Hempel on Intertheoretic Reduction - Florida Philosophical Review

Winner of the Gerrit and Edith Schipper Undergraduate Award for Outstanding Undergraduate Paper at the 47th annual meeting of the Florida Philosophical Association

David Barnett, New College of Florida

Introduction

The question of whether all living things are really just complex physical ones, or whether instead there are biological entities or characteristics that cannot be fully characterized in physical terms, has historical roots buried centuries deep. Carl Hempel considers this question as an empirical one for modern science to address. ¹ Hempel’s concern in this paper is not with the answer to the question, but rather with the methods by which it may be evaluated. He considers the position of those he calls “mechanists,” that all living things and their biological characteristics are nothing more than complex physical systems, as equivalent to the view that in some significant sense all accurate biological theories are implied by physical ones. ² In doing so, Hempel seeks to draw conclusions regarding the unity of science more broadly. I will argue that Hempel’s account, though perhaps succeeding in a crucial first step, fails on numerous points afterwards. Using the morals that may be drawn from these failures, I suggest rough outlines of some alternative accounts of intertheoretic reduction.

The Project Outlined: Reduction of Theories

Contrasted with vitalism, the position of the mechanists, says Hempel, amounts to the following two claims:

(M1) All the characteristics of living organisms are physico-chemical characteristics—they can be fully described in terms of the concepts of physics and chemistry. ³
(M2) All aspects of the behavior of living organisms that can be explained, can be explained by means of physico-chemical laws and theories. ⁴

This formulation of the mechanist position is never explicitly argued for, but I will not here draw it into question. Perhaps there are other conditions that must be the case in order for the mechanist position to be correct, or perhaps it might be that living things are nothing more than physical ones, although one or both of these conditions are not satisfied. Here, however, I will assume that Hempel has got this much right about what it is for a biological entity to be merely a physical one. Moreover, I will grant Hempel that generalized versions of M1 and M2 are both necessary and sufficient conditions for an analogous identity between, say, mental entities and physical ones, or sociological systems and complex systems of psychological entities.

Hempel further interprets M1 and M2 in terms of the relationship between biological and physical theories. M1, he claims, requires that the terms of biology be extensionally definable in physical terms.⁵ Contrasted with intensional definition, this sort of definition requires only that the biological term being defined share its extension with some physical term. He sees M2 as requiring that all biological facts, including all the laws of accurate biological theories, be deducible from the laws of physics. ⁶

The question whether biological systems are nothing more than physical ones is treated by Hempel as equivalent to the question whether biology is reducible to physics. The terms “biology” and “physics” refer to theories—linguistic entities that describe biological and physical things.

Equating mechanism with the view that biology is reducible to physics is accomplished by way of something analogous to the principle of semantic ascent. According to Quine, the principle of semantic ascent translates the claim that there are wombats in Australia as semantically equivalent to the claim that ‘wombat’ applies to something in Australia. ⁷ In so doing, it allows us to “ascend” from questions regarding things to questions regarding the words that refer to them. In an analogous manner, I believe, the conflation of mechanism with biological-physical reductionism requires us to treat the statement “biological properties are nothing more than physical properties” as equivalent to the statement “biological predicates are in some sense reducible to physical predicates.”

Using this analog to the principle of semantic ascent, we can convert M1 and M2 into the biological-physical reductionist claims R1 and R2:

(R1) The terms of biology are reducible to those of physics.
(R2) All laws of biology are reducible to those of physics.
R1 may be said to call for a reduction of terms and R2 for a reduction of laws.⁸ As it is, “reducibility” in the case of terms can be defined trivially as the relationship which obtains between two sets of theoretical terms, A and B, such that A is reducible to B just in case all of the things to which A-terms refer are really just the things to which B-terms refer. The reduction of laws proceeds likewise.

It is the job, then, of an account of intertheoretic reduction to tell us, in a non-trivial way, what the reducibility relation involves. By Hempel’s account, a reduction of terms amounts to extensional definition; deducibility is a necessary and sufficient condition for the reducibility of laws.

