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"The older positivists
wished to admit, as scientific or legitimate, only those *concepts*
(or notions or ideas) which were, as they put it, 'derived from
experience'; those concepts, that is, which they believed to be
logically reducible to elements of sense-experience, such as
sensations (or sense-data), impressions, perceptions, visual or
auditory memories, and so forth. Modern positivists are apt to see
more clearly that science is not a system of concepts but rather a
system of *statements.* (footnote on Wittgenstein omitted)
Accordingly, they wished to admit, as scientific or legitimate, only
those statements which are reducible to elementary (or 'atomic')
statements of experience - to 'judgments of perception' or 'atomic
propositions' or 'protocol-sentences' or what not. (footnote: Nothing
depends on names, of course. When I invented the new name 'basic
statement' (or 'basic proposition'; see below, section 7 and 28) I
did so only because I needed a term *not* burdened with the
connotation of a perception statement. But unfortunately it was soon
adopted by others, and used to convey precisely the kind of meaning
which I wished to avoid. Cf. also my Postscript, *29"
****LScD, 1959, page 34-35
"The problem of the 'Empirical Basis'.
If falsifiability is to be at all applicable as a criterion of demarcation then singular statements must be available which can serve as the premises in falsifying inferences. our criterion therefore appears only to shift the problem - to lead us back from the question of the empirical character of theories to the question of the empirical character of singular statements.
Yet even so, something has been gained. For in the practice of scientific research, demarcation is sometimes of immediate urgency in connection with theoretical systems, whereas in connection with singular statements, doubt as to their empirical character rarely arises. It is true that errors of observation occur and that they give rise to false singular statements, but the scientists scarcely ever has occasion to describe a singular statement as non-empirical or metaphysical.
*Problems of the empirical basis* - that is, problems concerning the empirical character of singular statements, and how they are tested - thus play a part within the logic of science that differs somewhat from that played by most of the other problems which will concern us. For most of these stand in close relation to the *practice* of research, whilst the problem of the empirical basis belongs almost exclusively to the *theory* of knowledge. I shall have to deal with them, however, since they have given rise to many obscurities. This is especially of the relation between *perceptual experiences* and *basic statements*. (What I call a 'basic statement' or a 'basic proposition' is a statement which can serve as a premise in an empirical falsification; in brief, a statement of a singular fact.)
Perceptual experiences have often been regarded as providing as kind of justification for basic statements. It was held that these statements are 'based upon' experiences; that their truth becomes 'manifest by inspection' through these experiences; or that it is made 'evident' by these experiences, etc. All these expressions exhibit the perfectly sound tendency to emphasize the close connection between basic statements and our perceptual experiences. Yet is was also rightly felt that *statements can be logically justified only by statements*. Thus the connection between the perceptions and the statements remained obscure, and was described by correspondingly obscure expressions which elucidated nothing, but slurred over the difficulties or, at best, adumbrated them through metaphors.
Here too a solution can be found, I believe, if we clearly separate the psychological from the logical and methodological aspects of the problem. We must distinguish between, on the one hand, *our subjective experiences or our feelings of conviction*, which can never justify any statement (though they can be made the subject of psychological investigation) and on the other hand, the *objective logical relations* subsisting among the various systems of scientific statements, and within each of them."
****LScD, 1959, page 34-35
"The problem of the 'Empirical Basis'.
If falsifiability is to be at all applicable as a criterion of demarcation then singular statements must be available which can serve as the premises in falsifying inferences. our criterion therefore appears only to shift the problem - to lead us back from the question of the empirical character of theories to the question of the empirical character of singular statements.
Yet even so, something has been gained. For in the practice of scientific research, demarcation is sometimes of immediate urgency in connection with theoretical systems, whereas in connection with singular statements, doubt as to their empirical character rarely arises. It is true that errors of observation occur and that they give rise to false singular statements, but the scientists scarcely ever has occasion to describe a singular statement as non-empirical or metaphysical.
*Problems of the empirical basis* - that is, problems concerning the empirical character of singular statements, and how they are tested - thus play a part within the logic of science that differs somewhat from that played by most of the other problems which will concern us. For most of these stand in close relation to the *practice* of research, whilst the problem of the empirical basis belongs almost exclusively to the *theory* of knowledge. I shall have to deal with them, however, since they have given rise to many obscurities. This is especially of the relation between *perceptual experiences* and *basic statements*. (What I call a 'basic statement' or a 'basic proposition' is a statement which can serve as a premise in an empirical falsification; in brief, a statement of a singular fact.)
Perceptual experiences have often been regarded as providing as kind of justification for basic statements. It was held that these statements are 'based upon' experiences; that their truth becomes 'manifest by inspection' through these experiences; or that it is made 'evident' by these experiences, etc. All these expressions exhibit the perfectly sound tendency to emphasize the close connection between basic statements and our perceptual experiences. Yet is was also rightly felt that *statements can be logically justified only by statements*. Thus the connection between the perceptions and the statements remained obscure, and was described by correspondingly obscure expressions which elucidated nothing, but slurred over the difficulties or, at best, adumbrated them through metaphors.
