduce everything to singular facts or states of affairs, and Armstrong and Keith Campbell have more recently advocated ontologies of tropes or elementary states of affairs. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Brian Ellis - The Philosophy of Nature: new essentialism Ch.3 n 11 | |
| A reaction: A very interesting historical link. Logical atomism strikes me as a key landmark in the history of philosophy, and not an eccentric cul-de-sac. It is always worth trying to get your ontology down to minimal small units, to see what happens. |
| 6060 | 'Existence' means that a propositional function is sometimes true [Russell] |
| Full Idea: When you take any propositional function and assert of it that it is possible, that it is sometimes true, that gives you the fundamental meaning of 'existence'. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918]), quoted by Colin McGinn - Logical Properties Ch.2 | |
| A reaction: Functions depend on variables, so this leads to Quine's slogan "to be is to be the value of a variable". Assertions of non-existence are an obvious problem, but Russell thought of all that. All of this makes existence too dependent on language. |
| 17945 | Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas] |
| Full Idea: The theory of Forms is not a theory of universals but a first attempt to explain how predication, the application of a single term to many objects - now considered one of the most elementary operations of language - is possible. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxvii) |
| 17946 | Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas] |
| Full Idea: Only Tallness and nothing else really is tall; everything else merely participates in the Forms and, being excluded from the realm of Being, belongs to the inferior world of Becoming. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxviii) | |
| A reaction: This is just as weird as the normal view (and puzzle of participation), but at least it makes more sense of 'metachein' (partaking). |
| 6099 | Modal terms are properties of propositional functions, not of propositions [Russell] |
| Full Idea: Traditional philosophy discusses 'necessary', 'possible' and 'impossible' as properties of propositions, whereas in fact they are properties of propositional functions; propositions are only true or false. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §V) | |
| A reaction: I am unclear how a truth could be known to be necessary if it is full of variables. 'x is human' seems to have no modality, but 'Socrates is human' could well be necessary. I like McGinn's rather adverbial account of modality. |
| 17944 | 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas] |
| Full Idea: The Greek 'episteme' is usually translated as 'knowledge' but, I argue, closer to our notion of understanding. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xvi) | |
| A reaction: He agrees with Julia Annas on this. I take it to be crucial. See the first sentence of Aristotle's 'Metaphysics'. It is explanation which leads to understanding. |
| 6098 | Perception goes straight to the fact, and not through the proposition [Russell] |
| Full Idea: I am inclined to think that perception, as opposed to belief, does go straight to the fact and not through the proposition. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §IV.4) | |
| A reaction: There seems to be a question of an intermediate stage, which is the formulation of concepts. Is full 'perception' (backed by attention and intellect) laden with concepts, which point to facts? Where are the facts in sensation without recognition? |
| 6097 | The theory of error seems to need the existence of the non-existent [Russell] |
| Full Idea: It is very difficult to deal with the theory of error without assuming the existence of the non-existent. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §IV.3) | |
| A reaction: This problem really bothered Russell (and Plato). I suspect that it was a self-inflicted problem because at this point Russell had ceased to believe in propositions. If we accept propositions as intentional objects, they can be as silly as you like. |
| 9022 | Russell uses 'propositional function' to refer to both predicates and to attributes [Quine on Russell] |
| Full Idea: Russell used the phrase 'propositional function' (adapted from Frege) to refer sometimes to predicates and sometimes to attributes. | |
| From: comment on Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Willard Quine - Philosophy of Logic Ch.5 | |
| A reaction: He calls Russell 'confused' on this, and he would indeed be guilty of what now looks like a classic confusion, between the properties and the predicates that express them. Only a verificationist would hold such a daft view. |
| 6091 | Propositions don't name facts, because each fact corresponds to a proposition and its negation [Russell] |
| Full Idea: It is obvious that a proposition is not the name for a fact, from the mere circumstance that there are two propositions corresponding to each fact, one the negation of the other. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §I) | |
| A reaction: Russell attributes this point to Wittgenstein. Evidently you must add that the proposition is true before it will name a fact - which is bad news for the redundancy view of truth. Couldn't lots of propositions correspond to one fact? |
| 21702 | In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts' [Russell, by Quine] |
| Full Idea: In 1918 Russell insists that the world does contain nonlinguistic things that are akin to sentences and are asserted by them; he merely does not call them propositions. He calls them facts. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Willard Quine - Russell's Ontological Development p.81 | |
| A reaction: Clarification! I have always been bewildered by the early Russell view of propositions as actual ingredients of the world. If we say that sentences assert facts, that makes more sense. Russell never believed in the mental entities I call 'propositions'. |
| 6094 | An inventory of the world does not need to include propositions [Russell] |
| Full Idea: It is quite clear that propositions are not what you might call 'real'; if you were making an inventory of the world, propositions would not come in. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §III) | |
| A reaction: I am not clear why this is "quite clear". Propositions might even turn up in our ontology as physical objects (brain states). He says beliefs are real, but if you can't have a belief without a proposition, and they aren't real, you are in trouble. |
| 6096 | I no longer believe in propositions, especially concerning falsehoods [Russell] |
| Full Idea: Time was when I thought there were propositions, but it does not seem to me very plausible to say that in addition to facts there are also these curious shadowy things going about as 'That today is Wednesday' when in fact it is Tuesday. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §IV.2) | |
| A reaction: You need to give some account of someone who thinks 'Today is Wednesday' when it is Tuesday. We can hardly avoid talking about something like an 'intentional object', which can be expressed in a sentence. Are there not possible (formulable) propositions? |
| 21712 | I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday [Russell] |
| Full Idea: Time was when I thought there were propositions, but it does not seem to me very plausible to say that in addition to facts there are also these curious shadowy things going about such 'That today is Wednesday' when it is in fact Tuesday. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], p.197), quoted by Bernard Linsky - Russell's Metaphysical Logic 3.1 | |
| A reaction: [Ref to Papers v8] I take Russell to have abandoned his propositions because his conception of them was mistaken. Presumably my thinking 'Today is Wednesay' conjures up a false proposition, which had not previously existed. |
| 6093 | The names in a logically perfect language would be private, and could not be shared [Russell] |
| Full Idea: A logically perfect language, if it could be constructed, would be, as regards its vocabulary, very largely private to one speaker; that is, all the names in it would be private to that speaker and could not enter into the language of another speaker. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §II) | |
| A reaction: Wittgenstein obviously thought there was something not quite right about this… See Idea 4147, for example. I presume Russell's thought is that you would have no means of explaining the 'meanings' of the names in the language. |
| 20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
| Full Idea: Taste is the faculty for judging an object or a kind of representation through a satisfaction or a dissatisfaction, ...where the object of such a satisfaction is called beautiful. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Elizabeth Schellekens - Immanuel Kant (aesthetics) 1 | |
| A reaction: We usually avoid the word 'faculty' nowadays, because it implies a specific mechanism, but 'capacity' will do. Kant is said to focus specifically on beauty, whereas modern aestheticians have a broader view of the type of subject matter. |
| 6119 | You can discuss 'God exists', so 'God' is a description, not a name [Russell] |
| Full Idea: The fact that you can discuss the proposition 'God exists' is a proof that 'God', as used in that proposition, is a description and not a name. If 'God' were a name, no question as to its existence could arise. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VI) | |
| A reaction: Presumably 'a being than which none greater can be conceived' (Anselm's definition) is self-evidently a description, and doesn't claim to be a name. Aquinas caps each argument with a triumphant naming of the being he has proved. |