Pseudo-assertions: The sort of sentence that may appear meaningful at first but in fact is not. It does not have a truth value and does not provide us with information. Assertions usually take the form of declarative sentences i. Consider for example:. This is NOT an assertion. Does there indeed burn a candle in the swirling vortex of love?
Has the candle in the swirling vortex of love gone out? Is there a light bulb there now? A neon sign instead perhaps? Perhaps a more environmentally friendly LED? I doubt anyone would be willing to say that this sentence is true or false. Rather, they would say that it is neither true nor false. Thus it is NOT an assertion. It neither informs nor misinforms.
But note: the sentence. This IS an assertion. Not the grammar. The grammar is identical to the first sentence. Both are declarative sentences with a subject and predicate. Further, consider these:. Kwai gives you all the goodness of garlic. This product was scientifically formulated to help you manage your hair-loss situation.
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They supported forms of Materialism , Naturalism and Empiricism , and, in particular, they strongly supported the verifiability criterion of meaning Verificationism , the doctrine that a proposition is only cognitively meaningful if it can be definitively and conclusively determined to be either true or false. Logical Positivism was also committed to the idea of "Unified Science" , or the development of a common language in which all scientific propositions can be expressed, usually by means of various "reductions" or "explications" of the terms of one science to the terms of another putatively more fundamental one.
The most important early figures in Logical Positivism were the Bohemian-Austrian Positivist philosopher Ernst Mach - and the Austrian Ludwig Wittgenstein especially his "Tractatus" of , a text of great importance for Logical Positivists.
Logical Positivism in Germany rose in response to the Metaphysics of Georg Hegel , which was the dominant philosophical view in Germany at the time, particularly the rejection of his concept of metaphysical entities that did not have any empirical basis. It grew from the discussions of the so-called "Vienna Circle" of Moritz Schlick - in the early 20th Century. A pamphlet jointly written by Otto Neurath - , Hans Hahn - and Rudolf Carnap - brought together some of the major proponents of the movement and summarized the doctrines of the Vienna Circle at that time.
The contemporaneous Berlin Circle of Hans Reichenbach - also propagated the new doctrines more widely in the s and early s. Ayer is considered responsible for the spread of Logical Positivism to Britain , and his book "Language, Truth and Logic" was very influential. Developments in logic and the foundations of mathematics , especially in the "Principia Mathematica" by the British philosophers Bertrand Russell and Alfred North Whitehead , particularly impressed the more mathematically-minded Logical Positivists.
The movement dispersed in the late 's, mainly because of political upheaval and the untimely deaths of Hahn and Schlick.
If the proposals constituting some version of verificationism are adopted, then in the language thus constituted it will be analytically true that there are no synthetic sentences that are both unverifiable and meaningful. The notion of meaning here is not some new technical invention. No grammatically well-formed sentence of this new language violates the verifiability principle.
And the principle itself is completely safe. Thought of in this way the verifiability principle does not describe natural language, it is not intended to. It is intended to reform language to make it a more useful tool for the purposes of science.
Carnap is under no illusion that natural languages are free from metaphysics. Nor is he under the illusion that defenders of the sort of metaphysics he targets will readily step up to the challenge of presenting precise rules of grammar and inference. Before tolerance, verificationism is stated in such a way that violations would count only as unintelligible gibberish. With tolerance in place, Carnap is prepared to imagine non-empiricist languages, though of course he thinks they are very unwise.
So instead of saying that sentences in non-empiricist languages are meaningless, he says that they are empirically meaningless.
And that has a very different flavor. There is no weakening of his defense of empiricism, but it is put on a somewhat different footing. Indeed it is hard to indicate any conditions under which any parts of them would be disconfirmed.
Leibniz had called them truths of reason. Hume said that they represented relations of ideas. Kant had held that the truths in these areas were a priori. Mathematics and geometry were not analytic for Kant, but logic was. Kant had two criteria of analyticity, apparently thinking them equivalent.
First, in subject-predicate sentences, an analytic sentence is one in which the concept of the predicate is contained in that of the subject. Second, an analytic sentence is one whose denial is self-contradictory. This seems to include not only the sentences whose surface logical form would be of the required sort but also those that can be got from such logical truths by making substitutions that were conceptually equivalent. The more modern rough analog of this is to say that the analytic sentences are those that are true in virtue of logic and definition.