Here too a solution can be found, I believe, if we clearly separate the psychological from the logical and methodological aspects of the problem. We must distinguish between, on the one hand, *our subjective experiences or our feelings of conviction*, which can never justify any statement (though they can be made the subject of psychological investigation) and on the other hand, the *objective logical relations* subsisting among the various systems of scientific statements, and within each of them."
****LScD, 1959 page
43-44
We may now return to a point made in the previous section: to my thesis that a subjective experience or a feeling of conviction, can never justify a scientific statement, and that within science it can play no part except that of an object of an empirical (a psychological) inquiry. No matter how intense a feeling of conviction it may be, it can never justify a statement. Thus I may be utterly convinced of a the truth of a statement; certain of the evidence of my perceptions; overwhelmed by the intensity of my experience; every doubt may seem to me absurd. But does this afford the slightest reason for science to accept any statements? Can any statement be justified by the fact that K.R.P. is utterly convinced of its truth? The answer is, 'No'; and any other answer would be incompatible with the idea of scientific objectivity. Even the fact, for me is firmly established, that I am experiencing this feeling of conviction, cannot appear within the field of objective science except in the form of a *psychological hypothesis* which, of course, call for inter-subjective testing; from the conjecture that I have this feeling of conviction the psychologist may deduce, with the help of psychological and other theories, certain predictions about my behaviour; and these may be confirmed or refuted in the course of experimental tests. But from the epistemological point of view, it is quite irrelevant whether my feeling of conviction was strong or weak; whether it came from a strong or even irresistible impression of indubitable certainty (or 'self-evidence'), or merely from a doubtful surmise. None of this has any bearing on the question of how scientific statements can be justified.
Consideration like these do not of course provide and answer to the problem of the empirical basis. But at least they help us to see its main difficulty. In demanding of objectivity for basic statements as well as of other scientific statements we deprive ourselves of any logical means by which we might have hope to reduce the truth of scientific statements, we deprive ourselves of any logical means by which we might have hoped to reduce the truth of scientific statements to our experiences. Moreover we debar ourselves from granting any favoured status to statements which describe experiences, such as those statement which describe our perceptions (and which are sometimes call 'protocol sentences'). They can occur in science only as psychological statements; and this means, as hypotheses of a kind whose standards of inter-subjective testing (considering the present state of psychology) are certainly not very high.
Whatever may be our eventual answer to the question of the empirical basis, one thing must be clear: if we adhere to our demand that scientific statements must be objective, then those statements which belong to the empirical basis of science must also be objective, i.e. inter-subjectively testable. Yet inter-subjective testability always implies that, from the statements which are to be tested, other testable statements can be deduced. Thus if the basic statements in their turn are to be inter-subjectively testable, there can be *no ultimate statements in science*: there can be no statements in science which cannot be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them.
We thus arrive at the following view. Systems of theories are tested by deducing from them statements of a lesser level of universality. These statements in their turn, since they are to be inter-subjectively testable, must be testable in like manner - and so *ad infinitum.*
It might be thought that this view leads to an infinite regress, and that it is therefore untenable. In section I, when criticizing induction, I raised the objection that it may lead to an infinite regress; and it might well appear to the reader now that the very same objection can be urged against that procedure of deductive testing which I myself advocate. However, this is not so. The deductive method of testing cannot establish or justify the statements which are being tested nor is it intended to do so. Thus there is no danger of an infinite regress. But it must be admitted that the situation to which I have drawn attention - testability *ad infinitum* and the absence of ultimate statements which are not in need of tests - does create a problem. For, clearly, tests cannot in fact be carried on *ad infinitum*: sooner or later we have to stop. Without discussing this problem here in detail, I only wish to point out that that fact that the test cannot go on for ever does not clash with my demand that every scientific statement must be testable. For I do not demand that every scientific statement must *have in fact been tested* before it is accepted. I only demand that every such statement must be *capable* of being tested; or in other words, I refuse to accept the view that there are statements in science which we have, resignedly, to accept as true merely because it does not seem possible, for logical reason, to test them."
We may now return to a point made in the previous section: to my thesis that a subjective experience or a feeling of conviction, can never justify a scientific statement, and that within science it can play no part except that of an object of an empirical (a psychological) inquiry. No matter how intense a feeling of conviction it may be, it can never justify a statement. Thus I may be utterly convinced of a the truth of a statement; certain of the evidence of my perceptions; overwhelmed by the intensity of my experience; every doubt may seem to me absurd. But does this afford the slightest reason for science to accept any statements? Can any statement be justified by the fact that K.R.P. is utterly convinced of its truth? The answer is, 'No'; and any other answer would be incompatible with the idea of scientific objectivity. Even the fact, for me is firmly established, that I am experiencing this feeling of conviction, cannot appear within the field of objective science except in the form of a *psychological hypothesis* which, of course, call for inter-subjective testing; from the conjecture that I have this feeling of conviction the psychologist may deduce, with the help of psychological and other theories, certain predictions about my behaviour; and these may be confirmed or refuted in the course of experimental tests. But from the epistemological point of view, it is quite irrelevant whether my feeling of conviction was strong or weak; whether it came from a strong or even irresistible impression of indubitable certainty (or 'self-evidence'), or merely from a doubtful surmise. None of this has any bearing on the question of how scientific statements can be justified.
