Tag: logic

The testability of facts

Higher level empirical statements have always the character of hypotheses relative to the lower level statements de­ducible from them: they can be falsified by the falsification of these less universal statements. But in any hypothetical deductive system, these less universal statements are themselves still strictly universal statements, in the sense here understood. Thus they too must have the character of hypotheses—a fact which has often been overlooked in the case of lower-level universal statements.

I shall say even of some singular statements that they are hypothetical, seeing that conclusions may be derived from them (with the help of a theoretical system) such that the falsification of these conclusions may falsify the singular statements in question. [55]

Assumptional contraband

Scientific theories are perpetually changing. This is not due to mere chance but might well be expected, according to our characterization of empirical science.

Perhaps this is why, as a rule, only branches of science—and these only temporarily—ever acquire the form of an elab­orate and logically well-constructed system of theories. In spite of this, a tentative system can usually be quite well sur­veyed as a whole, with all its important consequences. This is very necessary; for a severe test of a system presup­poses that it is at the time sufficiently definite and final in form to make it impossible for new assumptions to be smug­gled in. In other words, the system must be formulated sufficiently clearly and definitely to make every new assumption easily recognizable for what it is: a modification and therefore a revision of the system. [50]

Falsifying universal statements

Statements in which only universal names and no individual names occur will here be called ‘strict’ or ‘pure’. Most important among them are the strictly universal statements which I have already discussed. In addition to these, I am especially interested in statements of the form ‘there are black ravens’, which may be taken to mean the same as ‘there exists at least one black raven’. Such statements will be called strictly or purely existential state­ments (or ‘there-is’ statements).

The negation of a strictly universal statement is always equivalent to a strictly existential statement and vice versa. For example, ‘not all ravens are black’ says the same thing as ‘there exists a raven which is not black’, or ‘there are non-black ravens’.

The theories of natural science, and especially what we call natural laws, have the logical form of strictly universal statements; thus they can be expressed in the form of negations of strictly existential statements or, as we may say, in the form of non-existence statements (or ‘there-is-not’ statements). For example, the law of the conservation of energy can be expressed in the form: ‘There is no perpetual motion machine’, or the hypothesis of the electrical elementary charge in the form: ‘There is no electrical charge other than a multiple of the electrical elementary charge’.

In this formulation we see that natural laws might be compared to ‘proscriptions’ or ‘prohibitions’. They do not assert that something exists or is the case; they deny it. They insist on the non-existence of certain things or states of affairs, proscribing or prohibiting, as it were, these things or states of affairs: they rule them out. And it is precisely because they do this that they are falsifiable. If we accept as true one singular statement which, as it were, infringes the prohibition by asserting the existence of a thing (or the occurrence of an event) ruled out by the law, then the law is refuted. [47-8]

The goal of the scientist’s endeavours

My only reason for proposing my criterion of demarcation is that it is fruitful: that a great many points can be clarified and explained with its help. ‘Definitions are dogmas; only the conclusions drawn from them can afford us any new in­sight’, says Menger. This is certainly true of the definition of the concept ‘science’. It is only from the consequences of my definition of empirical science, and from the methodological decisions which depend upon this definition, that the scientist will be able to see how far it conforms to his intuitive idea of the goal of his endeavours. [33-4]

Science’s methodological rules

Two simple examples of methodological rules may be given. They will suffice to show that it would be hardly suitable to place an inquiry into method on the same level as a purely logical inquiry.

(1) The game of science is, in principle, without end. He who decides one day that scientific statements do not call for any further test, and that they can be regarded as finally verified, retires from the game.

