49 ideas
| 6891 | Quine's naturalistic and empirical view is based entirely on first-order logic and set theory [Quine, by Mautner] |
| Full Idea: Quine has aimed at a naturalistic and empirical world-view, and claims that first-order logic and set theory provide a framework sufficient for the articulation of our knowledge of the world. | |
| From: report of Willard Quine (Word and Object [1960]) by Thomas Mautner - Penguin Dictionary of Philosophy p.465 | |
| A reaction: Consequently he is fairly eliminativist about meaning and mental states, and does without universals in his metaphysics. An impressively puritanical enterprise, taking Ockham's Razor to the limit, but I find it hard to swallow. |
| 6310 | Enquiry needs a conceptual scheme, so we should retain the best available [Quine] |
| Full Idea: No enquiry is possible without some conceptual scheme, so we may as well retain and use the best one we know. | |
| From: Willard Quine (Word and Object [1960], §01) | |
| A reaction: This remark leads to Davidson's splendid paper 'On the Very Idea of a Conceptual Scheme'. Quine's remark raises the question of how we know which conceptual scheme is 'best'. |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| Full Idea: A proof of the consistency of propositional logic was given by Emil Post in 1921. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2.1) |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| Full Idea: Propositional language is very rudimentary and has limited powers of expression. The only relation between various statements it can handle is that of identity and difference. As are all the same, but Bs can be different from As. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 7 Intro) | |
| A reaction: [second sentence a paraphrase] In predicate logic you could represent two statements as being the same except for one element (an object or predicate or relation or quantifier). |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| Full Idea: Boolean connectives are interpreted as functions on the set {1,0}. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 5.1) | |
| A reaction: 1 and 0 are normally taken to be true (T) and false (F). Thus the functions output various combinations of true and false, which are truth tables. |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| Full Idea: The empty set is mainly a mathematical convenience - defining a set by describing the properties of its members in an involved way, we may not know from the very beginning what its members are. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| Full Idea: Without the assumption of the empty set, one would often have to take special precautions for the case where a set happened to contain no elements. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) | |
| A reaction: Compare the introduction of the concept 'zero', where special precautions are therefore required. ...But other special precautions are needed without zero. Either he pays us, or we pay him, or ...er. Intersecting sets need the empty set. |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| Full Idea: Ordinals play the central role in set theory, providing the paradigmatic well-orderings. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: When you draw the big V of the iterative hierarchy of sets (built from successive power sets), the ordinals are marked as a single line up the middle, one ordinal for each level. |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| Full Idea: In order to construct precise and valid patterns of arguments one has to determine their 'building blocks'. One has to identify the basic terms, their kinds and means of combination. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History Intro) | |
| A reaction: A deceptively simple and important idea. All explanation requires patterns and levels, and it is the idea of building blocks which makes such things possible. It is right at the centre of our grasp of everything. |
| 12798 | Plurals can in principle be paraphrased away altogether [Quine] |
| Full Idea: By certain standardizations of phrasing the contexts that call for plurals can in principle be paraphrased away altogether. | |
| From: Willard Quine (Word and Object [1960], §19) | |
| A reaction: Laycock, who quotes this, calls it 'unduly optimistic', but I presume that it was the standard view of plural reference until Boolos raised the subject. |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| Full Idea: A specification of a domain of objects, and of the rules for interpreting the symbols of a logical language in this domain such that all the theorems of the logical theory are true is said to be a 'model' of the theory. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.1.3) | |
| A reaction: The basic ideas of this emerged 1915-30, but it needed Tarski's account of truth to really get it going. |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| Full Idea: The L-S Theorem is ...a shocking result, since it implies that any consistent formal theory of everything - even about biology, physics, sets or the real numbers - can just as well be understood as being about natural numbers. It says nothing more. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2) | |