Consideration like these do not of course provide and answer to the problem of the empirical basis. But at least they help us to see its main difficulty. In demanding of objectivity for basic statements as well as of other scientific statements we deprive ourselves of any logical means by which we might have hope to reduce the truth of scientific statements, we deprive ourselves of any logical means by which we might have hoped to reduce the truth of scientific statements to our experiences. Moreover we debar ourselves from granting any favoured status to statements which describe experiences, such as those statement which describe our perceptions (and which are sometimes call 'protocol sentences'). They can occur in science only as psychological statements; and this means, as hypotheses of a kind whose standards of inter-subjective testing (considering the present state of psychology) are certainly not very high.
Whatever may be our eventual answer to the question of the empirical basis, one thing must be clear: if we adhere to our demand that scientific statements must be objective, then those statements which belong to the empirical basis of science must also be objective, i.e. inter-subjectively testable. Yet inter-subjective testability always implies that, from the statements which are to be tested, other testable statements can be deduced. Thus if the basic statements in their turn are to be inter-subjectively testable, there can be *no ultimate statements in science*: there can be no statements in science which cannot be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them.
We thus arrive at the following view. Systems of theories are tested by deducing from them statements of a lesser level of universality. These statements in their turn, since they are to be inter-subjectively testable, must be testable in like manner - and so *ad infinitum.*
It might be thought that this view leads to an infinite regress, and that it is therefore untenable. In section I, when criticizing induction, I raised the objection that it may lead to an infinite regress; and it might well appear to the reader now that the very same objection can be urged against that procedure of deductive testing which I myself advocate. However, this is not so. The deductive method of testing cannot establish or justify the statements which are being tested nor is it intended to do so. Thus there is no danger of an infinite regress. But it must be admitted that the situation to which I have drawn attention - testability *ad infinitum* and the absence of ultimate statements which are not in need of tests - does create a problem. For, clearly, tests cannot in fact be carried on *ad infinitum*: sooner or later we have to stop. Without discussing this problem here in detail, I only wish to point out that that fact that the test cannot go on for ever does not clash with my demand that every scientific statement must be testable. For I do not demand that every scientific statement must *have in fact been tested* before it is accepted. I only demand that every such statement must be *capable* of being tested; or in other words, I refuse to accept the view that there are statements in science which we have, resignedly, to accept as true merely because it does not seem possible, for logical reason, to test them."
****LScD,1959, page
45-46
"In this way we are lead to the demand that the theory should allow us to deduce, roughly speaking, more *empirical* singular statements than we can deduce from the initial conditions alone.
(Footnote: Foundations equivalent to the one given here have been put forward as criteria of the *meaningfulness* of *sentences* (rather than as criteria of *demarcation* applicable to theoretical *systems*) again and again after the publication of my book, even by critics who pooh-poohed my criterion of falsifiability. But it is easily seen that, if used as a criterion of *demarcation*, our present formulations is equivalent to falsifiability.
For if the basic statement b2 does not follow from b1, but follows from b1 in conjunction with the theory t (this is the present formulation) then this amounts to saying that the conjunctions of b1 with the negation of b2 contradicts the theory t. But the conjunction of b1 with the negation of b2 is a basic statements (cf. section 28). Thus our criterion demands the existence of a falsifying basic statement, i.e. it demands falsifiability in precisely my sense. (See also note *1 to section 82).
As a criterion of *meaning* (or 'weak verifiability') it breaks down, however, for various reasons. First, because the negations of some meaningful statements would become meaningless, according to this criterion. Secondly, because the conjunction of a meaningful statements and a 'meaningless pseudo-sentence' would become meaningful - which is equally absurd.
If we now try to apply these two criticism to our criterion of *demarcation, they both prove harmless. As to the first, see section 15 above, especially note *2 (and section *22 of my *Postscript). As to the second, empirical theories (such as Newton's) may contain 'metaphysical' elements. But these cannot be eliminated by a hard and fast rule; though if we succeed in so presenting the theory that it becomes a conjunction of a testable and a non-testable part, we know, of course, the we can now eliminate one of its metaphysical components.
The preceding paragraph of this note may be taken as illustrating another *rule of method.* (cf. the end of note *5 to section 80); that after having produced some criticisms of a rival theory, we should always make a serious attempt to apply this or a similar criticism to our own theory.)