(2) Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out with­out ‘good reason’. A ‘good reason’ may be, for instance: replacement of the hypothesis by another which is better test­able; or the falsification of one of the consequences of the hypothesis. (The concept ‘better testable’ will later be ana­lysed more fully.) …

In establishing these rules we may proceed systematically. First a supreme rule is laid down which serves as a kind of norm for deciding upon the remaining rules, and which is thus a rule of a higher type. It is the rule which says that the other rules of scientific procedure must be designed in such a way that they do not protect any statement in science against falsification. [32-3]

The meaninglessness of a criterion of meaning

The positivist dislikes the idea that there should be meaningful problems outside the field of ‘positive’ empirical science—problems to be dealt with by a genuine philosophical theory. He dislikes the idea that there should be a genuine theory of knowledge, an epistemology or a methodology. He wishes to see in the alleged philosophical problems mere ‘pseudo-problems’ or ‘puzzles’. Now this wish of his—which, by the way, he does not express as a wish or a proposal but rather as a statement of fact—can always be gratified. For nothing is easier than to unmask a problem as ‘meaning­less’ or ‘pseudo’. All you have to do is to fix upon a conveniently narrow meaning for ‘meaning’, and you will soon be bound to say of any inconvenient question that you are unable to detect any meaning in it. Moreover, if you admit as meaningful none except problems in natural science, any debate about the concept of ‘meaning’ will also turn out to be meaningless. The dogma of meaning, once enthroned, is elevated forever above the battle. It can no longer be at­tacked. It has become (in Wittgenstein’s own words) ‘unassailable and definitive’. [29-30]

Strict logical analysis only gets you nowhere

I am quite ready to admit that there is a need for a purely logical analysis of theories, for an analysis which takes no account of how they change and develop. But this kind of analysis does not elucidate those aspects of the empirical sciences which I, for one, so highly prize. A system such as classical mechanics may be ‘scientific’ to any degree you like; but those who uphold it dogmatically—believing, perhaps, that it is their business to defend such a successful system against criticism as long as it is not conclusively disproved—are adopting the very reverse of that critical attitude which in my view is the proper one for the scientist. In point of fact, no conclusive disproof of a theory can ever be pro­duced; for it is always possible to say that the experimental results are not reliable, or that the discrepancies which are asserted to exist between the experimental results and the theory are only apparent and that they will disappear with the advance of our understanding. (In the struggle against Einstein, both these arguments were often used in support of Newtonian mechanics, and similar arguments abound in the field of the social sciences.) If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.

If therefore we characterize empirical science merely by the formal or logical structure of its statements, we shall not be able to exclude from it that prevalent form of metaphysics which results from elevating an obsolete scientific theory into an incontrovertible truth.

Such are my reasons for proposing that empirical science should be characterized by its methods: by our manner of dealing with scientific systems: by what we do with them and what we do to them. Thus I shall try to establish the rules, or if you will the norms, by which the scientist is guided when he is engaged in research or in discovery, in the sense here understood. [28-9]

Scientific objectivity

The words ‘objective’ and ‘subjective’ are philosophical terms heavily burdened with a heritage of contradictory usages and of inconclusive and interminable discussions.

My use of the terms ‘objective’ and ‘subjective’ is not unlike Kant’s. He uses the word ‘objective’ to indicate that scien­tific knowledge should be justifiable, independently of anybody’s whim: a justification is ‘objective’ if in principle it can be tested and understood by anybody. ‘If something is valid’, he writes, ‘for anybody in possession of his reason, then its grounds are objective and sufficient.’

Now I hold that scientific theories are never fully justifiable or verifiable, but that they are nevertheless testable. I shall therefore say that the objectivity of scientific statements lies in the fact that they can be inter-subjectively tested. [22]

The problem of the empirical basis

[I]n 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 scientist scarcely ever has occasion to describe a singular statement as non-empirical or metaphysical. [21]

Evading falsification

A third objection may seem more serious. It might be said that even if the asymmetry is admitted, it is still impossible, for various reasons, that any theoretical system should ever be conclusively falsified. For it is always possible to find some way of evading falsification, for example by introducing ad hoc an auxiliary hypothesis, or by changing ad hoc a defini­tion. It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsi­fying experience whatsoever. Admittedly, scientists do not usually proceed in this way, but logically such procedure is possible; and this fact, it might be claimed, makes the logical value of my proposed criterion of demarcation dubious, to say the least.

I must admit the justice of this criticism; but I need not therefore withdraw my proposal to adopt falsifiability as a criterion of demarcation. For I am going to propose that the empirical method shall be characterized as a method that excludes precisely those ways of evading falsification which, as my imaginary critic rightly insists, are logically possible. Accord­ing to my proposal, what characterizes the empirical method is its manner of exposing to falsification, in every conceiv­able way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival. [19-20]