However fundamentally this was not the real source of the attack on the demarcation project. The project came to be seen as not viable because its central notion of a criterion separating the empirical significant from the empirically non-significant came to be seen as untenable. Of course, certain attempts to explain the notion of empirical significance made recourse to the notion of analyticity.
Thus in Carnap Carnap invokes the notion of analytically true bilateral reduction sentences, and in Carnap analytically true meaning postulates, in order to forge a link between sentences containing theoretical terms and sentences containing observational terms.
However in this paper we will be concerned with first examining and then defending the kind of holistic account of empirical significance advocated by Ayer and the early Carnap. Such holistic accounts need make no use of any allegedly analytically based links between theoretical and observational terms.
Therefore we shall now set aside the problems of the analytic-synthetic distinction. Our inquiry then concerns the demarcation criterion narrowly construed as a means of demarcating the empirically significant from the empirically non-significant rather than the meaningful from the meaningless or the cognitively significant from the cognitively non- significant.
Indeed Carnap himself came to adopt this more moderate language. Such propositions included Reichenbach's favorite example that everything is doubling in size every ten minutes.
Feigl [ , p. There are of course many reasons for the abandonment of the effort to find a demarcation criterion.
Here I will briefly outline what I take to be the major criticisms of Positivism, as they bear on the question of the demarcation criterion. When the likes of Carnap, Neurath, Schlick, Hempel and Ayer failed after years of concerted effort to find a clear grounds for demarcating metaphysics from science even philosophers sympathetic to Positivism came to wonder if the project itself was feasible.
Of course this does not demonstrate that the construction of an adequate criterion is not possible but it lends some credence to the claim that there may be some principled reason behind those failures. The best candidates for principled reasons for the failure to find an adequate demarcation criterion come from the challenges from holism, the Kuhnian challenge, the challenge from the failure of formal accounts of confirmation and the challenge from the failure of verificationist accounts of meaning.
If an adequate demarcation criterion is possible then empirically significant hypotheses can be distinguished from empirically non-significant hypotheses by the fact that only the former have empirical consequences.
If holism is true then no single hypothesis has empirical consequences on its own. If holism is true there is no substantive i. Therefore 4. If holism is true then an adequate demarcation criterion is not possible. Before addressing this argument directly we should consider where the Positivists themselves actually stood on the question of holism. Interestingly, the Positivists, taking a note from Duhem, at times sounded holistic themes.
Thus Carnap in his classic of Positivism The Logical Syntax of Language writes, [I]t is, in general, impossible to test even a single hypothetical sentence. In the case of a single sentence of this kind, there are in general no suitable L-consequences of the form of protocol-sentences; hence for the deduction of sentences having the form of protocol- sentences the remaining hypotheses must also be used. Thus the test applies, at bottom, not to a single hypothesis but to the whole system of physics as a system of hypotheses Duhem, Poincare.
A similar acknowledgment of the holism is contained in Ayer's classic Language, Truth and Logic, When one speaks of hypotheses being verified in experience, it is important to bear in mind that it is never just a single hypothesis which an observation confirms or discredits, but always a system of hypotheses.
Of course it may be argued that while Carnap and Ayer paid lip-service to holism they did not seriously take it into consideration in attempting to construct a demarcation criterion. This reply is rendered ineffective by the fact that their actual attempts to construct a demarcation criterion often explicitly incorporated the lessons of holism.
For instance, Ayer, in framing his criteria of verifiability, famously, says that a statement is verifiable if "some observation-statement can be deduced from it in conjunction with certain other premises, without being deducible from those premises alone. This type of proposal, of course, met with various convincing objections and perhaps it is the case that all such attempts to incorporate the lessons of holism make for an unworkable criterion.
In that case the problem would not be, as popularly represented, that the Positivists notion of a demarcation criterion was predicated on a refusal to acknowledge holism. Rather the criticism would be that any attempt to incorporate holism in a demarcation criterion is doomed to failure. However the claim that there is no adequate version of the demarcation criterion which allows for holism has not been demonstrated.
In a sense, once we recognize that the Positivists were willing to construct their criterion of demarcation within a holistic frame- work, the only effective argument from holism would be that somehow holism precluded the construction of an adequate demarcation criterion.
But no one has shown why this should be so. What we do know is that various attempts, particularly those by Ayer and Carnap, to construct such a demarcation criterion have failed. But this simply brings us back to the argument from past failures. At best the argument from holism strikes a knockout blow against that form of reductive verificationism which sought to analyze all meaningful statements in terms of their individual implications for experience.