This means that we must base our definition upon a particular class of singular statements; and this is the purpose for which we need the basic statements. Seeing that it would not be very easy to say in detail how a complicated theoretical system helps in the deduction of singular or basic statements, I propose the following definition. A theory is to be called 'empirical' or 'falsifiable' if it divides the class of all possible basic statements unambiguously into the following two non-empty subclasses. First, the class of all those basic statements with which it is inconsistent (or which it rules out, or prohibits); we call this the class of the *potential falsifiers* of the theory; and secondly, the class of those basic statements which it does not contradict (or which it 'permits'). We can put this more briefly by saying: a theory is falsifiable if the class of its potential falsifiers is not empty.
It may be added that a theory makes assertion only about its potential falsifiers. (It asserts their falsity.) About the 'permitted' basic statements it says nothing. in particular, it does not say that they are true. (footnote: In fact, many of the 'permitted' basic statements will, in the presence of the theory, contradict each other. (Cf. section 38.) For example, the universal law 'All planets move in circles' (i.e. 'Any set of positions of any one planet is co-circular' is trivially 'instantiated' by any set of no more than three positions of one planet; but two such 'instances' together will in most cases contradict the law.)
****LScD, 1959, page 85-86
"The requirement that the falsifying hypothesis must be empirical, and so falsifiable, only means that it must stand in a certain logical relationship to possible basic statements; thus the requirement only concerns the logical form of the hypothesis. The rider that the hypothesis should be corroborated refers to test which it ought to have passed - tests which confront it with accepted basic statements.
"In this way we are lead to the demand that the theory should allow us to deduce, roughly speaking, more *empirical* singular statements than we can deduce from the initial conditions alone.
(Footnote: Foundations equivalent to the one given here have been put forward as criteria of the *meaningfulness* of *sentences* (rather than as criteria of *demarcation* applicable to theoretical *systems*) again and again after the publication of my book, even by critics who pooh-poohed my criterion of falsifiability. But it is easily seen that, if used as a criterion of *demarcation*, our present formulations is equivalent to falsifiability.
For if the basic statement b2 does not follow from b1, but follows from b1 in conjunction with the theory t (this is the present formulation) then this amounts to saying that the conjunctions of b1 with the negation of b2 contradicts the theory t. But the conjunction of b1 with the negation of b2 is a basic statements (cf. section 28). Thus our criterion demands the existence of a falsifying basic statement, i.e. it demands falsifiability in precisely my sense. (See also note *1 to section 82).
As a criterion of *meaning* (or 'weak verifiability') it breaks down, however, for various reasons. First, because the negations of some meaningful statements would become meaningless, according to this criterion. Secondly, because the conjunction of a meaningful statements and a 'meaningless pseudo-sentence' would become meaningful - which is equally absurd.
If we now try to apply these two criticism to our criterion of *demarcation, they both prove harmless. As to the first, see section 15 above, especially note *2 (and section *22 of my *Postscript). As to the second, empirical theories (such as Newton's) may contain 'metaphysical' elements. But these cannot be eliminated by a hard and fast rule; though if we succeed in so presenting the theory that it becomes a conjunction of a testable and a non-testable part, we know, of course, the we can now eliminate one of its metaphysical components.
The preceding paragraph of this note may be taken as illustrating another *rule of method.* (cf. the end of note *5 to section 80); that after having produced some criticisms of a rival theory, we should always make a serious attempt to apply this or a similar criticism to our own theory.)
This means that we must base our definition upon a particular class of singular statements; and this is the purpose for which we need the basic statements. Seeing that it would not be very easy to say in detail how a complicated theoretical system helps in the deduction of singular or basic statements, I propose the following definition. A theory is to be called 'empirical' or 'falsifiable' if it divides the class of all possible basic statements unambiguously into the following two non-empty subclasses. First, the class of all those basic statements with which it is inconsistent (or which it rules out, or prohibits); we call this the class of the *potential falsifiers* of the theory; and secondly, the class of those basic statements which it does not contradict (or which it 'permits'). We can put this more briefly by saying: a theory is falsifiable if the class of its potential falsifiers is not empty.
It may be added that a theory makes assertion only about its potential falsifiers. (It asserts their falsity.) About the 'permitted' basic statements it says nothing. in particular, it does not say that they are true. (footnote: In fact, many of the 'permitted' basic statements will, in the presence of the theory, contradict each other. (Cf. section 38.) For example, the universal law 'All planets move in circles' (i.e. 'Any set of positions of any one planet is co-circular' is trivially 'instantiated' by any set of no more than three positions of one planet; but two such 'instances' together will in most cases contradict the law.)
****LScD, 1959, page 85-86
"The requirement that the falsifying hypothesis must be empirical, and so falsifiable, only means that it must stand in a certain logical relationship to possible basic statements; thus the requirement only concerns the logical form of the hypothesis. The rider that the hypothesis should be corroborated refers to test which it ought to have passed - tests which confront it with accepted basic statements.
(footnote: This reference to accepted basic statements may seem to contain the seed of an infinite regress. For our problem here is this. Since a hypothesis is falsified by *accepting* a basic statement, we need *methodological rules for the acceptance of basic statements.* Now if these rules in their turn refer to accepted basic statements, we may get involved in an infinite regress. To this I reply that the rules we need are merely rules for accepting basic statements that falsify a well-tested and so far successful hypothesis; and the accepted basic statements to which the rule has recourse need not be of this character. Moreover the rule formulated in the text is far from exhaustive; it only mentions an important aspect of the acceptance of basic statements that falsify an otherwise successful hypothesis, and it will be expanded in chapter v (especially in section 29).
