The Logic of Scientific Discovery

Moreover, it seems clear that the growth of scientifc knowledge is the most important and interesting case of the growth of knowledge

From Thales to Einstein, from ancient atomism to Descartes’s speculation about matter, from the speculations of Gilbert and Newton and Leibniz and Boscovic about forces to those of Faraday and Einstein about fields of forces, metaphysical ideas have shown the way

Tags: #epistemology

Now it is far from obvious, from a logical point of view, that we are justifed in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white.

Tags: #rationality #epistemology

Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement.Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in deductive logic. Thus the principle of induction must be a synthetic statement; that

Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement.Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in deductive logic.

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To justify it, we should have to employ inductive inferences; and to justify these we should have to assume an inductive principle of a higher order; and so on. Thus the attempt to base the principle of induction on experience breaks down, since it must lead to an infnite regress

The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as ‘metaphysical’ systems on the other, I call the problem of demarcation.

Tags: #epistemology

do not even go so far as to assert that metaphysics has no value for empirical science. For it cannot be denied that along with metaphysical ideas which have obstructed the advance of science there have been others—such as speculative atomism—which have aided it. And looking at the matter from the psychological angle, I am inclined to think that scientifc discovery is impossible without faith in ideas which are of a purely speculative kind, and sometimes even quite hazy; a faith which is completely unwarranted from the point of view of science, and which, to that extent, is ‘metaphysical

I do not even go so far as to assert that metaphysics has no value for empirical science. For it cannot be denied that along with metaphysical ideas which have obstructed the advance of science there have been others—such as speculative atomism—which have aided it. And looking at the matter from the psychological angle, I am inclined to think that scientifc discovery is impossible without faith in ideas which are of a purely speculative kind, and sometimes even quite hazy; a faith which is completely unwarranted from the point of view of science, and which, to that extent, is ‘metaphysical

a survey of some fundamental problems 17non-contradictory, a possible world.Secondly, it must satisfy the criterion of demarcation (cf. sections 6 and 21), i.e. it must not be metaphysical, but must represent a world of possible experience.Thirdly, it must be a system distinguished in some way from other such systems as the one which represents our world of experience. But how is the system that represents our world of experience to be distinguished? The answer is: by the fact that it has been submitted to tests, and has stood up to tests. This means that it is to be distinguished by applying to it that deductive method which it is my aim to analyse, and to describe.‘Experience’, on this view, appears as a distinctive method whereby one theoretical system may be distinguished from others; so that empirical science seems to be characterized not only by its logical form but, in addition, by its distinctive method.(This, of course, is also the view of the inductivists, who try to characterize empirical science by its use of the inductive method. ) The theory of knowledge, whose task is the analysis of the method or procedure peculiar to empirical science, may accordingly be described as a theory of the empirical method—a theory of what is usually called ‘experience’. 6 FALSIFIABILITY AS A CRITERION OF DEMARCATION The criterion of demarcation inherent in inductive logic—that is, the positivistic dogma of meaning—is equivalent to the requirement that all the statements of empirical science (or all ‘meaningful’ statements) must be capable of being fnally decided, with respect to their truth and falsity

The criterion of demarcation inherent in inductive logic—that is, the positivistic dogma of meaning—is equivalent to the requirement that all the statements of empirical science (or all ‘meaningful’ statements) must be capable of being finally decided, with respect to their truth and falsity

Tags: #epistemology

If there is no possible way to determine whether a statement is true then that statement has no meaning whatsoever. For the meaning of a statement is the method of its verifcation

These considerations suggest that not the verifability but the falsifability of a system is to be taken as a criterion of demarcation

These considerations suggest that not the verifability but the falsifability of a system is to be taken as a criterion of demarcation.* 3 In other words: I shall not require of a scientifc system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientifc system to be refuted by experience

My proposal is based upon an asymmetry between verifability and falsifability; an asymmetry which results from the logical form of universal statements.* 4 For these are never derivable from singular statements, but can be contradicted by singular statements

My use of the terms ‘objective’ and ‘subjective’ is not unlike Kant’s. He uses the word ‘objective’ to indicate that scientifc knowledge should be justifable, independently of anybody’s whim: a justifcation is ‘objective’ if in principle it can be tested and understood by anybody

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 scientifc statements, and within each of them

