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A.J. Ayer - What is a Law of Nature?
What does 'law' mean in this context?
* Not imperative (though Hobbes included imperatives in his laws of nature)
* Rather the commands issued by nature are so powerful that they cannot be disobeyed
* To disobey the commands would represent a contravention of the laws of logic (??) To think of the laws of nature in this way may suggest some form of logical necessity or necessary relation between events. This could lead us to the belief that the laws of nature can be discovered a priori.
* Hume refutes this suggestion by claiming there is no intrinsic relation between cause and effect, thus we can only understand the 'laws' of nature through experience
* But what if Hume is wrong? If we examine statements/laws of the form 'All Xs are Y' then when we come to accept the law we change our understanding of X. It was discovered that loadstones attract iron and steel, now it is accepted that all loadstones attract iron and steel, and this is an 'analytic truth' If we accept this reasoning, we may conclude that some laws of nature are analytically true, whereas some are not. But if the ultimate goal of physics (and maybe even biology, social sciences) is a unified theory in which everything is axiomatized, then surely all generalizations would be logically necessary.
* the problem with this understanding of the laws of nature is that it the tighter it is logically, the more sterile it would be and the harder empirical applications would become. Conversely, the more easily applicable it is, the looser it would have to be logically (i.e. fewer analytic truths)
# the more we put into our definitions, the more uncertain it becomes when anything satisfies them e.g. if we say hydrogen has 303,000,000,000,000,000,000,000 molecules then we restrict what we can call hydrogen
* We may claim that it is a property of 'laws of nature' that they are not analytically true; hence such an axiomatic system of science would be qualitatively different to current science
* Thus to object to Hume that cause and effect are necessarily distinct is simply to say that there may be necessary, axiomatic systems that can take the place of natural laws. But science is generally far from here today, and certainly was in Hume's day
* In any case, Hume is right in saying that the relations between things, events and properties cannot both be factual and logical. We cannot describe empirical laws of nature as logically necessary.
Having rid the confusion between logical and factual relations the 'obvious course is to hold that a proposition expresses a law of nature when it states what invariably happens'
* there is not, has never been, and will never be exceptions. Thus 'necessity' on this view is the simple lack of exceptions
* this can be extended to statistical laws without problem One problem: if we formalise 'All S is P' as 'for all X, if X is S then X is P' and the antecedent is false, i.e. X is not S, then X will be P but also A, F, H, U, Z...in short, anything can be logically inferred from a false antecedent, but we would not with to term such generalizations as laws of
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