Pofessor HJ. H. Woodger, in a personal communication, has raised the question *how often has an effect to be actually reproduced in order for it to be a 'reproducible effect' (or a 'discovery')? The answer is: in some cases *not even once.* If I assert that there is a family of white ravens in the New York Zoo, then I assert something which can be tested *in principle.* If somebody wishes to test it and is informed, upon arrival, that the family has died, or that it has never been heard of, it is left to him to accept or reject my falsifying basic statement. As a rule, he will have means for forming an opinion by examining witnesses, documents, etc.: that is to say, by appealing to other intersubjectively testable and reproducible facts.)
****LScD, 1959, page 87
"„ĪPerhaps it will make matters clearer and more intuitive if I now express my criterion in a more 'realistic' language. Although it is equivalent to the formal mode of speech, it may be a little nearer to ordinary usage.
In this 'realistic' mode of speech we can say that a singular statement (a basic statement) describes an *occurrence.* Instead of speaking of basic statements which are ruled out or prohibited by a theory, we can then say that the theory rules out certain possible occurrences, and that it will be falsified if these possible occurrences do in fact occur. <cut>
Another term, 'event', will now be introduced, to denote what may be *typical or universal* about an occurrence, or what, if an occurrence, can be described with the help of universal names. (Thus we do not understand by an event a complex, or perhaps a protracted, occurrence, whatever ordinary usage may suggest.) We define: Let P(K), P (1) „Ī be elements of a class of occurrences which differ *only* in respect of the individuals (the spatio-temporal positions or regions) involved; then we call this class 'the event (P).' In accordance with this definition, we shall say, for example, of the statement 'A glass of water has just been upset here' that the class of statements which are equivalent to it is an element of the event, 'upsetting of a glass of water'.
Speaking of the singular statement p(k), which represents an occurrence P(k), one may say, in the realistic mode of speech, that this statement asserts the occurrence of the event (P) at the spatio-temporal position k. And we take this to mean the same as 'the class P(k), of the singular statements equivalent to p(k), is an element of the event (P)'. We will now apply this terminology to our problem. We can say of a theory, provided it is falsifiable, that it rules out, or prohibits not merely one occurrence, but always *at least one event*. Thus the class of the prohibited basic statements, i.e. of the potential falsifiers of the theory, will always contain, if it is not empty, an unlimited number of basic statements; for a theory does not refer to individuals as such. We may call the singular basic statements which belong to *one* even 'homotypic', so as to point to the analogy between *equivalent* statements describing *one* occurrence, and *homotypic* statements describing one (typical) event. We can then say that every non-empty class of potential falsifiers of a theory contains at least one non-empty class of homotypic basic statements."
****LScD, 1959, page
88-90
"The doctrine that the empirical sciences are reducible to sense perception, and thus to our experiences, is one which many accept as obvious beyond all question. However, this doctrine stand or falls with inductive logic, and is here rejected along with it. I do not wish to deny that there is a grain of truth in the view that mathematics and logic are based on thinking, and the factual sciences on sense-perception. But what is true is this view has little bearing on the epistemological problem. And indeed, there is hardly any problem in epistemology which has suffered more severely from the confusion of psychology with logic and this problem on the basis of statements of experience.
<cut long digression about Fries and Fries's trilemma>
The doctrine flounders in my opinion on the problems of induction and of universals. For we can utter no scientific statement that does not go far beyond what can be known with certainty 'on the basis of immediate experience'. (This fact may be referred to as the 'transcendence inherent in any description'. Every description uses *universal* names (or symbols, or ideas); every statement has that character of a theory, or a hypothesis. The statement, 'Here is a glass of water' cannot be verified by any observational experience. The reason is that the *universals* which appear in it cannot be correlated with any specific sense-experience. (An 'immediate experience' is *only once 'immediately given'; it is unique.) By the word 'glass', for example, we denote physical bodies which exhibit a certain *law-like behaviour*, and the same holds for the word 'water'. Universals cannot be reduced to classes of experiences; they cannot be 'constituted'.
****LScD, 1959, page 93-94
"There is only one way to make sure of the validity of a chain of logical reasoning. This is to put it in the form in which it is most easily testable: we break it up into many small steps, each easy to check by anybody who has learn the mathematical or logical technique of transforming sentences. If after this anybody still raises doubts then we can only beg him to point out an error in the steps of the proof, or to think the matter over again. In the case of empirical sciences, the situation is much the same. Any empirical scientific statement can be presented (by describing experimental arrangements, etc.) in such a way that anyone who has learned the relevant technique can test it. If, as a result, he rejects the statement, then it will not satisfy us if he tells us all about his feelings of doubt or about his feelings of conviction as to his perceptions. What he must do is to formulate an assertion which contradicts our own, and give us his instructions for testing it. If he fails to do this we can only ask him to take another and perhaps a more careful look at our experiment, and think again.