| A reaction: Illuminating. Particularly the point that no theory about the real numbers can say anything more than a theory about the natural numbers. So the natural numbers contain all the truths we can ever express? Eh????? |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| Full Idea: Having such a compact [axiomatic] presentation of a complicated field [such as Euclid's], makes it possible to relate not only to particular theorems but also to the whole field as such. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| Full Idea: Axiomatic systems, their primitive terms and proofs, are purely syntactic, that is, do not presuppose any interpretation. ...[142] They never address the world directly, but address a possible semantic model which formally represents the world. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| Full Idea: Every member of an ordinal is itself an ordinal, and every ordinal is a transitive set (its members are also its subsets; a member of a member of an ordinal is also a member of the ordinal). | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17905 | Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine] |
| Full Idea: The condition on an explication of number can be put succinctly: any progression will do nicely. Russell once held that one must also be able to measure multiplicity, but this was a mistake; any progression can be fitted to that further condition. | |
| From: Willard Quine (Word and Object [1960], §54) | |
| A reaction: [compressed] This is the strongest possible statement that the numbers are the ordinals, and the Peano Axioms will define them. The Fregean view that cardinality comes first is redundant. |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| Full Idea: The collection of ordinals is defined inductively: Basis: the empty set is an ordinal; Ind: for an ordinal x, the union with its singleton is also an ordinal; and any arbitrary (possibly infinite) union of ordinals is an ordinal. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: [symbolism translated into English] Walicki says they are called 'ordinal numbers', but are in fact a set. |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| Full Idea: We can form infinite ordinals by taking unions of ordinals. We can thus form 'limit ordinals', which have no immediate predecessor. ω is the first (the union of all finite ordinals), ω + ω = sω is second, 3ω the third.... | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| Full Idea: There may be several ordinals for the same cardinality. ...Two ordinals can represent different ways of well-ordering the same number (aleph-0) of elements. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: This only applies to infinite ordinals and cardinals. For the finite, the two coincide. In infinite arithmetic the rules are different. |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| Full Idea: An ordinal can be defined as a transitive set of transitive sets, or else, as a transitive set totally ordered by set inclusion. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| Full Idea: Since non-Euclidean geometry preserves all Euclid's postulates except the fifth one, all the theorems derived without the use of the fifth postulate remain valid. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| Full Idea: Inductive proof is not guaranteed to work in all cases and, particularly, it depends heavily on the choice of the ordering. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.1.1) | |
| A reaction: There has to be an well-founded ordering for inductive proofs to be possible. |
| 9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
| Full Idea: Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects. | |
| From: Willard Quine (Word and Object [1960], §55) | |
| A reaction: Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually). |
| 16462 | The quest for ultimate categories is the quest for a simple clear pattern of notation [Quine] |
| Full Idea: The quest of a simplest, clearest overall pattern of canonical notation is not to be distinguished from a quest of ultimate categories, a limning of the most general traits of reality. | |
| From: Willard Quine (Word and Object [1960], §33) | |
| A reaction: I won't disagree, as long as we recognise that reality calls the shots, not the notation, and that even animals must have some sort of system of categories, achieved without 'notation'. |
| 15723 | Either dispositions rest on structures, or we keep saying 'all things being equal' [Quine] |
| Full Idea: The further a disposition is from those that can confidently be pinned on molecular structure or something comparably firm, the more our talk of it tends to depend on a vague factor of 'caeteris paribus' | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: I approve of this. It is precisely the point of scientific essentialism, I take it. We are faced with innumerable uncertain dispositions, but once the underlying mechanisms are known, their role in nature becomes fairly precise. |
| 15490 | Explain unmanifested dispositions as structural similarities to objects which have manifested them [Quine, by Martin,CB] |
| Full Idea: Quine claims that an unmanifested disposition is explicable in terms of an object having a structure similar to a structure of an object that has manifested the supposed disposition. | |
| From: report of Willard Quine (Word and Object [1960], §46) by C.B. Martin - The Mind in Nature 07.4 | |
| A reaction: This is probably the best account available for the firm empiricist who denies modal features in the actual world. In other words, a disposition is the result of an induction, not a conditional statement. |
| 8504 | Quine aims to deal with properties by the use of eternal open sentences, or classes [Quine, by Devitt] |
| Full Idea: Quine is not an 'ostrich', because his strategy for dealing with property sentences is clear enough: all talk of attributes is to be dispensed with in favour of talk of eternal open sentences or talk of classes. | |
| From: report of Willard Quine (Word and Object [1960], §43) by Michael Devitt - 'Ostrich Nominalism' or 'Mirage Realism'? p.100 | |
| A reaction: [See p.209 'Word and Object'] The proposal seems to be that a property like being-human (a category) would be dealt with by classes, and qualitative properties would be dealt with simply as predicates. I like the split, and the first half, not the second. |