The Reduction of Terms

Let us now take a closer look at extensional definition as the mode by which a reduction of terms takes place. A biological term, by Hempel’s account, can be defined by means of any physical term with the same extension. As Hempel explains things, the only relationship between a biological and a physical term necessary for a reduction is that which obtains between “human” and “featherless biped.”⁹

This unusual view is based on a process of elimination. As Hempel sees it, extensional definition is our only plausible candidate for a mode of terminological reduction. He points out that it would be impossibly restrictive to expect the reduction of a particular biological term to follow analytically from the meaning of that term.¹⁰ He fails to consider, however, any other possible modes of terminological reduction, never explaining why he considers these two possibilities exhaustive.

If an account of intertheoretic reduction is to be possible, then it is to be hoped that these two options—extensional definition and analytic equivalence—are not exhaustive, as neither of them work. As Hempel points out, analytic equivalence is not necessary for a terminological reduction.¹¹ It would be crazy to say that an equivalence with a physical term must be contained in the meaning of the biological term to be reduced for a reduction to be possible. However, extensional definition, which Hempel actually endorses, seems like an unnecessarily restrictive criterion for terminological reduction as well.

Hempel himself notes that the adoption of a particular terminological reduction often involves changing the intension as well as the extension of the term being reduced. He gives, as an example, the word “testosterone,” which he says was originally defined as a male sex hormone produced by the testes. Once the term was reduced, the intension changed to a physico-chemical characterization, thereby widening the extension to include synthetic substances of the same chemical structure.¹² What Hempel fails to note is that, if the extension of “testosterone” was altered to include these substances, then its previous extension was not identical to the physico- chemical description to which it was reduced. Since the physico-chemical description to which testosterone was reduced includes synthetic substances under its extension and “testosterone” did not include these substances initially, then the two terms were not co-extensional.

One can try to avoid this dilemma by suggesting various ad hoc modifications to extensional definition. For instance, one could require, rather than complete extensional equivalence of the terms between which the reduction is taking place, merely a substantial overlap of some sort. But, it cannot be a matter merely of having nearly identical extensions. First, there are the obvious difficulties that mass terms like “testosterone” and “gold” present to such a story (how might one compare the degree to which their extensions overlap with corresponding physical terms, without the presence of discrete items in their extensions?). Second, it seems to make no difference, for example, whether synthetic testosterone exists in tiny or enormous quantities. In other words, the quantity of synthetic material that falls under the extension of the physico-chemical description in question but not under the extension of “male sex hormone produced by the testes,” seems to make no difference in determining whether a reduction is appropriate.

A direction which seems much more plausible is to deny that extensions do indeed change after a reduction, thereby allowing one to maintain Hempel’s overall account of terminological reduction. The extension of “testosterone,” then, has always included chemically similar synthetic substances, even before its chemical structure was ever examined. As the standard definition of “testosterone” currently does include a physico-chemical characterization not included prior to reduction, one must either 1) claim that the definition of the biological term does not in fact determine its extension, or 2) grant that the definition determines the extension, although it never alters in such a way as to change the reduced term’s extension.

Since synthetic substances are within the extension of “testosterone” now, yet clearly would not be included under the definition “male sex hormone produced by the testes,” the apparent way to go is with option 1. A causal account of reference might be suitable for this task. One could claim, for instance, that once the reference of “testosterone” is fixed to some batch of testosterone, then the term will refer to all other instances of the same natural kind. Unfortunately, this view, coupled with Hempel’s account of terminological reduction, makes it difficult to see how one might ever know whether a reduction is appropriate. If terminological reduction requires that the extensions of the terms in question match up, one needs a way of determining the extensions of those terms. If definitions do determine reference, then we can investigate the matter by checking to see whether all male sex hormones produced by the testes fall under the physical description being considered for reduction. Otherwise, it is not obvious how one might go about determining if a biological and a physical term had the same extensions, as the extensions themselves are unknown. This is not to say, of course, that causal theories of reference for natural kind terms imply that we can never know the extension of a term. Clearly, we know the extension of “water,” and can know whether a particular liquid is water or not by testing to see if it is H2O, as opposed to XYZ. However, this is a determination which we can make after the reduction has taken place. Before “water” was reduced to “H2O,” it is not obvious how we might have determined whether these terms were co-extensional.