Frege certainly developed logic beyond that which was available to Kant, but he did not think of himself as changing the analytic status of it. Logic is after all the only avenue we have for giving meaning to the notion of logical contradiction.
Of course Frege also attempted to reduce mathematics to logic including both first and second order logic , and insofar as that reduction was successful it would have implied that mathematics was analytic as well. Frege said little of geometry, but for him it was synthetic a priori. Carnap had not only studied with Frege, but like many of the logical empiricists he had started out as a neo-Kantian as well. Geometry could be handled in several different ways that we will not discuss here.
But from fairly early on there was widespread agreement among the logical empiricists that there was no synthetic a priori, and that logic and mathematics and perhaps much else that seemed impervious to empirical disconfirmation should be thought of as analytic. The point of drawing the analytic-synthetic distinction, then, is not to divide the body of scientific truths or to divide philosophy from science, but to show how to integrate them into a natural scientific whole.
Along the way the distinction clarifies which inferences are to be taken as legitimate and which are not. If, as Carnap and Neurath were, you are impressed by Duhemian arguments to the effect that generally claims must be combined in order to test them, the analytic-synthetic distinction allows you to clarify which combinations of claims are testable. If analytic, a sentence is true in virtue of the conventions of language.
In saying that, however, we must pause to confront two widespread confusions. First, Quine alleges , f that the notion of analyticity was developed and purports to explain for both Kant and Carnap how certainty is possible. In fact certainty has little or nothing to do with analyticity for the leading logical empiricists. In saying that such claims are based on convention they were explicitly calling attention to the revisability of conventions and the sentences that owed their meanings to those conventions.
No proposition can be made true by our conventions or decisions. But it is also completely irrelevant. Analyticity applies to sentences rather than propositions. Our conventions and decisions can and do affect what expressions mean and thus what sentences mean. Once the meaning is specified, it may well be that any sentence that has this meaning would be true even if, for example, the point masses of the universe were arranged quite otherwise than they in fact are.
These are the analytic sentences. No claim is being made that meaning causes anything or that convention makes anything true. It is just that in these cases the truth value of the sentence may well be functionally dependent on meaning alone. If it is, then in this special sense, truth value depends on meaning, and that depends on convention.
Other sentences whose meanings are specified might well be true or false depending on how things in the external world, so to speak, are arranged. In this other category of sentence the truth value is not functionally dependent on meaning alone.
They are the synthetic sentences. Now this puts matters extremely informally. But at least the nature of the confusions over certainty and convention should be clear. The method used was to distinguish between a derivation relation the relation that holds between some premises and what can be got from them in a finite number of steps and a consequence relation. The latter is an essentially semantic relation that holds between some premises and some other claim such that on all valuations under which the premises are all true, so is that other claim.
In any case, Carnap is able to show that for any sentence of pure mathematics either it or its negation is a consequence of the null set of premises. As noted above, another innovation of Logical Syntax is the Principle of Tolerance. In the late s Carnap began exploring a and how a notion of analyticity might be developed for novel theoretical terms where the theories in which those terms are embedded are presented by means of a system of postulates. It is not clear that the account he developed was intended to supersede his earlier account.
Also let R TC be the Ramsey sentence for TC , that is, the result of replacing each of the non-observational terms in TC with predicate variables and closing that open sentence with corresponding existential quantifiers.
Quine began having doubts about analyticity about , though he seems not to have been firmly committed against it until later. First, it relies on the demand that theoretical terms must satisfy some empirical significance criterion.
Many people at the time, including some who followed Quine in rejecting analyticity, also rejected any general empirical significance demand for theoretical terms. Second, one could accept the demand for theoretical terms in physics or chemistry and deny, as Carnap did, that the demand applied to his own work.
This is because Carnap saw himself as working in an area within metamathematics rather than in empirical linguistics. Third, Quine did not pretend to have considered all of the possibilities for the explication of analyticity. Insofar as that sketch can be filled out successfully it would constitute a dispensability argument against analyticity. Whether it can be thus filled out, however, remains to be seen.
As with most topics in philosophy there is no uniform agreement in the literature as to whether the notion of analyticity is or can be made sufficiently clear for use in scientific philosophy. Both approaches have their defenders and their detractors. But between them they seem to be the most promising avenues for integrating the logic-mathematical part of science with the more straightforwardly empirical parts.