I shall, therefore, neither adopt nor reject the ‘principle of causality’; I shall be content simply to exclude it, as ‘metaphysical’, from the sphere of science

existential statements are not falsifable

however, to difculties which are connected with the problem of the empirical basis

This means that a defnite empirical meaning is assigned to a concept by correlating it with certain objects belonging to the real world. It is then regarded as a symbol of those objects. But it should have been clear that only individual names or concepts can be fxed by ostensively referring to ‘real objects’—say, by pointing to a certain thing and uttering a name, or by attaching to it a label bearing a name, etc. Yet the concepts which are to be used in the axiomatic system should be universal names, which cannot be defned by empirical indications, pointing, etc. They can be defned if at all only explicitly, with the help of other universal names; otherwise they can only be left undefned. That some universal names should remain undefned is therefore quite unavoidable; and herein lies the difculty

For the conventionalist, theoretical natural science is not a picture of nature but merely a logical construction. It is not the properties of the world which determine this construction; on the contrary it is this construction which determines the properties of an artifcial world: a world of concepts implicitly defned by the natural laws

For the conventionalist, theoretical natural science is not a picture of nature but merely a logical construction. It is not the properties of the world which determine this construction; on the contrary it is this construction which determines the properties of an artifcial world: a world of concepts implicitly defned by the natural laws which we have chosen. It is only this world of which science speaks

I do not demand any fnal certainty from science

We must clearly distinguish between falsifability and falsifcation. We have introduced falsifability solely

We must clearly distinguish between falsifability and falsifcation. We have introduced falsifability solely as a criterion for the empirical character of a system of statements

We say that a theory is falsifed only if we have accepted basic statements which contradict it (

The doctrine that the empirical sciences are reducible to senseperceptions, and thus to our experiences, is one which many accept as obvious beyond all question

Admittedly it is not incorrect to say that science is ‘… an instrument’ whose purpose is ‘… to predict from immediate or given experiences later experiences, and even as far as possible to control them

It has already been briefy indicated what rôle the basic statements play within the epistemological theory I advocate. We need them in order to decide whether a theory is to be called falsifable, i.e.empirical.(Cf. section 21. ) And we also need them for the corroboration of falsifying hypotheses, and thus for the falsifcation of theories

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 basic statement must also satisfy a material requirement—a requirement concerning the event which, as the basic statement tells 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

Statements about personal experiences—i.e. protocol sentences

‘Basic statements’ are ‘test statements’: they are, like all language, impregnated with theories

Thus it can be said that the amount of empirical information conveyed by a theory, or its empirical content, increases with its degree of falsifability

classes of ‘higher’ and ‘lower’ dimension, will be used here to tackle the problem of comparing degrees of testability. This is possible because basic statements, combined by conjunction with other basic statements, again yield basic statements which, however, are ‘more highly composite’ than their components; and this degree of composition of basic statements may be linked with the concept of dimension

Thus I regard the comparison of the empirical content of two statements as equivalent to the comparison of their degrees of falsifability. This makes our methodological rule that those theories should be given preference which can be most severely tested (cf. the anticonventionalist rules in section 20) equivalent to a rule favouring theories with the highest possible empirical content

If a statement p is more easy to falsify than a statement q, because it is of a higher level of universality or precision, then the class of the basic statements permitted by p is a proper subclass of the class of the basic statements permitted by q.

the superiority of methods that employ measurements over purely qualitative methods

Not for nothing do we call the laws of nature “laws”: the more they prohibit, the more they say

One of the issues which played a major rôle in most of the discussions of the theory of relativity was the simplicity of Euclidean geometry. Nobody ever doubted that Euclidean geometry as such was simpler than any non-Euclidean geometry with given constant curvature—not to mention non-Euclidean geometries with curvatures varying from place to place

The task of the calculus of probability consists, according to von Mises, simply and solely in this: to infer certain ‘derived collectives’ with ‘derived distributions’ from certain given ‘initial collectives’ with certain given ‘initial distributions

The task of the calculus of probability consists, according to von Mises, simply and solely in this: to infer certain ‘derived collectives’ with ‘derived distributions’ from certain given ‘initial collectives’ with certain given ‘initial distributions’;

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The task of the calculus of probability consists, according to von Mises, simply and solely in this: to infer certain ‘derived collectives’ with ‘derived distributions’ from certain given ‘initial collectives’ with certain given ‘initial distributions’; in short, to calculate probabilities which are not given from probabilities which are given