The option that I see as more promising is 2. If the definition of “testosterone” really does denote all of the same things as the physical term to which it is being reduced, then a change of definition to include this physical term will not alter the extension of “testosterone.” What has been taken for granted until this point is that the definition of “testosterone” as “a male sex hormone produced by the testes,” was in fact the one in use prior to its reduction. Suppose that chemists have just provided a chemical description that apparently characterizes all instances of testosterone. They have also found that a particular synthetic substance, which has been produced in a laboratory as a byproduct of their experiments for years, falls under the same chemical characterization. It seems to me as though a terminological reduction would be appropriate just in case the synthetic substance had the same effects as natural testosterone if released into the male bloodstream. If the synthetic substance failed to promote growth in men in the same manner in which natural testosterone does so, we would say that the chemical characterization fails to capture something important about what it is for a substance to be testosterone. Conversely, if the synthetic substance shared all of these biological properties with natural testosterone, a reduction of the term would be in order. Despite the fact that “male sex hormone produced by the testes” is what one will find under the heading “testosterone” in the glossary of a pre-reduction biology textbook, it might be that the biological characteristics which in fact determine the extension of “testosterone” are associated with the effects of this substance on the male body.

Whether or not Hempel’s account of terminological reduction can in this manner be defended against the charge of stringency (i.e., that it rules out legitimate cases of reduction), I will argue that it is clearly guilty of its converse, permissiveness. That extensional definition is insufficient for reduction should be apparent from the fact that many biological terms (especially those with very limited extensions) may have multiple unique physical descriptions with which they are co-extensional. In the cases in which these physical descriptions are theoretically equivalent (e.g., in the sense that having a particular net charge is equivalent to producing a certain electric field), this seems perfectly unproblematic. But in instances in which the physical properties in question are not theoretically equivalent, there will be multiple independent but equally correct reductions of the same biological term.

That it is possible for a particular biological term to be co-extensional with multiple physical terms, I take it, is prima facie quite plausible. Additionally, I will argue, this, in fact, is the case quite often. It is not difficult to come up with bizarre disjunctive physical properties that ought to be co- extensional with any particular biological term. This is especially easy in cases in which the biological term has only one or several items in its extension. For example, for a biological term that has only one object in its extension, any physical property that is possessed uniquely by that object will be co-extensional with the biological term. Were Hempel’s account of terminological reduction correct, the biological term in question would be reducible to any physical property (however bizarre and disjunctive) that applied uniquely to this object.

This is not the case merely with terms with limited extensions. Take, for instance, the common example of the identification of water with the chemical compound H2O. By Hempel’s account, a reduction such as this is appropriate if and only if “x is H2O” is co-extensional with “x is water.” But similarly, “x is water” is also co-extensional with “x is H2O or Li3,” as there are, presumably, no instances of trilithium anywhere.

One might make an ad hoc requirement that if we are to reduce some biological or descriptive term to a disjunctive physico-chemical description, then each of the disjuncts of the physico- chemical description must have something in their own extensions. Minor modifications like these, I think, must ultimately fail. The problems with extensional definition as a criterion for terminological reduction run much deeper than this.

Let’s assume that there is some physical description—call it “ORGANISM”—to which the biological term “organism” is reducible. In order for there to be a complete reduction of the terms of biology to those of physics, it would also need to be the case that terms referring to particular species of organisms also be reducible to physical terms. In other words, just because “organism” has some physical reduction, it does not follow trivially that “bumble bee,” “oak tree” and “turkey” all have physical reductions. By Hempel’s account, a species term like “turkey” is reducible to a physical description if and only if that description applies to all turkeys and only to turkeys.

A particular turkey might have a mass of, say,4.56968360857kg at time t1.¹³ It is plausible to suppose that at the exact instant at which the turkey has this mass, this particular turkey will be the only organism to have precisely this mass. (If this does not seem equally plausible to the reader, substitute for a turkey some organism with an abnormally large mass, such as a blue whale.) Indeed, if we are specifying mass to the nearest ten nanograms, as above, it is probably true of any turkey with a mass mi that it is the only organism at time ti with that mass. The following physical property, then, is co-extensional with “x is a turkey”:

x is ORGANISM AND [x has mass m1 at time t1 OR x has mass m2 at time t2 OR …x has mass mn at time tn]where m1….mn specify the mass of each turkey that
will ever live at times t1 . . . tn
Yet it is counter-intuitive that “turkey” is reducible to this physical description, which we may call “TURKEY.” What seems to be delinquent about TURKEY is that, while it is co- extensional with “turkey,” it fails to capture any of the salient biological features of turkeys. As in the case of testosterone, we would want to reduce the biological term only to a physical term that captures the biological properties that we most closely associate with that type of biological entity. In the case of testosterone, this means, roughly, that if we took any chemical of the given description and placed it in the bloodstream of a man, it would have the same effects as natural testosterone.