In particular, the form of reductionism favored by Carnap in his book Der Logische Aufbau der Welt and in his article "The Elimination of Metaphysics Through Logical Analysis of Language" is prima facie incompatible with holism.
But Carnap himself by had abandoned that kind of reductive analysis yet still did not despair of constructing a criterion of demarcation. Indeed Friedman even argues that the centrality of phenomenalist reductionism to Carnap's Aufbau project has been exaggerated.
Where then is the fault in the argument from holism? Given the above, it is clear that the problem lies in the transition from the first conclusion 3. At most the argument shows that if holism is true a demarcation criterion framed in terms of single hypotheses having empirical consequences is not viable.
This leaves open the possibility of a holistically framed demarcation criterion. The second premise of the argument asserts the lack of empirical consequences of single hypotheses yet in the final conclusion 4. What can be validly inferred from the premises is the conclusion 3. More precisely the distinction would be empty since all single hypotheses would fall on that same side of that distinction, namely, they would all be in the class of propositions without their own empirical consequences.
This commitment to explanatory reductionism has no direct bearing on the demarcation question. Thus I talk of "hypotheses" rather than simply of propositions or statements suggesting that this excludes observational claims whether these be taken to be claims about experience or observable physical objects which presumably do have their own empirical consequences.
Moreover in keeping with the fairly deplorable standards that go with the holism discussion I omit consideration of the possibility of long conjunctive hypotheses which include a mix of observation statements and hypotheses and which presumably are capable of having their own observational consequences.
I do this because I am here not seeking a clarification, defense or rebuttal of holism. This paper was written early in at the request of Professor Schilpp, for inclusion in a volume on Carnap which he had been planning.
Selected portions, running to somewhat less than half, have appeared also in American Philosophers at Work Sidney Hook, ed.
Reprints and Permissions. Quine, W. Carnap and logical truth. But a remark of Kreisel establishes that a conviction that they hold can be obtained sometimes. Kreisel called attention to the fact that 6 together with 4 implies that model-theoretic validity is sound with respect to logical truth, i. This means that when 6 holds the notion of model-theoretic validity offers an extensionally correct characterization of logical truth.
See Etchemendy , ch. Also, 6 , together with 4 , implies that the notion of derivability is complete with respect to logical truth the second implication in 5 and hence offers an extensionally correct characterization of this notion. Note that this reasoning is very general and independent of what our particular pretheoretic conception of logical truth is.
An especially significant case in which this reasoning can be applied is the case of first-order quantificational languages, under a wide array of pretheoretic conceptions of logical truth.
It is typical to accept that all formulae derivable in a typical first-order calculus are universally valid, true in all counterfactual circumstances, a priori and analytic if any formula is. This means that one can convince oneself that both derivability and model-theoretic validity are extensionally correct characterizations of our favorite pretheoretic notion of logical truth for first-order languages, if our pretheoretic conception is not too eccentric.
The situation is not so clear in other languages of special importance for the Fregean tradition, the higher-order quantificational languages. We may call this result the incompleteness of second-order calculi with respect to model-theoretic validity. In this situation it's not possible to apply Kreisel's argument for 5.
Different authors have extracted opposed lessons from incompleteness. A common reaction is to think that model-theoretic validity must be unsound with respect to logical truth. This is especially frequent in philosophers on whose conception logical truths must be a priori or analytic.
One idea is that the results of a priori reasoning or of analytic thinking ought to be codifiable in a calculus. Wagner , p. But even if we grant this idea, it's doubtful that the desired conclusion follows.
Suppose that i every a priori or analytic reasoning must be reproducible in a calculus. From iii and i it follows of course that there are model-theoretically valid formulae that are not obtainable by a priori or analytic reasoning.
But the step from ii to iii is a typical quantificational fallacy. From i and ii it doesn't follow that there is any model-theoretically valid formula which is not obtainable by a priori or analytic reasoning. The only thing that follows from ii alone under the assumptions that model-theoretic validity is sound with respect to logical truth and that logical truths are a priori and analytic is that no calculus sound with respect to model-theoretic validity can by itself model all the a priori or analytic reasonings that people are able to make.
But it's not sufficiently clear that this should be intrinsically problematic. After all, a priori and analytic reasonings must start from basic axioms and rules, and for all we know a reflective mind may have an inexhaustible ability to find new truths and truth-preserving rules by a priori or analytic consideration of even a meager stock of concepts. But this view is just one problematic idea about how apriority and analyticity should be explicated.