Since Carnap is and Quine can be argued to be within the logical empiricist tradition, this progress toward such unification can be counted as part of the legacy of the movement.
The commitment of some of the logical empiricists to the unity of science has been in recent years often discussed but less often understood. One hears in conversation that it was a sort of rearguard action designed to preserve as much as possible of a phenomenalist version of ontological reduction. One reads in print that it can be refuted by the obvious fact that the various sciences have quite distinct theoretical vocabularies Suppes Both reactions are misplaced.
It was the left wing of the Vienna Circle, and above all Otto Neurath, that championed the unity of science. They also promoted physicalism, anti-foundationalism, and a generally naturalistic viewpoint. A great many philosophers of many different persuasions participated in that project. The project may have been unified science, but they did not have a completely unified view of what that project was. Here we will discuss the Neurath and Carnap versions of it to see what their central concerns were.
Neurath seems to have had two primary motivations to advance under the banner of the unity of science. First, he was concerned that there be no a priori methodological cleavage between the natural and the social sciences. On the social scientific side he was concerned that these sciences not condone some private, mysterious mode of insight empathy whose results could not be checked against more ordinary public observation.
Such a methodology would be a harbor for metaphysics. On the natural scientific side, he was concerned to point out that, for Duhemian and other reasons, the situation is much messier than is sometimes supposed, and so invidious comparisons by natural scientists at the expense of social science were unwarranted.
Second, because Neurath was socially and politically engaged he was concerned that the various sciences be connected in such a way that they could be used together to solve complex human and social problems. In recent years it is sometimes claimed that Neurath meant by the unity of science what some contemporary philosophers have defended as the disunity of science.
One cannot rule this claim out a priori. But the often substantial differences among the current defenses of disunity make evaluating this claim difficult. It is fair to say, however, that Neurath was suspicious of grand hypotheses, familiar since the 19 th century to derive all of chemistry, biology, psychology, and the social sciences in that order from a few basic principles of physics.
It is unclear whether this stems from a general opposition to system building, since he was eager to develop inferential connections among the various sciences. Perhaps this is better expressed as an opposition to speculative system building and to the idea that there is only one way of systematizing our science than to systematicity as such.
Carnap distinguished the unity of the language of science from the unity of the laws of science. He wanted to defend the former and to say what would be required for the latter. As far as the unity of the language of science, Carnap did in the Aufbau try to initiate a program for defining all of scientific concepts on the basis of a very small number of basic concepts, perhaps only one basic concept. That does afford a certain conceptual economy, but it is now generally held by Carnap scholars see especially Friedman and Richardson that ontological reduction and reduction to a phenomenalist basis was far from his motive.
Carnap explicitly acknowledged that another system of definitions, one with a physicalist basis, might also be possible. The answer is given in terms of shared inferential structure and identifying any given concept with a unique place within that shared overall structure.
This is a highly holistic conception of concepts and it depends on thinking of the body of scientific commitments as a whole, as a unity. The Aufbau was largely drafted before Carnap joined the Vienna Circle. Once there and under some influence from Neurath, Carnap campaigned more insistently for physicalism and for the unity of science.
They seemed often to be two sides of the same coin. Until his death in , Neurath was in each case the main editor and Carnap either the associate editor or one of the associate editors.
The International Encyclopedia of Unified Science , begun in is undoubtedly the most famous of these. The dates here are relevant because by the time of this essay Carnap had already decided Carnap —37 that theoretical terms could not in general be given explicit definitions in the observation language even though the observation reports were already in a physicalist vocabulary.
The partially defined theoretical terms could not be eliminated. This seems to have caused Carnap no consternation at all, and it never seems to have occurred to him that there was any conflict whatever between this result and the unity of science. This is because by this point the elimination of concepts was not the point of the exercise; their inferential and evidential integration was.
This is also the key to what Carnap means by the unity of the language of science. The language of science is unified, no matter how different and exotic its various technical vocabularies may be, when each of its terms is reduced to can be tested in a common public observation vocabulary.
The call for the unity of the language of science, then, amounts to no more than the demand that the various claims of the separate sciences should be publicly testable in a common observation language. Controversies will of course arise as to what the observational vocabulary should be and what are the acceptable forms of linkage.