Similarly, while there are not in fact any physical objects which are in the extension of TURKEY which do not posses the biological properties of turkeys, it is possible, say, that a physical object with the biological properties of a dog was an organism with a mass of 4.56968360857 kg at time t1. What is needed is a physical description that, as a matter of physical necessity, will have to apply to all and only those things with the biological properties exclusive to turkeys.

This matter is complicated by the fact that whether a particular physical description necessitates the possession of certain biological properties depends on the reductions which can be given for those biological properties. This is quite evident, again, in the case of testosterone. Whether a particular chemical structure will necessarily have the biological property of, say, causing growth in male humans, depends on the particular physico-chemical reductions that can be given for “growth,” “male,” and “human.” If, for instance, the physico-chemical structure of the human body were drastically different from the way it actually is, then the chemical compound with which testosterone is actually identical would not have the biological properties that it actually possesses. There are probably numerous ways in which the chemical structure of organisms could be different (at least in an epistemic sense of “could”) which would yield the same biological laws and observations. For this reason, the reduction of any biological term to a physical term depends on the physical reduction of other biological terms. A reduction of terms is an all or nothing affair— terminological reductions cannot be considered on a term by term basis.

As an illustration of this conclusion, let us consider the reduction of biological terms that are the result of the combination of other biological terms. For instance, “female mammal,” “primate with no tail,” and “purple swan.” It is intuitively obvious that a reduction of one of these terms should be physically equivalent to the logical combination of the physical properties to which the individual terms can be reduced. If “purple” is reducible to the physical description PURPLE, and “swan” to the physical description SWAN, then “purple swan” is reducible to the physical description [PURPLE AND SWAN]. However, as has been argued previously, there will often be multiple physical properties with which a particular biological term is co-extensional. This is particularly obvious in the case of “purple swan,” which is co-extensional with every physical description with nothing in its extension. Of these, clearly the appropriate description to which to reduce “purple swan” is [PURPLE AND SWAN]. But if we require for reduction extensional definition alone, rather than incorporating the reductions of other biological terms into our story, then any of these physical descriptions will be an equally appropriate candidate for reduction.

What is important to notice here is that the mode of terminological reduction endorsed by Hempel, extensional definition, is not exclusively susceptible to this argument. Any mode of terminological reduction that treats reduction on a term by term basis will be equally vulnerable. By ignoring the relation between the reduction of “purple swan” and that of its component terms, we leave something out about what reduction requires.

It might, of course, be the case that phrases like “purple swan,” which are the logical combinations of discrete semantic parts, should not themselves be treated as biological terms suitable for reduction. That is, the above illustration may be problematic because of its treatment of phrases such as “primate with no tail” as biological terms in the same sense that “primate” and “tail” are biological terms. But one can always coin a biological term by reference to other biological terms, and define a new word, “pur-swan,” as “any swan that is purple.” The above considerations regarding the reduction of “purple swan” still ought to apply to the term “pur-swan”—it ought to be reduced to [PURPLE AND SWAN], rather than to some other physical property with which it just happens to be co-extensional. But although “pur-swan” is one syntactical unit—one word—it may still be argued that this word should be treated as if it were a combination of multiple semantic parts. Just as a physical reduction of the sociological term “bachelor” ought to be the logical combination of the physical reductions of “unmarried” and “man,” so too for biological terms like “pur-swan.” It may be claimed, therefore, that if a biological word is analytically equivalent to the combination of other biological terms, it ought not be treated as an atomic biological term that should itself be reduced.