An assertion which owning to its logical form is not testable can at best operate, within science, as a stimulus: it can suggest a problem. In the field of logic and mathematics, this may be exemplified by Fermat's problem, and in the field of natural history, say, by reports about sea-serpents. In such cases science does not say that the reports are unfounded; that Fermat was in error or that all the records of observed sea-serpents are lies. Instead, it suspends judgment."
****LScD, 1959, page 99-100
"It has already been briefly indicated what role the basic statements play within the epistemological theory I advocate. We need them in order to decide whether a theory is to be called falsifiable, i.e. empirical. (Cf. section 21) And we also need them for the corroboration of falsifying hypotheses, and thus for the falsification of theories. (Cf. section 22.)
Basic statements must therefore satisfy the following conditions. (a) From a universal statement without initial conditions, no basic statement can be deduced.
Footnote *1: When writing this, I believed that it was plain enough that from Newton's theory alone, without initial conditions, nothing of the nature of an observation statement can be deducible (and therefore certainly no basic statements). Unfortunately, it turned out that this fact, and its consequences for the problem of observation statements or 'basic statements' was not appreciated by some of the critics of my book. I may therefore add here a few remarks.
"The doctrine that the empirical sciences are reducible to sense perception, and thus to our experiences, is one which many accept as obvious beyond all question. However, this doctrine stand or falls with inductive logic, and is here rejected along with it. I do not wish to deny that there is a grain of truth in the view that mathematics and logic are based on thinking, and the factual sciences on sense-perception. But what is true is this view has little bearing on the epistemological problem. And indeed, there is hardly any problem in epistemology which has suffered more severely from the confusion of psychology with logic and this problem on the basis of statements of experience.
<cut long digression about Fries and Fries's trilemma>
The doctrine flounders in my opinion on the problems of induction and of universals. For we can utter no scientific statement that does not go far beyond what can be known with certainty 'on the basis of immediate experience'. (This fact may be referred to as the 'transcendence inherent in any description'. Every description uses *universal* names (or symbols, or ideas); every statement has that character of a theory, or a hypothesis. The statement, 'Here is a glass of water' cannot be verified by any observational experience. The reason is that the *universals* which appear in it cannot be correlated with any specific sense-experience. (An 'immediate experience' is *only once 'immediately given'; it is unique.) By the word 'glass', for example, we denote physical bodies which exhibit a certain *law-like behaviour*, and the same holds for the word 'water'. Universals cannot be reduced to classes of experiences; they cannot be 'constituted'.
****LScD, 1959, page 93-94
"There is only one way to make sure of the validity of a chain of logical reasoning. This is to put it in the form in which it is most easily testable: we break it up into many small steps, each easy to check by anybody who has learn the mathematical or logical technique of transforming sentences. If after this anybody still raises doubts then we can only beg him to point out an error in the steps of the proof, or to think the matter over again. In the case of empirical sciences, the situation is much the same. Any empirical scientific statement can be presented (by describing experimental arrangements, etc.) in such a way that anyone who has learned the relevant technique can test it. If, as a result, he rejects the statement, then it will not satisfy us if he tells us all about his feelings of doubt or about his feelings of conviction as to his perceptions. What he must do is to formulate an assertion which contradicts our own, and give us his instructions for testing it. If he fails to do this we can only ask him to take another and perhaps a more careful look at our experiment, and think again.
An assertion which owning to its logical form is not testable can at best operate, within science, as a stimulus: it can suggest a problem. In the field of logic and mathematics, this may be exemplified by Fermat's problem, and in the field of natural history, say, by reports about sea-serpents. In such cases science does not say that the reports are unfounded; that Fermat was in error or that all the records of observed sea-serpents are lies. Instead, it suspends judgment."
****LScD, 1959, page 99-100
"It has already been briefly indicated what role the basic statements play within the epistemological theory I advocate. We need them in order to decide whether a theory is to be called falsifiable, i.e. empirical. (Cf. section 21) And we also need them for the corroboration of falsifying hypotheses, and thus for the falsification of theories. (Cf. section 22.)
Basic statements must therefore satisfy the following conditions. (a) From a universal statement without initial conditions, no basic statement can be deduced.
Footnote *1: When writing this, I believed that it was plain enough that from Newton's theory alone, without initial conditions, nothing of the nature of an observation statement can be deducible (and therefore certainly no basic statements). Unfortunately, it turned out that this fact, and its consequences for the problem of observation statements or 'basic statements' was not appreciated by some of the critics of my book. I may therefore add here a few remarks.
First, nothing
observable follows from any pure all-statement -- 'All swans are
white' say. This is easily seen if we contemplate the fact that 'All
swans are white' and 'All swans are black' do not, of course,
contradict each other, but together merely imply that there are no
swans - clearly not an observation statement, and not even one that
can be verified'. (A unilaterally falsifiable statement like 'All
swans are white', by the way, has the same logical form as 'There are
no swans', for it is equivalent to 'There are no non-White
swans'.)