That does not seem to be an unreasonable demand. The unity of the language of science so far discussed is quite a different issue from the unity of the laws of science. The latter issue concerns the extent to which the laws of one special science can be inferred from those of another.
Carnap tries to articulate what would be involved in such a unification, but he nowhere says that such a unity is either possible or mandatory.
Finding any sort of inferential connections among sets of laws would be welcome of course. But the question of how much unity there is, if any, among the various sciences is an empirical question that philosophers are ill equipped to answer.
Philosophers should not make pronouncements, especially in advance of having putative laws in hand, either that scientific laws are unified or that they are not. A certain modest deference to the empirical facts that philosophers generally do not have, again, does not seem unreasonable.
Taking unity as a working hypothesis, as some philosophers have done, amounts to looking for inferential and nomological connections among various sets of laws, but not to the assertion that such connection will be found. Even if we accept the idea that such connections would be welcome if found, the question of whether one should spend significant effort in looking for them is not thereby answered.
There are two broad approaches to probability represented in logical empiricism. One of these, the so-called frequentist approach, has an extensive 19 th century history and was further developed from about onward by Richard von Mises and Hans Reichenbach. The other is the epistemic approach to probability.
This goes back at least to Laplace at the end of the 18 th century. While Ramsey visited the Vienna Circle he was not much influenced by its members on these matters.
By contrast, Jeffrey studied and later collaborated with Carnap but also made significant contributions of his own. It is natural to begin thinking about probabilities with a simple mathematical account that takes as its point of departure various games of chance involving cards, dice, or coins.
Bettors have long noted that some outcomes are much more likely than others. In this context it is convenient to take the probability of a kind of outcome to be the ratio of such outcomes to all possible outcomes. Usually for reasons of symmetry in the physical set up, the possible outcomes are assumed to be equally likely. Where that assumption happens to be true or nearly so the empirical results of, say, a great many throws of a pair of dice tends to be close to what the simple mathematical account would suggest.
Conversely, where the outcomes deviate from the expected ratios, bettors begin to suspect that the dice, coins, and cards or the manipulations of them are not all that they seem. The suspicion is that the outcomes are not equally likely and that the simple mathematical account does not apply. These facts suggest both two limitations of the simple account and the beginnings of a way around them. The first limitation is that the account applies only where the outcomes can be partitioned into alternatives that are equally likely.
This is not the case when dice are loaded or in such real world cases as radioactive decay or weather forecasting. A second limitation is that the account, in describing the possible outcomes as equally likely, implicitly appeals to the very probability notion for which clarification was sought.
The realization that we can sometimes discover the falsehood of the assumption of equal likelihood and make a much more reasonable estimate of probability by making a large number of trials is very suggestive.
And from his dissertation onward Reichenbach worked out a variety of imagined physical models that could guide ones thinking about probability in useful ways. The result is what is often called the frequency theory of probability or sometimes the statistical frequency theory or the limit frequency theory. Even a perfectly fair coin in an odd number of flips will never result in exactly the same number of heads and of tails. When the coin is fair and the number of flips is even, an outcome perfectly balanced between heads and tails is not guaranteed either.
We will never make an infinite number of flips either, and in actual cases a large finite number of flips might so erode the coin as to bias the coin and discredit the result. Notwithstanding these limitations on an actual series of trials one can imagine an infinite series of trials and define a notion of probability with respect to it. This raises its own difficulty, namely that ratios are not defined for infinite collections. They would be defined, however, for any finite initial segment of such an infinite series, thus giving a sequence of ratios.
If this sequence of ratios settles down on a limit, the probability of the coin showing a head given that it has been flipped can be defined as the limit of the ratio of heads to total flips as the number of flips goes to infinity. While probability thus defined has a somewhat counterfactual character, that is not an obvious defect.
Moreover, this notion of probability applies perfectly well to biased coins and loaded dice, as well as to radioactive decay. On the surface at least it also seem to avoid using the notion of probability in its own definition, and in these respects it seems to be an important improvement over the simple mathematical model with which we began.
A problem that remained troublesome concerns the fact that one often wants to assign probabilities to particular events, events that in the nature of things cannot be repeated in all their particularity. Thus it is unclear how a frequency theory of probability is to be applied to such individual cases.