Without a distinction between analytic and synthetic truth, however, such a position would be untenable. If all biological terms are partially defined by their relations to other biological terms, then, to some extent, all biological terms are similar to “pur-swan.” A successful reduction of biology to physics is one in which, in addition to establishing extensional equivalences between biological and physical terms, also establishes the associations between closely related biological terms as physical necessities. For example, the physical reductions of “testosterone,” “male,” “human,” and “growth” ought all be appropriately related so that, as a matter of physical necessity, TESTOSTERONE causes GROWTH in something that is MALE AND HUMAN. This sort of relationship is less important in the case of highly revisable biological sentences, such as “No swans are purple”—these may turn out to be physical contingencies. But, as discussed above, a true reduction of “turkey” ought to capture all (or at least most) of the important biological features of turkeys. This means that the physical description to which “turkey” is reducible ought to imply, by the laws of physics, the physical properties to which a turkey’s important biological features are reducible.

The Reduction of Laws

The lessons we have learned from our consideration of Hempel’s account of the reduction of terms may be applied to his account of the reduction of laws. Hempel claims that the reduction of biological laws to physical laws is a matter of the logical deducibility of the former from the latter. This deducibility cannot, as he notes, be established without the help of bridge principles that connect some biological terms or states of affairs with physical ones. ¹⁴

Consider an ideal case in which this sort of reduction works precisely as Hempel intends, beginning with an example of a non-reductive explanation: Maggie walks into a room, arranges a pile of crumpled newspaper in the center, and lights it on fire. The temperature of the room then increases. Why does it increase? According to Hempel’s account of scientific explanation, we can explain why this is the case by deducing this state of affairs from natural laws. One can explain the increase in temperature by means of a folk theoretic (or “theoretic”) covering law of the form: If a fire is started in a room, and the fire is not extinguished, then the temperature of the room will increase. Given this law, and the initial conditions, 1) a fire was started in a room, and 2) the fire was not extinguished, we may logically deduce that the temperature of the room will increase. Therefore, by Hempel’s account, we can explain the increase of temperature in the room by means of the fact that an unextinguished fire was started in the room, and the covering law, “when a fire is started in a room and is not extinguished, the temperature of the room will increase.”

In order to satisfy M2, it must be the case that all biological facts (including the laws and generalizations of biology) are explainable by way of physical laws and principles. Assuming Hempel provides an accurate account of the above case, if certain laws and principles of physics implied the covering law given above, then we could use these physical laws to explain all of the cases in which that covering law could be employed in an explanation. Further, as Hempel equates the deducibility of a fact from laws with the explanation of that fact by means of those laws, a deduction of the covering laws would also explain the covering law itself in terms of physics.

Clearly, the folk law that a fire increases the temperature of the surrounding air could never have been deduced a priori from physics and chemistry. The help of bridge principles, which link concepts like “fire” and “temperature” to physico-chemical concepts, are required for such a deduction to take place. In this case, the relevant bridge principles would be something like “all cases of fire are cases of the physico-chemical reaction COMBUSTION” (where “COMBUSTION” stands for some physico-chemical characterization), and “all cases of an increase in mean molecular kinetic energy are cases of an increase in temperature.” If the physical process of COMBUSTION implies, by the laws of physics and chemistry, an increase in the mean molecular kinetic energy of the surrounding area, then we have successfully provided a reductive explanation for the fact that fire increases temperature.

A crucial weakness with Hempel’s account of a reduction of laws lies in his characterization of bridge principles. As he sees it, bridge principles often, and perhaps always, take the form of the generalization, “all instances of X are instances of Y, where X and Y are terms of the theories between which the reduction is taking place.” ¹⁵ Extensional definitions are just a special case of bridge principles in which we can say both that “all instances of X are instances of Y” and that “all instances of Y are instances of X.”

Applying what we have gathered from our consideration of extensional definition here, we can see how the problems of Hempel’s account of terminological reduction extend to his account of the reduction of laws as well. Considering the physical property TURKEY, which we have said is co-extensional with the biological term “turkey,” we can see that one can, by Hempel’s view, construct the bridge principle, “all instances of ‘x is a turkey’ are instances of ‘x is TURKEY.’” By Newton’s Second Law, if an object has a mass of m, then a force of 5 N will accelerate it at a rate of (5 N)/m. By the laws of physics, then, all instances of TURKEY are instances of the physical property of NOBUFFALO, which is defined as

x is NOBUFFALO iff x is ORGANISM AND [x would accelerate at a rate of (5 N)/m1 if a force of 5 N were applied to it at time t1 OR x would accelerate at a rate of (5N)/m2 ifaforceof5Nwereappliedtoitattimet2 OR…x would accelerate at a rate of (5N)/mn if a force of 5N were applied to it at time tn]