See also Etchemendy , chs. Another type of unsoundness arguments attempt to show that there is some higher-order formula that is model-theoretically valid but is intuitively false in a structure whose domain is a proper class. These arguments thus question the claim that each meaning assignment's validity-refuting power is modeled by some set-theoretic structure, a claim which is surely a corollary of the first implication in 5.
The most widespread view among set theorists seems to be that there are no formulae with that property in Fregean languages, but it's certainly not an absolutely firm belief of theirs. Note that these arguments offer a challenge only to the idea that universal validity as defined in section 2. The arguments we mentioned in the preceding paragraph and in 2. In fact, worries of this kind have prompted the proposal of a different kind of notions of validity for Fregean languages , in which set-theoretic structures are replaced with suitable values of higher-order variables in a higher-order language for set theory, e.
Both set-theoretic and proper class structures are modeled by such values, so these particular worries of unsoundness do not affect this kind of proposals. In general, there are no fully satisfactory philosophical arguments for the thesis that model-theoretic validity is unsound with respect to logical truth in higher-order languages. Are there then any good reasons to think that derivability in any calculus sound for model-theoretic validity must be incomplete with respect to logical truth?
There don't seem to be any absolutely convincing reasons for this view either. The main argument the first version of which was perhaps first made explicit in Tarski a, b seems to be this. It's certainly not a formula false in a proper class structure. The argument concludes that for any calculus there are logically true formulae that are not derivable in it. From this it has been concluded that derivability in any calculus must be incomplete with respect to logical truth.
On these assumptions it is certainly very reasonable to think that derivability, in any calculus satisfying 4 , must be incomplete with respect to logical truth. But in the absence of additional considerations, a critic may question the assumptions, and deny relevance to the argument.
The second assumption would probably be questioned e. The first assumption actually underlies any conviction one may have that 4 holds for any one particular higher-order calculus. Note that if we denied that the higher-order quantifiers are logical expressions we could equally deny that the arguments presented above against the soundness of model-theoretic validity with respect to logical truth are relevant at all.
It is often pointed out in this connection that higher-order quantifications can be used to define sophisticated set-theoretic properties that one cannot define just with the help of first-order quantifiers. Defenders of the logical status of higher-order quantifications, on the other hand, point to the wide applicability of the higher-order quantifiers, to the fact that they are analogous to the first-order quantifiers, to the fact that they are typically needed to provide categorical axiomatizations of mathematical structures, etc.
See Quine , ch. Zalta for very helpful comments on an earlier version of this entry. On standard views, logic has as one of its goals to characterize and give us practical means to tell apart a peculiar set of truths, the logical truths, of which the following English sentences are paradigmatic examples: 1 If death is bad only if life is good, and death is bad, then life is good. The Nature of Logical Truth 1.
The Mathematical Characterization of Logical Truth 2. Wallies ed. Allison, H. Aristotle, Analytica Priora et Posteriora , W. Ross ed. Azzouni, J. Oxford: Oxford University Press. Beall, Jc and G. Belnap, N. Bernays, P. Mancosu, in Mancosu ed. Boghossian, P. Hale and C. Wright eds. Boghossian and C. Peacocke eds. Bolzano, B. George, Oxford: Blackwell, BonJour, L. Bonnay, D. Boolos, G. Capozzi, M. Haaparanta ed. Carnap, R. Schilpp ed. Carroll, L.
Chihara, C. Schirn ed. Coffa, J. Dogramaci, S. Dummett, M. Etchemendy, J. Patterson ed. Feferman, S. Field, H. Caret and O. Hjortland eds. Franks, C. Rush ed. Frege, G. Bauer-Mengelberg, in J. McGuinness ed. Grice, P. But the question is whether the contradictions are not symp- toms for a fundamental unsoundness. The contradictions which issue from platonism can indeed be staved off by various artificial devices, and in my view the theory of types is merely one such artificial device.
The paradoxes show this notion of set to be inconsistent, and all further developments of set theories or type theories are simply ad hoc devices designed to avoid paradox. Consider for example: But we cannot simply withhold each antinomy-producing member- ship condition and assume classes corresponding to the rest. We are driven to seeking op- timum consistent combinations of existence assumptions, and con- sequently there is a great variety of proposals for the foundations of general set theory.