| 8464 | Physical objects in space-time are just events or processes, no matter how disconnected [Quine] |
| Full Idea: Physical objects, conceived four-dimensionally in space-time, are not to be distinguished from events or concrete processes. Each comprises simply the content, however heterogeneous, of a portion of space-time, however disconnected and gerrymandered. | |
| From: Willard Quine (Word and Object [1960], §36) | |
| A reaction: I very much like the suggestion that objects should be thought of as 'processes', but I dislike the idea that they can be gerrymandered. This is a refusal to cut nature at the joints (Idea 7953), which I find very counterintuitive. |
| 7924 | The notion of a physical object is by far the most useful one for science [Quine] |
| Full Idea: In a contest of sheer systematic utility to science, the notion of physical object still leads the field. | |
| From: Willard Quine (Word and Object [1960], §48) | |
| A reaction: A delightful circumlocution from someone who seems terrified to assert that there just are objects. Not that I object to Quine's caution. It would be disturbing if his researches had revealed that we could manage without objects. But compare Idea 6124. |
| 8482 | Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine] |
| Full Idea: Mathematicians are necessarily rational, and not necessarily two-legged; cyclists are the opposite. But what of an individual who counts among his eccentricities both mathematics and cycling? | |
| From: Willard Quine (Word and Object [1960], §41) | |
| A reaction: Quine's view is that the necessity (and essence) depends on how this eccentric is described. If he loses a leg, he must give up cycling; if he loses his rationality, he must give up the mathematics. Quine is wrong. |
| 12136 | Cyclist are not actually essentially two-legged [Brody on Quine] |
| Full Idea: Cyclists are not essentially two-legged (a one-legged cyclist exists, but can't cycle any more), and mathematicians are not essentially rational (as they can lose rationality and continue to exist, though unable to do mathematics). | |
| From: comment on Willard Quine (Word and Object [1960], §41.5) by Baruch Brody - Identity and Essence 5.1 | |
| A reaction: Was Quine thinking of the nominal essence of this person - that 'cyclists' necessarily cylce, and 'mathematicians' necessarily do some maths? It is as bad to confuse 'necessary' with 'essential' as to confuse 'use' with 'mention'. |
| 17594 | We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine] |
| Full Idea: For general terms write 'if Fx then Fy' and vice versa, and 'if Fxz then Fyz'..... The conjunction of all these is coextensive with 'x=y' if any formula constructible from the vocabulary is; and we can adopt that conjunction as our version of identity. | |
| From: Willard Quine (Word and Object [1960], §47) | |
| A reaction: [first half compressed] The main rival views of equality are this and Wiggins (1980:199). Quine concedes that his account implies a modest version of the identity of indiscernibles. Wiggins says identity statements need a sortal. |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| Full Idea: The link between time and modality was severed by Duns Scotus, who proposed a notion of possibility based purely on the notion of semantic consistency. 'Possible' means for him logically possible, that is, not involving contradiction. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History B.4) |
| 15725 | Normal conditionals have a truth-value gap when the antecedent is false. [Quine] |
| Full Idea: In its unquantified form 'If p then q' the indicative conditional is perhaps best represented as suffering a truth-value gap whenever its antecedent is false. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: That is, the clear truth-functional reading of the conditional (favoured by Lewis, his pupil) is unacceptable. Quine favours the Edgington line, that we are only interested in situations where the antecedent might be true. |
| 15722 | Conditionals are pointless if the truth value of the antecedent is known [Quine] |
| Full Idea: The ordinary conditional loses its point when the truth value of its antecedent is known. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: A beautifully simple point that reveals a lot about what conditionals are. |
| 15719 | We feign belief in counterfactual antecedents, and assess how convincing the consequent is [Quine] |
| Full Idea: The subjunctive conditional depends, like indirect quotation and more so, on a dramatic projection: we feign belief in the antececent and see how convincing we then find the consequent. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: This seems accurate. It means that we are only interested in when the antecedent is true, and when it is false is irrelevant. |
| 15721 | Counterfactuals are plausible when dispositions are involved, as they imply structures [Quine] |
| Full Idea: The subjunctive conditional is seen at its most respectable in the disposition terms. ...The reason is that they are conceived as built-in, enduring structural traits. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: Surprisingly, this is very sympathetic to a metaphysical view that seems a long way from Quine, since dispositions seem to invite commitment to modal features of reality. But the structural traits are not, of course, modal, in any way! |
| 15724 | Counterfactuals have no place in a strict account of science [Quine] |
| Full Idea: The subjunctive conditional has no place in an austere canonical notation for science - but that ban is less restrictive than would at first appear. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: Idea 15723 shows what he has in mind - that what science aims for is accounts of dispositional mechanisms, which then leave talk of other possible worlds (in Lewis style) as unnecessary. I may be with Quine one this one. |