As the following generalization is evidently true, Hempel’s account will in addition treat it as a legitimate bridge principle: “All instances of ‘x is NOBUFFALO’ are instances of ‘x does not eat buffalo for breakfast.’” We have just provided the bridge principles, “All instances of ‘x is a turkey’ are instances of ‘x is TURKEY’” and “All instances of ‘x is NOBUFFALO’ are instances of ‘x does not eat buffalo for breakfast.’” We have also shown that, by the laws of physics, something is TURKEY implies that it is NOBUFFALO. By Hempel’s account, then, we have just given a reductive explanation of why turkeys do not eat buffalo for breakfast.

This counter-example to Hempel’s account of a reduction of laws is based on the illegitimacy of the bridge principles involved. Yet there are additional problems that are not limited to the kind which are drawn from his account of terminological reduction. Using only intuitively legitimate bridge principles and physical laws, I provide below an illustration of the insufficiency of the deduction of laws for the reduction of laws. Although this example uses non-biological (as well as biological) terms, it may be regarded as an illustration of how a genuine counter-example to Hempel’s view might proceed.

Maggie enters a room, as before, and begins to gather a pile of crumpled newspaper. She then drops to the floor, unconscious. Why is there no fire in the room? The air in the room is not nutritious,¹⁶ and humans can only remain conscious in the absence of nutritious air for a minute or two. Further, preparing and starting a fire takes more than a minute or two (and cannot be performed while unconscious). From these folk/biological laws, we can deduce the covering law, “if the air in a room is not nutritious, then a human cannot start a fire in that room.”

We can deduce this covering law from the laws of physics and chemistry, with the help of legitimate bridge laws, in a way that, intuitively, is not a reduction of our covering law. Above, I gave as an example of a bridge law, the principle, “All cases of fire are cases of COMBUSTION.” In addition, we shall also use the bridge law, “All cases of a room with non-nutritious air—that is, air which lacks the positive characteristics necessary to sustain life—are cases of an enclosed area in which the air contains no oxygen” (see endnote 16). The physico-chemical process of COMBUSTION requires a supply of oxygen. And so, by the laws of physics and chemistry alone, all cases of an enclosed area in which the air contains no oxygen are cases in which COMBUSTION cannot occur. Given this, one can deduce the covering folk/biological law that a human cannot start a fire in a room in which the air is not nutritious.

That the preceding paragraphs do not provide a reduction of this covering law is just as apparent as the fact that we could not explain why Maggie failed in her attempt to start a fire by the fact that COMBUSTION cannot occur without oxygen in the air. Laws are, by Hempel’s view, the devices of a theory that are invoked when giving a theoretical explanation of some state of affairs. The fact that covering laws about what humans can and cannot do without oxygen explain Maggie’s failure in starting a fire, while the bridge principles and physical law discussed above do not explain Maggie’s failure, shows that the latter are not an adequate reduction of the former.

While the fact that COMBUSTION cannot occur without oxygen does tell us that Maggie will fail to start a fire, it does not tell us why she, in fact, does fail. The folk/biological law that successfully explains Maggie’s failure is derived from a number of other folk/biological laws, namely: “A human will fall unconscious in a minute or two in absence of nutritious air” and “A human must be conscious for more than a minute or two in order to prepare and start a fire.” To successfully reduce our covering law, these more fundamental laws must have their own reductions incorporated. In other words, it may be possible to reduce the covering law in question to physics and chemistry, but this will have to be done in a way which makes use of the fact that a HUMAN (given some physico-chemical characterization), by the laws of physics, must have a breathable supply of oxygen available to remain CONSCIOUS long enough to perform the task at hand.

This seems closely related to the conclusion drawn regarding terminological reduction—that reduction cannot be done on a term by term basis. Here, we see that, when reducing a law, it essential that this reduction be carried out in a manner that incorporates the more basic laws from which the covering law is derived. This seems to entail a conclusion for a reduction of laws similar to the conclusion of the preceding section regarding a reduction of terms.