Each proposal is unnatural, because the natu- ral scheme is the unrestricted one that the antinomies discredit; and each has advantages, in power and simplicity or in attractive con- sequences in special directions, that its rivals lack. Quine, , p. But, so far, these are arguments against a set theory or type theory, since he sees this too as an ad hoc means of avoiding paradox in general, and not an argument as to why they do not count as logic.
Every truth of elementary logic is obvious whatever this really means , or can be made so by a se- ries of individually obvious steps. Set theory, in its present state anyway, is otherwise. N]o consistent set theory is both adequate to the purposes envisioned for set theory and capable of substanti- ation by steps of obvious reasoning from obviously true principles.
What we do is develop one or another set theory by obvious rea- soning, or elementary logic, from unobvious first principles which are set down, whether for good or the time being, by something very like convention. Quine takes it as a feature of our intuitive notion of logic that it must involve reason- ing by obvious steps from obvious in some sense first principles, and then shows that, whatever we mean by obvious, set theory fails this test.
Of course, Quine is not putting forward, as a serious theory, that logic proceeds from ob- vious steps from obvious first principles. But despite the not fully worked out nature of the account, this argument does give us insight into why Quine thought set theory was not logic.
Set theory is not logic because it proceeds from non-obvious arbitrarily stipulated conventions. There is another argument, in his Philosophy of Logic, for why set theory and higher order logic are not properly parts of logic. Here Quine defines logical truth as a truth such that sentences with the same grammatical structure is also true. That is to say a true sentence is a logical truth if truth is preserved over any substitution on its atomic components.
Quine shows, for first order lan- guages, assuming the language is expressive enough, this definition coincides with other definitions of logical truth such as being true in all models. He then argues that because set theoretic truths and truths of higher order logic can- not be captured substitutionally, they ought not be considered logical truths.
Higher order quantifiers must be seen as either quantifying over attributes in- tensions or over sets extensions. Quine clearly sees ontological economy as a norm for logic. Logic should make minimal ontological demands even at the level of metatheory. It is for this reason that he proposes to capture logical truth substitutionally instead of talking about models. In this work, Quine is dealing with the same issues that Carnap faced in Syntax.
There Carnap thought logic should make minimal existence assump- tions, and had originally wanted to define higher order logic substitutionally. Quine, as we will see in the next section, continued to see Carnap as hold- ing a version of the Syntax position on existential assumption in logic. It is for this reason that Quine sees Carnap as helping himself to existence assumptions without being willing to pay the ontological price.
Up until the fifties most systems of logic did assume sets, extensions or other similar notions. So an explication of logical truth that includes such a notion is not a break from his- torical precedent.
This is not to argue for a return to the view that set theory is logic, but merely to demonstrate that, at the time, it would not have seemed as unnatural as it does today to claim that logic includes set theory or type theory.
The translation into the formal mode of speech involved the elimination of universal words. Given his views on meaning, Quine doubts that such a distinction can be made. It is evident that the question whether there are numbers will be a category question only with respect to languages which appropriate a separate style of variables for the exclusive purpose of referring to numbers. So Quine believed for at least eighteen years that the position of ESO was a fairly minor modification of the Syntax position on existential assumptions in logic.
It is important, however, to note something else about this last quote. Quine continues: [Carnap] is thinking of languages which contain fundamentally seg- regated styles of variables before any definitional abbreviations; and he is thinking of styles of variables that are sealed off from one another so utterly that it is commonly ungrammatical to use a variable of one style where a variable of another style would be grammatical.
We have seen that Quine interprets the mature Carnap as trying to main- tain some version of his Syntax position against universal words. We began this section by saying that the position in Syntax on ontology had two main com- ponents. First is the necessity of translation into the formal mode of speech — including the elimination of universal words. The second is the instumental- ist stance towards the logical portion of the language. Quine takes it that Carnap wants to divide existential claims into two groups which Quine calls emprirical and ontological existence claims, in order to then ignore the ontological existence claims on the ground that they are analytic.
The issue over there being classes seems more a question of con- venient conceptual scheme; the issue over there being centaurs, or brick houses on Elm Street, seems more a question of fact. But I have been urging that this difference is only one of degree[. In Syntax Carnap has a clear double standard towards existence claims.
He recognizes that he is making existential assumptions in the logical portion of the language, but as we saw, employs several strategies to dismiss these assumptions rather than address them. On the other hand the descriptive por- tion stands in need of a material interpretation. By the time of ESO, Carnap does not need a way to avoid dealing with existential assumptions concerning abstract objects.