| 15720 | What stays the same in assessing a counterfactual antecedent depends on context [Quine] |
| Full Idea: The traits to suppose preserved in a counterfactual depend on sympathy for the fabulist's purpose. Compare 'If Caesar were in command, he would use the atom bomb', and 'If Caesar were in command, he would use catapults'. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: This seems to be an important example for the Lewis approach, since you are asked to consider the 'nearest' possible world, but that will depend on context. |
| 4630 | Two theories can be internally consistent and match all the facts, yet be inconsistent with one another [Quine, by Baggini /Fosl] |
| Full Idea: Duhem and Quine have maintained that it may be possible to develop two or more theories that are 1) internally consistent, 2) inconsistent with one another, and 3) perfectly consistent with all the data we can muster. | |
| From: report of Willard Quine (Word and Object [1960]) by J Baggini / PS Fosl - The Philosopher's Toolkit §1.06 | |
| A reaction: Obviously this may be a contingent truth about our theories, but why not presume that this is because we are unable to collect the crucial data (e.g. about prehistoric biology), rather than denigrate the whole concept of a theory, and undermine science? |
| 3131 | Quine expresses the instrumental version of eliminativism [Quine, by Rey] |
| Full Idea: Quine expresses the instrumental version of eliminativism. | |
| From: report of Willard Quine (Word and Object [1960]) by Georges Rey - Contemporary Philosophy of Mind Int.3 |
| 3988 | Indeterminacy of translation also implies indeterminacy in interpreting people's mental states [Dennett on Quine] |
| Full Idea: Quine's thesis of the indeterminacy of radical translation carries all the way in, as the thesis of the indeterminacy of radical interpretation of mental states and processes. | |
| From: comment on Willard Quine (Word and Object [1960]) by Daniel C. Dennett - Daniel Dennett on himself p.239 | |
| A reaction: Strong scepticism seems wrong here. Davidson's account of charity in interpretation, and the role of truth, seems closer. |
| 6311 | The firmer the links between sentences and stimuli, the less translations can diverge [Quine] |
| Full Idea: The firmer the direct links of a sentence with non-verbal stimulation, the less drastically its translations can diverge from one another from manual to manual. | |
| From: Willard Quine (Word and Object [1960], §07) | |
| A reaction: This implies (plausibly) that talk about farming will have fairly determinate translations into foreign languages, but talk of philosophy will not. An interesting case is logic, where we might expect tight translation with little non-verbal stimulation. |
| 6312 | We can never precisely pin down how to translate the native word 'Gavagai' [Quine] |
| Full Idea: There is no evident criterion whereby to strip extraneous effects away and leave just the meaning of 'Gavagai' properly so-called - whatever meaning properly so-called may be. | |
| From: Willard Quine (Word and Object [1960], §09) | |
| A reaction: Quine's famous assertion that translation is ultimately 'indeterminate'. Huge doubts about meaning and language and truth follow from his claim. Personally I think it is rubbish. People become fluent in very foreign languages, and don't have breakdowns. |
| 6313 | Stimulus synonymy of 'Gavagai' and 'Rabbit' does not even guarantee they are coextensive [Quine] |
| Full Idea: Stimulus synonymy of the occasion sentences 'Gavagai' and 'Rabbit' does not even guarantee that 'gavagai' and 'rabbit' are coextensive terms, terms true of the same things. | |
| From: Willard Quine (Word and Object [1960], §12) | |
| A reaction: Since this scepticism eventually seems to result in the reader no longer knowing what they mean themselves by the word 'rabbit', I doubt Quine's claim. Problems after hearing one word of a foreign language disappear after years of residence. |
| 6317 | Dispositions to speech behaviour, and actual speech, are never enough to fix any one translation [Quine] |
| Full Idea: Rival systems of analytical hypotheses can fit the totality of speech behaviour to perfection, and can fit the totality of dispositions to speech behaviour as well, and still specify mutually incompatible translations of countless sentences. | |
| From: Willard Quine (Word and Object [1960], §15) | |
| A reaction: This is Quine's final assertion of indeterminacy, having explored charity, bilingual speakers etc. It seems to me that he is a victim of his underlying anti-realism, which won't allow nature to dictate ways of cutting up the world. |
| 6314 | Weird translations are always possible, but they improve if we impose our own logic on them [Quine] |
| Full Idea: Wanton translation can make natives sound as queer as one pleases; better translation imposes our logic upon them. | |
| From: Willard Quine (Word and Object [1960], §13) | |
| A reaction: This begins to point towards the principle of charity, on which Davidson is so keen, and even on doubts whether two different conceptual schemes are possible. Personally I think there is only one logic (deep down), and the natives will have it. |
| 6315 | We should be suspicious of a translation which implies that a people have very strange beliefs [Quine] |
| Full Idea: The more absurd or exotic the beliefs imputed to a people, the more suspicious we are entitled to be of the translations. | |
| From: Willard Quine (Word and Object [1960], §15) | |
| A reaction: Quine is famous for his relativist and indeterminate account of translation, but he gradually works his way towards the common sense which Davidson later brought out into the open. |