Now if this is admitted, it will be seen at once that the singular statements which *can* be deduced from purely universal statements cannot be basic statements. I have in mind statements of the form *'If there is a swan at the place k, then there is a white swan at the place k' (Or, 'At k, there is either no swan or a white swan.') We see now at once why these 'instantial statements' (as they may be called) are not basic statements. The reason is that these instantial statements *cannot play the role of test statements (or of potential falsifiers) which is precisely the role which basic statements are supposed to play. If we were to accept instantial statements as test statements, we should obtain for any theory (and thus both for 'All swans are white' *and* for 'All swans are black' ) an overwhelming number of verifications - indeed, an infinite number, once we accept as a fact that the overwhelming part of the world is empty of swans.
Since 'instantial statements' are derivable from universal ones, their negations must be potential falsifiers, and *may* therefore be basic statements (if the conditions stated below in the text are satisfied). Instantial statements, *vice versa*, will then be of the form of negated basic statements (see also note *4 to section 80). It is interesting to note that basic statements (which are too strong to be derivable from universal laws alone) will have a greater informative content than their instantial negations; which means that *the content of basic statements exceed their logical probability* (since it must exceed 1/2).
These were some of the considerations underlying my theory of the logic al form of basic statements. (See my Conjectures and Refutations, 1963, pp. 386 f.)
On the other hand, (b) a universal statement and a basic statement can contradict each other. Condition (b) can only be satisfied if it is possible to derive the negation of a basic statement from the theory which it contradicts. From this and condition (a) it follows that a basic statement must have a logical form such that its negations cannot be a basic statement in its turn.
We have already encountered statements whose logical form is different from that of their negations. These were universal statements and existential statements: they are negations of one another, and they differ in their logical form. *Singular* statements can be constructed in an analogous way. The statement: 'There is a raven in the space-time region k' may be said to be different in its logical form - and not only in its linguistic form - from the statement 'There is no raven in the space-time region k'. A statement of the form 'There is a so-and-so in the region k' or 'such-and-such an event is occurring in the region k' (cf. section 23 ) may be called a '*singular* existential statement' or a '*singular* there-is statement'. And the statement which results from negating it. i.e. "There is no so-and-so in the region k' or 'No event of such-and-such a kind is occurring in the region k', may be called '*singular* non-existence statement', or a '*singular* there-is-not statement'.
We may now lay down the following rule concerning basic statements: *basic statement have the form of singular existential statements.* This rule means that basic statements will satisfy condition (a), since a singular existential statement can never be deduced from a strictly universal statement, i.e. from a strict non-existence statement. They will also satisfy condition (b), as can be seen from the fact that from every singular existential statement a purely existential statement can be derived simply by omitting any reference to any individual space-time region; as we have seen, a purely existential statement may indeed contradict a theory.
Now if this is admitted, it will be seen at once that the singular statements which *can* be deduced from purely universal statements cannot be basic statements. I have in mind statements of the form *'If there is a swan at the place k, then there is a white swan at the place k' (Or, 'At k, there is either no swan or a white swan.') We see now at once why these 'instantial statements' (as they may be called) are not basic statements. The reason is that these instantial statements *cannot play the role of test statements (or of potential falsifiers) which is precisely the role which basic statements are supposed to play. If we were to accept instantial statements as test statements, we should obtain for any theory (and thus both for 'All swans are white' *and* for 'All swans are black' ) an overwhelming number of verifications - indeed, an infinite number, once we accept as a fact that the overwhelming part of the world is empty of swans.
Since 'instantial statements' are derivable from universal ones, their negations must be potential falsifiers, and *may* therefore be basic statements (if the conditions stated below in the text are satisfied). Instantial statements, *vice versa*, will then be of the form of negated basic statements (see also note *4 to section 80). It is interesting to note that basic statements (which are too strong to be derivable from universal laws alone) will have a greater informative content than their instantial negations; which means that *the content of basic statements exceed their logical probability* (since it must exceed 1/2).
These were some of the considerations underlying my theory of the logic al form of basic statements. (See my Conjectures and Refutations, 1963, pp. 386 f.)
On the other hand, (b) a universal statement and a basic statement can contradict each other. Condition (b) can only be satisfied if it is possible to derive the negation of a basic statement from the theory which it contradicts. From this and condition (a) it follows that a basic statement must have a logical form such that its negations cannot be a basic statement in its turn.
We have already encountered statements whose logical form is different from that of their negations. These were universal statements and existential statements: they are negations of one another, and they differ in their logical form. *Singular* statements can be constructed in an analogous way. The statement: 'There is a raven in the space-time region k' may be said to be different in its logical form - and not only in its linguistic form - from the statement 'There is no raven in the space-time region k'. A statement of the form 'There is a so-and-so in the region k' or 'such-and-such an event is occurring in the region k' (cf. section 23 ) may be called a '*singular* existential statement' or a '*singular* there-is statement'. And the statement which results from negating it. i.e. "There is no so-and-so in the region k' or 'No event of such-and-such a kind is occurring in the region k', may be called '*singular* non-existence statement', or a '*singular* there-is-not statement'.