Given an explication of, for instance, our arithmetical vocabu- lary and given an explication of our semantic notions relative to that systematic account of number, the statement that numbers exist and that numerical terms refer become theorems of the appropriate formalized languages. It is true Car- nap takes claims about abstract objects to be analytic. Of course, Carnap and Quine had very different views on the epistemology of mathematics and the empirical sciences, and analyticity played an important epistemlogical role for Carnap.
But the concept of analyticity was not meant to support taking a dis- missive stance towards all analytic existence claims. That was a view Carnap held at the time of Syntax, but it was abandoned shortly after. Carnap maintained that to use, for instance, the language of set theory is a practical decision of language choice. Quine interprets this to mean that talk of sets is a mere manner of speaking. Of course Quine did not think that Carnap was entitled to this position if it could not be shown that quantification over sets was eliminable from our best scientific theories.
But Carnap did not think talk of sets was a mere manner of speaking. To do so would be to hold that we prove that many sets exist while working in some system of set theory, and also hold that sets do not exist according to the ordinary notion of existence in natural language. But Carnap takes no position on whether sets exist in the ordinary sense of existence, because he takes this notion to be unclear.
There is nothing mere about the existence of sets for Carnap. Carnap often suggested that his differences with what Quine says about ontol- ogy are purely terminological. We saw as early as , Quine is seeking a language transcendent way of asking about the existence of an entity. This position is preserved in his later views. We can- not answer questions of existence and reference before explicating a certain range of vocabulary, and then explicating various semantic notions as they ap- ply to the explication of that vocabulary.
It is a basic feature of explications that they are not correct or incorrect. Since the notion of correctness does not apply, there is no further, sufficiently clear question that needs to be addressed ac- cording to Carnap. The difference then, between Carnap and Quine, is clearly not merely terminological. Furthermore, to understand how Quine intended to rehabilitate this gen- eral question of existence, we need to look again at the difference in their ac- counts of explication.
Explications are not to be evaluated in terms of correctness, but in terms of usefulness. The explicandum and exclicatum, of course, are not required to be identical, but they do, for Quine, need to agree on the core mean- ing. Any explication of what we take to exist must view us as committed to all those entities we ineliminably quantify over in our best scientific theories. Quine was amazingly ingenious in his attempts to rehabilitate the general question of existence that Carnap dismissed.
Quine was not trying to identify exactly what metaphysicians meant by these terms, but does think he has identified a core meaning that is useful and preserved by his use of the terms.
Can we reformulate all of science in a language that does not involve quantification over abstract entities? Carnap, as we saw, agrees that this is a meaningful question, but sees any connection to the old problem of nominalism as undesirable.
Quine is unhappy with language spe- cific answer to existence claims — language A quantifies over abstract objects, but language B does not — and seeks a language independent way of posing ontological questions.
The reformulation of the question of nominalism is a case in point. By asking if there is any nominalistic language suitable for the purposes of science, Quine has severed the ties between this problem of nomi- nalisnm and any specific language. That is, we are likely to draw a stonger conclusion than we are really entitled to.
I am not claiming that Quine is under any illusions about this, but certainly many people influenced by Quine take it that we would learn something else about the world if we were to learn that real numbers, for instance, are ineliminable from our best scientific theo- ries. All questions about the logical portion of the language were labeled quasi-syntactic, and so all ques- tions about the abstract ontology assumed by the language of science are ill- posed.
It could be shown that, relative to this explication, there was no motivation for the nominalistic scruples held by many empiricists. Carnap did not attempt to show that talk of numbers, sets or propositions was a mere manner of speaking. His goal was to show how we can speak in very clear terms about abstract objects as the referents of terms.
Quine understood Carnap as continuing to hold a position on ontology similar to the one at the time of Syn- tax. Quine wanted to reformulate ontological questions so as to be independent of any particular language. Carnap accepted that Quine had formulated a problem that is independent of the features of any specific language, but thought that making the connection to the traditional problem of nominalism might lead some to think that something more had been established. References Beth, E. Schilpp Ed.
The philosophy of Rudolf Carnap, vol. Carnap, R. The Logical Syntax of Language. Foundations of logic and mathematics. Neurath, R. Morris Eds. International Encyclopaedia of Unified Science.
Chicago: University of Chicago Press, combined ed. Introduction to Semantics. The two concepts of probability: The problem of probability. Philosophy and Phenomenological Research, 5 4 , —
0コメント