In the Novum Organum, Francis Bacon lays out a method of induction, a method which is the correct path to knowledge of Nature. After briefly sketching this method, I shall argue that the making of hypotheses about the invisible internal structure of things plays a crucial role in Bacon's method of induction, and that our knowledge of the laws of nature is inseparable from our knowledge of this invisible inner structure.
Bacon states at the beginning of book II of the Novum Organum that "It is the task and purpose of human knowledge to discover the form of a given nature, or its true specific difference, or nature-engendering nature, or source of emanation" (II, 1). Bacon means by each of these phrases the same thing, viz. the law governing the given nature we are interested in: "For when I speak of forms I mean nothing but those laws and definitions of pure actuality, which govern and constitute any simple nature, such as heat, light, weight, in every kind of material and subject that is capable of receiving them. Therefore the form of heat or the form of light are the same things as the law of heat or the law of light" (II, 17).
We go about discovering these laws by the process of induction, or "Interpretation of Nature" (I, 115), according to Bacon. In doing induction we come up with what Bacon calls "axioms," which we would now call "lawlike hypotheses." These axioms must meet certain standards, stated in the following "precept":
So for a true and perfect axiom of knowledge the proposition or precept would be as follows: that another nature be discovered which is interchangeable with the given nature, and yet is a limitation of a more general nature, as of a true genus. (II, 4)1 An example of an axiom that meets this precept is Bacon's "First Vintage concerning the Form of Heat":
Heat is an expansive motion, checked, and exerting itself through the smaller parts of bodies. But the expansion is modified, in that while it expands towards the circumference, it yet has some tendency to go upwards. And this exertion through the parts is also qualified in that it is not sluggish at all, but hurried and somewhat violent. (II, 20) Hurried, expansive motion, with some tendency to go upwards, is a nature which, to the best of Bacon's knowledge, was interchangeable with the nature of heat. That is, anything which is hot (to some degree) has this sort of motion, and anything which has this sort of motion is hot (to some degree). Furthermore, this nature is obviously "a limitation of a more general nature," viz. the nature of motion, and thus the laws governing heat will be "limitations" of the laws governing motion in general.
Induction begins with the compilation of three tables. First, there is the "Table of Existence and Presence," which is "a simple account, with no premature speculation or refinement" of all instances of the given nature, roughly classified into kinds (II, 11). Second, there is the "Table of Deviation, or Absence in Proximity," a list of those things which lack the given nature, but which are otherwise similar to the things on the first table (II, 12). Third, at least for those natures which admit of degrees, is the "Table of Degrees," a list of "instances in which the nature under inquire exists to a greater or lesser degree" (II, 13). Using these tables, induction proceeds to find the nature "interchangeable with the given nature" (II, 4) by a process of "rejection and exclusion" (II, 16). Any nature not present in some instance of the first table is ruled out; any nature which is present in some instance of the second table is ruled out; and any nature which increases when the given nature (the subject of inquiry) decreases, or decreases when the given nature increases, according to the third table, is also ruled out. "Then indeed, after the rejection and exclusion has been properly made, . . . there will remain . . . the affirmative form, solid, true, and well-defined" (II, 16).
Human knowledge also has a "subordinate" task, the discovery of "latent [i.e. hidden] processes" and "latent schematisms" (II, 1). By "latent process" Bacon means a description, possibly non-lawlike, of the intermediate events between a "manifest efficient" cause and its effect. Purely descriptive embryology, for example, investigates the latent process between a certain sort of manifest efficient cause, copulation, and the effect it sometimes has, childbirth. In what way is knowledge of latent processes "subordinate" to knowledge of laws? Bacon seems at some points to suggest that knowledge of latent processes is easier to come by than knowledge of laws; but surely this cannot be the case for all latent processes, especially not when the details of the process become finer and finer, to the point where the individual events in the process are "too small" to be perceived in any direct manner (cf. II, 40). For example, detailed knowledge of the latent process of respiration in animals, including the intricacies of the Krebs cycle, were much harder to come by than the laws of chemistry which govern the process. Indeed, knowledge of the laws of chemistry were a necessary step on the way to knowledge of the latent process of respiration.
The best way to understand Bacon's claim that knowledge of latent processes is subordinate to knowledge of laws, I think, is to construe it as a claim that knowledge of laws has more explanatory power than mere knowledge of a latent process. I may have knowledge, memorized from a textbook, of the individual steps in the Krebs cycle, but if I do not also have knowledge of the laws governing each of the events in the cycle, there is a sense in which I do not have a full understanding of respiration. This lesser degree of explanatory power is reflected in what we can do with our knowledge of latent processes. Bacon says that "the operative part [i.e. the changes we can bring about using our knowledge of latent processes] . . . starts from the ordinary things that are found in nature and extends its operation to those things that are nearest, or at least not far removed from them; but deeper, radical operations on nature depend entirely on primary axioms" (II, 5). If, for example, I knew that there was a natural latent process consisting, in order, of event-types A, B, C, and D, I could bring about an event of type D by artificially bringing about an event of type B or C and letting nature run its course. If, however, I had knowledge of the laws governing such processes, I might discover that there was another way of bringing about an event of type D, a way that does not require first bringing about an event of type A, B, or C.