We may now lay down the following rule concerning basic statements: *basic statement have the form of singular existential statements.* This rule means that basic statements will satisfy condition (a), since a singular existential statement can never be deduced from a strictly universal statement, i.e. from a strict non-existence statement. They will also satisfy condition (b), as can be seen from the fact that from every singular existential statement a purely existential statement can be derived simply by omitting any reference to any individual space-time region; as we have seen, a purely existential statement may indeed contradict a theory.
It should be noticed that he conjunction of two basic statements, p and r, which do not contradict each other, is in turn a basic statement. Sometimes we may even obtain a basic statement by joining one basic statement to another statement which is not basic. For example, we may form the conjunction of the basic statement, r 'There is a pointer at place k' with the singular non-existence statement ~p, 'There is no pointer in motion at the place k'. For clearly, the conjunction r'~p ('r-and-non-p') of the two statements is equivalent to the singular existential statement 'There is a pointer at rest at the place k'. This has the consequence that, if we are given a theory t and the initial conditions r, from which we deduce the prediction p, then the statement r'~p will be a falsifier of the theory, and so a basic statement. (On the other hand, the conditional statement 'r->p' i.e. 'If r then p' is no more basic than the negation ~p, since it is equivalent to the negation of a basic statement, viz. to the negation of r'~p.)
These are the formal requirements for basic statements; they are satisfied by all singular existential statements. In addition to these a basic statement must also satisfy a material requirement - a requirement concerning the event which, as the basic statement tell us, is occurring at the place k. This event must be an '*observable*' event; that is to say, basic statements must be testable, inter-subjectively, by 'observation.' Since they are singular statements, this requirement can of course only refer to observers who are suitably placed in space and time (a point which I shall not elaborate).
No doubt it will now seem as though in demanding observability, I have, after all, allowed psychologism to slip back quietly into my theory. But this is not so. Admittedly, it is possible to interpret the concept of an *observable event* in a psychologistic sense. But I am using it in such a sense that it might just as well be replaced by 'an event involving position and movement of macroscopic physical bodies'. Or we might lay it down, more precisely, that every basic statement must either be itself a statement about relative positions of physical bodies, or that it must be equivalent to some basic statement of this 'mechanistic' or 'materialistic' kind. (That this stipulation is practicable is connected with the fact that a theory which is inter-subjectively testable will also be inter-sensually (footnote omitted) testable. This is to say that tests involving the perception of one of our senses can, in principle, be replaced by tests involving other sense.) Thus the charge that, in appealing to observability, I have stealthily readmitted psychologism would have no more force than the charge that I have admitted mechanism or materialism. This shows that my theory is really quite neutral and that neither of these labels should be pinned to it. I say all this only so as to save the term 'observable', as I use it, from the stigma of psychologism. (Observations and perceptions may be psychological, but observability is not.) I have not intention of *defining* the term 'observable' or 'observable event', though I am quite ready to elucidate it by means of either psychologistic or mechanistic examples. I think that it should be introduced as an undefined term which becomes sufficiently precise in use: as a primitive concept whose use the epistemologist has to learn, much as he has to learn to use the term 'symbol', or as the physicist has to learn the use of the term 'mass-point'.
Basic statements are therefore -in the material mode of speech - statements asserting that an observable event is occurring in a certain individual region of space and time. The various terms used in this definition, with the exception of the primitive term 'observable', have been explained more precisely in section 23; 'observable' is undefined, but can also be explained fairly precisely, as we have seen here."
****LScD, 1959, page 100-103
"Every test of a theory, whether resulting in its corroboration or falsification, must stop at some basic statement or other which we *decide to accept*. If we do not come to any decision, and do not accept some basic statement or other, then the test will have led nowhere. But considered from a logical point of view, the situation is never such that it compels us to stop at this particular basic statement rather than at that, or else give up the test altogether. For any basic statement can again in its turn be subjected to test, using as a touchstone any of the basic statements which can be deduced from it with the help of some theory, either the one under test, or another. This procedure has no natural end (footnote omitted). Thus if the test is to lead us anywhere, nothing remains but to stop at some point or other and say that we are satisfied, for the time being.
It is fairly easy to see that we arrive in this way at a procedure according to which we stop only at a kind of statement that is especially easy to test. For it means that we are stopping at statements about whose acceptance or rejection the various investigators are likely to reach agreement. And if they do not agree, they will simply continue with the tests, or else start them all over again. If this too lead to no result, then we might say that the statements in question were not inter-subjectively testable, or that we were not, after all dealing with observable events. If some day it should no longer be possible for scientific observers to reach agreement about basic statements this would amount to a failure of language as a means of universal communication. It would amount to a new 'Babel of Tongues': scientific discovery would be reduced to absurdity. In this new Babel, the soaring edifice of science would soon lie in ruins."
****LScD, 1959, page 104
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