A.J. Ayer, What is a Law of Nature? Logical Positivism Common Method (simplified): Analyze a claim or position to see if it can be derived from observation and logic alone. If it cannot be, then it is suspect, and must be further analyzed in order to see whether some confusion or error might have led otherwise smart people to hold the position. The analysis that helps us rid ourselves of certain confusions should also make it more or less obvious what the right way to approach the issue under consideration is. All that remains, then, is to articulate the approach further and respond to whatever remaining objections there might be. Particular Case: Laws of Nature The claim that there are necessary connections between things and events in nature cannot be established by observation or by logic Some confusion about laws arises from the traditional conception of nature as being subject to the commands of some supernatural being or beings—things in nature happen the way they do because they have to happen that way, and they have to happen that way because a supernatural being orders them to happen that way. Even if we reject the conception of a supernatural law-giver, the confusion between logical and factual relations may remain, making otherwise smart people continue to maintain that there are necessary connections between things, events, and properties in nature. (Necessitarian Approach) The same analysis that allows us to identify the confusions involved in the Necessitarian Approach makes it obvious that the right way to think about laws of nature is the Regularity Approach: “…a proposition expresses a law of nature when it states what invariably happens.” (815) “…all that is required for there to be laws in nature is the existence of de facto constancies… the constancy consists in the fact that events, or properties, or processes of different types are invariably conjoined with one another” (816) In other words, the existence of laws of nature does not require that there be any necessity to the way things are, or that there be some necessary connection between things that explains the de facto (actual) constancies or regularities that we observe. The constancy that we observe in nature is itself the basis of laws, and not simply evidence that things in nature are subject to laws. Now that the correct approach has been articulated, Ayer needs to respond to objections. 1. The Problem of Vacuous Laws—Universally quantified conditional statements are true whenever the predicate in the antecedent of the statement refers to an empty class. (‘For all x, if x is a unicorn, then x is green’ is true because there are no unicorns—‘For all x, if x is a unicorn, then x is red’ is true for the same reason.) This is a convention of logic, and we don’t want the generalizations that we treat as laws of nature to be true only because of this logical convention. They would be true, but vacuous (not to mention telling us all kinds of contradictory things.) Reply—The easiest way to reply would be to say that universal generalizations count as natural laws only when they refer to existing things. [Like bodies, or trees, or electrons, and not unicorns or winged horses] That is, the law implies both (x) (Fx Gx) AND (x)Fx. 2. Problem with Reply—The Problem of Noninstantial Laws--There are universal statements that we take to express laws of nature that don’t meet this condition: o All bodies on which no external net force is acting either remain at rest or move at uniform velocity in a straight line (Newton’s first law of motion—the principle of rectilinear inertia) o If two perfectly elastic bodies were to collide, the total kinetic energy of the system would be the same before and after impact o In a perfectly reversible process, the entropy remains constant In each of these cases, we have a noninstantial law—there are no particular things that actually satisfy the conditions expressed in the law (bodies on which no external net force is acting, perfectly elastic bodies, perfectly reversible processes). If these statements are expressions of laws of nature, it must be that they are true despite the fact that there are no actual things that instantiate them, rather than because of this fact. How can we make sense of the counter-factual component involved in laws like this? The regularity theorist has a problem here, because he or she takes laws to be statements that “describe how actual objects behave, not how possible objects would behave if, contrary to fact, they were to exist” (p. 882) Reply—One way to reply is to follow C.D. Broad’s idea that noninstantial laws like these are not ultimate laws of nature. They are derivative laws, or laws that can be derived from more fundamental laws that are instantiated. For example, Newton’s first law can be derived from Newton’s second law, which refers to net forces acting on massive bodies. If it turns out that all ultimate laws of nature really do describe how actual objects behave, then the regularity theory can be maintained, and the apparently counter-factual aspect of laws that are derived from them (by thinking about ideal cases) need not worry us. 3. Problem with Reply—The Missing-Values Problem for Functional Laws—Even if Broad’s suggestion works, the theory still has to deal with laws that assert functional relations between variables that range over an infinite number of values (i.e., natural laws that are expressed as mathematical equations, like Hooke’s law, F = kx, which expresses the relation between the ‘force exerted by a spring’ (F) and the ‘amount the spring is stretched’ (x)). Not all of these values will ever be realized, yet the law describes the relations that would hold be the case, if they were to be realized. Laws of nature may not be describing “how possible objects would behave if, contrary to fact, they were to exist” but they certainly seem to describe how actual objects would behave if, contrary to fact, they were in some state other than the one they are in (e.g., Hooke’s law describes the force this spring right here would exert if, contrary to fact, it were stretched twice as far as it currently is stretched). Either way, it seems clear that propositions expressing laws of nature do not merely state what invariably happens. Thus, the regularity theory appears to be false in it’s claim about what laws of nature are. 4. The Problem of Accidental Generalizations—Ayer claims that “…a proposition expresses a law of nature when it states what invariably happens.” (815) It is not clear, however, that this provides a sufficient condition for being a law of nature. We tend to distinguish between true universal statements that express laws of nature and true universal statements that merely express what invariably happens (accidental generalizations)—laws of nature rule out certain possibilities, whereas statements about what invariably happens do not. For example, up to this point in our history it has invariably happened that the winner of the election for U.S. President is a man; however, we don’t think that it is impossible for a woman to get elected. Even if no woman ever does actually get elected, the possibility that a woman could be elected would not be ruled out. The law of inertia, in contrast, does rule out the possibility that a body could change its state of motion or rest without being acted on externally. This means, once again, that we tend to think there is something more expressed by a law of nature than is expressed by a description of what invariably happens, and this something more has to do with the counter-factual implications of laws. Response—Ayer’s Epistemic Regularity Theory—“the difference between our two types of generalization [i.e., generalizations of fact and generalizations of law] lies not so much on the side of the facts which make them true or false, as in the attitude of those who put them forward” (822). The something more that is expressed by a statement of a law of nature is just our own attitude towards the statement. To say that some generalization about what invariably happens is a generalization of law, rather than a generalization of fact, is to say that our attitude is one that rules out the possibility of our accepting any claim that purports to disprove the truth of the generalization. If an otherwise reliable source tells us that a woman has been elected President of the United States, we are willing to accept this claim, even though it forces us to give up our belief in the statement ‘All U.S. Presidents are men’. If the same source tells us that a body changed its state without being acted on externally, we are not willing to accept this claim—rather than doing so, we would give up our belief that the source is trustworthy, or we would assume either that the body in question had not actually changed its state (despite whatever evidence supports the claim that it had) or that the body had actually been acted upon externally (despite whatever evidence supports the claim that it had not). If Ayer is right, we can defend the regularity theory from objections based on the counter-factual implications of laws by saying that the appeal to these implications is simply an appeal to our own attitudes concerning statements of what invariably happens in nature. Our attitudes provide all the tools we need to explain our tendency to distinguish between generalizations of fact and generalizations of law. The difference is not one that stems from recognizing that some connections between objects and events in nature are necessary, while others are contingent or accidental. Rather, the difference is one that stems from our willingness or lack of willingness to consider the possibility that one of our previously formed beliefs about the way things are is false.