One might suspect, as Bacon seems to suggest in book II, aphorism 1, that the role of "latent schematisms" in his theory of induction is much the same as the role of latent processes: easier to have knowledge of (at least in some cases), but inferior in explanatory power. But latent schematisms, i.e. the largely hidden inner arrangements of parts of material bodies, play a much more crucial role in Bacon's theory of induction. Bacon says the following about the role of knowledge of latent schematisms in the practical side of induction: "Yet no one can bestow a new nature on a given body, or successfully and appositely transform it into a new body, unless he has a good knowledge of the body that is to be altered or transformed" (II, 7). This role on the practical side of Baconian induction presumably has a counterpart on the "contemplative" side of induction: knowledge of the latent schematism of things of a certain may be necessary for arriving at knowledge of laws governing the nature of thing. For example, knowledge of the laws governing nuclear decay would not have been possible without the familiar model of the atom as consisting of a nucleus of protons and neutrons surrounded by a "cloud" of electrons "orbiting" the nucleus, a theory about the inner schematism of the atom.
Insofar as the familiar macroscopic objects we can readily observe have complex and highly diverse latent schematisms, there can be no hope of establishing some simple set of laws governing their actions short of knowledge of their latent schematisms. Two metals may be quite similar in superficial appearance, weight, malleability, and ductility, but react very differently when placed in a solvent. It may be the case that there is no readily observable difference between the two; in such a case, we are compelled to hypothesize some hidden difference, which may be in their latent schematism, such as the number of valence electrons had by atoms of the two respective metals.
Bacon emphasizes that knowledge of the latent schematism of bodies is arrived at by the same process of induction by which one arrives at axioms (II, 7). And just as knowledge of latent schematism may be necessary to formulate axioms, knowledge of axioms may be necessary to acquire knowledge of latent schematisms. A concrete example of this is given in book II, aphorism 40, in which Bacon describes method whereby he determined the density (a latent schematism) of vaporized alcohol. Unlike the density of a solid, which can be calculated relatively directly by measuring the weight of a quantity of the solid and dividing by the volume, measurement of the density of a gas must be made indirectly, for the weight cannot be directly measured on a scale. Bacon affixed an empty bladder of known volume to the top of a phial containing a known mass of "spirit of wine" (ethanol alcohol). He heated the phial so that some of the alcohol evaporated, filling the bladder, then removed the bladder and measured how much of the alcohol had evaporated from the phial. Using the principle of conservation of mass, an axiom of nature, he reasoned that the mass lost from the phial was equal to the mass that filled the bladder, and hence he was able to calculate the density of the vapor. He might well have gone on from there to use this knowledge to determine whether there is a relationship between the density of a gas and some other property; and this might in turn go on to help determine the density of some gas that never is found in liquid form, the density of which cannot be determined by the method Bacon describes. This illustrates Bacon's point in book I, aphorism 103, that the road to knowledge "is not level, but rises and falls; first ascending to axioms, then descending to particulars." Another simpler example of this is the way in which knowledge of the laws of optics made possible the development of the microscope, which in turn revealed the hidden inner schematism of objects, which led to knowledge of further laws.
A Laplacean demon would require knowledge of two things in order to infallibly predict the future states of the world: knowledge of the laws according to which the state of the world evolves over time (Bacon's true and perfect axioms) and the knowledge of the initial state of the world (the schematism of the world). Prediction is impossible without both a hypothesized law and a hypothesized initial state. And since our hypotheses are tested by their ability to make successful predictions, our axioms and our hypothesized schematisms are always tested together. There can be no knowledge of laws without knowledge of latent schematisms, and no knowledge of latent schematism without knowledge of laws. 1Obviously we cannot demand that the most general laws involve a nature that is "a limitation of a more general nature," for there have to be some natures which are the most general, some genus which is not a species of a higher genus. Bacon seems aware of this when in book I he condemns the demand for explanation of everything as one of the Idols of the Tribe: "For while the most general things in nature must be positive, just as we find them, and cannot themselves be caused [explained], nevertheless the human understanding, unable to rest, still seeks greater generality. . . . It is no less the mark of an unskillful and superficial philosopher to require a cause [explanation] in the most general things, than not to do so in things that are dependent and particular" (I, 48, italics and comments in brackets added). I would suggest that this demand, that our axioms involve a nature which is a limitation of a more general nature, be restricted to what Bacon calls "intermediate axioms" (I, 104).
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