It may be the case, however, that there are genuinely basic laws of biology, which are not derived from any others, but from which all others may be derived. Were this the case, their reduction could be treated individually and then the reductions of all derived laws would trivially follow. This is related to the objection voiced above to treating words like “bl-swan” as terms in their own right, suitable for reduction in the same way as “black” and “swan” may be. This objection, it was said, relies on the controversial analytic/synthetic distinction. In the case of laws, however, nobody would want to say that laws cannot be logically derivable from one another, so it seems as though this picture of reduction could work. It might be that a reduction of laws could successfully proceed one law at a time, just so long as we are careful to distinguish between the genuine basic laws of biology and mere derivatives of these laws which themselves are not candidates for reduction.

This is a question that I will here leave somewhat open-ended, although I suspect that a reduction of laws, like a reduction of terms, cannot be carried out one law at a time. While it is clear that the law that a human cannot light a fire in a room with non-nutritious air can be derived from other folk/biological laws, it is unclear why these others ought to be treated as more basic. While, in fact, this covering law was obtained by derivation from other laws, there seems to be no reason to believe that this could not have happened the other way around. One might, for example, observe the inability of Maggie and other humans to start a fire in a room with non-nutritious air and, knowing that humans can remain conscious without air for a minute or two, conclude that preparing and starting a fire takes more than a minute or two. This appears to indicate that, as a reduction of the laws of biology to physics needs to preserve the logical relationships between biological laws, one cannot carry out reduction one law at a time, but rather must consider the reductions of the laws to which it is logically related.

Works Cited

Giere, R. “The Skeptical Perspective: Science Without the Laws of Nature.” Philosophies of Science: From Foundations to Contemporary Issues. Ed. Jennifer McErlean. Belmont, CA: Wadsworth, 2000. 180-189.

Hempel, C. “Theoretical Reduction.” Philosophies of Science: From Foundations to Contemporary Issues. Ed. Jennifer McErlean. Belmont, CA: Wadsworth, 2000. 470-476.

Quine, W. V. O.

Carl Hempel, “Theoretical Reduction,” Philosophies of Science: From Foundations to Contemporary Issues, ed. Jennifer McErlean (Belmont, CA: Wadsworth, 2000).
Hempel 470.
Hempel 470.
Hempel 470.
Hempel 470.
Hempel 470.
W. V. O. Quine, Word and Object (Cambridge: Cambridge UP, 1960) 271-72.
“Law” is here intended in its broadest and most neutral sense. As laws have traditionally been viewed as the explanatory devices employed by theories to explain the phenomena that they do, I have adopted use of this term here. However, R2 may be read in such a way as to call for the reduction of whatever theoretical devices are employed in an explanation provided by that theory. In this sense, Ronald Giere’s principles would be just as suitable a candidate as natural laws for satisfaction of R2. See Ronald Giere, “The Skeptical Perspective: Science Without the Laws of Nature,” Philosophies of Science: From Foundations to Contemporary Issues, ed. Jennifer McErlean (Belmont, CA: Wadsworth, 2000).
Hempel 471.
Hempel 471.
Hempel 471.
Hempel 471-72.
t1 is here intended to specify an instant. If one has metaphysical discomforts with instants, one may instead consider t1 to be of very small but non-zero duration. By this reading, t1must be precise enough so that turkey’s mass does not fluctuate by more than one half of a nanogram in the interval to which t1 applies. For instance, it would be illegitimate to claim that a turkey had some particular mass, specified to the nearest ten nanograms, on May 29, 2001, as its mass will fluctuate significantly during this time.
Hempel 472.
Hempel 472.
“Nutritious” should be taken as equivalent to a biological characterization such as “possessing the positive characteristics required of air to sustain homeostasis in humans.” It is imperative for this example that “nutritious” be defined in terms of the possession of positive characteristics. For instance, just as a glass of milk laced with poison will still posses the calories and vitamins necessary to be nutritious (as opposed to being edible), so too may some oxygen-rich air with a toxic chemical in it be considered nutritious (as opposed to being breathable). Nutritious-ness is a perfectly legitimate folk biological property, which can be characterized without any appeal to the chemical composition of air. Adding poison to food, as is evident without any appeal to caloric or vitamin content, does not eliminate its nutritional value. If it merely did this, poison would be a diet aid, rather than a means of killing someone. Similarly, taking a whiff of non-nutritious air will merely leave one short of breath. Breathing toxic air will kill you.