This is often called the problem of the single case. It is a little difficult to assess how serious this is, because in actual practice we often have no difficulty in making probability assignments to single cases.
Suppose we are interested in the probability of rain tomorrow. Tomorrow will never be repeated, and we want to estimate the probability now. What we do is to look back through the records to find days relevantly like today and determine in what fraction of those cases those days were followed by rainy days and use that as our estimate.
Even if we are comfortable with this practice, however, it is another matter to say why this should give us a reasonable estimate of the value of the limit involved in a logically impossible infinite sequence. This problem of the single case was much discussed, and Wesley Salmon made progress in dealing with it.
Salmon There are residual difficulties in making estimates of the probabilities on the basis of finite evidence. The problem is that even when we are assured that the sequence of ratios has a limit, we have no a priori grounds for saying how close the current ratio is to that limit.
This just takes the most recent ratio as the desired estimate. This is a good practical solution where the number of trials is already high, but this does not really say why the estimate should be good, how good it is supposed to be, or how many trials would be high enough. In addition, the straight rule can yield counterintuitive results where the number of trials is small.
Though there are these issues outstanding, frequency theories define a concept of probability indispensable for quantum theories and for a wide variety of other applications in the natural and social sciences. It was not the only concept of probability to be developed by the logical empiricist tradition. The primary other such concept was the epistemic conception of probability. We will begin with Carnap and then move to those who developed a subjectivist account. Carnap is addressing a different issue than was addressed by von Mises and Reichenbach.
Instead of focusing on physical phenomena and ratios within them, Carnap focuses on arguments and takes as his point of departure the widespread conviction that some arguments are stronger, in varying degrees, than others, even for the same conclusion.
Similarly some bodies of evidence can give us more reason to believe a given conclusion than would another body of evidence. Carnap sets as his task the development of a quantitative concept of probability that will clarify and explicate these widespread convictions. Such a quantitative concept would be an extraordinarily useful tool, and it would be a useful successor to our ordinary, somewhat scattered notions of confirmation and induction.
Carnap approaches the problem by first considering extremely limited artificial languages and trying to find a confirmation function that will work for that. If he succeeds he would then try to develop an account that would work for a broader and richer range of languages. In this his approach is like that of a physicist developing a physical theory for the highly artificial situation of a billiard table or air track and then broadening the theory to deal with a wider range of cases.
In any case, Carnap is not trying to describe our linguistic habits but to clarify or even to replace them with something more useful.
By Carnap also distinguished the two approaches described here, insisting that they were not competitors but were attempting to explicate two different concepts of probability. One need not choose one as the only concept; both concepts were useful. Reichenbach, by contrast, never conceded that both concepts were needed and insisted that his frequency notion could serve all epistemic purposes for which any notion of probability is needed.
The confirmation functions have to meet some basic mathematical conditions. The axioms that state these conditions partially define a function, and this function can be interpreted in a number of ways.
Carnap himself lists three in Carnap This took Carnap even closer in conception to the work of such subjectivists as Ramsey and de Finetti. Indeed, the discussion of fair betting quotients, and related issues of Dutch book arguments had been initiated by de Finetti. As his work proceeded Carnap tended to explain probabilities by reference to events and propositions rather than speak overtly about sentences. It is not clear, however, whether this amounts to a major change of view or a change in what he sees as the most felicitous mode of expression.
As the years progressed Carnap tended to see the remaining differences between himself and his subjectivist co-workers as chiefly differences in emphasis. In any case the subjectivist tradition is now dominant in philosophical discussions of probability Zabell , Jeffrey himself made major contributions including a principle for updating ones beliefs when the evidence one learns is not certain. Unlike the epistemic approach of Carnap and others, Popper was not trying to clarify inductive relations because he did not believe that there are inductive inferences.
Theories can be corroborated by their passing severe tests, but they are not thereby inductively confirmed or made more probable. Propensities are thought of as tendencies of a physical event or state to produce another event or state. Popper has specifically applied propensities to single non-repeatable events , and that suggests that the concept of propensity does not involve any essential reference to long sequences of events.
Popper has also taken propensities as producing outcomes with a certain limit frequency This does suggest a rather closer tie to the statistical frequency approach.
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