Being Used by Metaphor: The Fallacy of Taking a Metaphor Literally
Turbayne distinguishes between two sides of the metaphor which cast a Janus profile on it: on the one hand, it can be used to express the otherwise un-expressible; but, on the other hand, it can abuse its users. Metaphor abuses its users when the "make believe" is taken seriously. This is where one must be vigilant. Otherwise, the "make-believe" is transformed into "believe" and the "as if" loses its meaning and becomes "is". Thus, from enjoying the tension created by the metaphor one can easily end up, if one is not careful, dwelling in an unreal world. This is what happened to Descartes, for example.
What Descartes intended to do with his Mathesis Universalis was to "transfer the certainty of geometrical demonstration to the procedure of scientific discovery, that is, the certainty of synthesis to analysis" (Turbayne 1970, 38). What this means is that Descartes’ quest for certainty had to take in the advantages of the mathematical method, "more geometrico".
Now, is this conjunction of scientific discovery and geometrical demonstration a valid one? According to Turbayne, it is not. Descartes engaged himself this in a sort-trespassing process. Unaware of the outcome of his quest, Descartes acted as if by saying that "man is a wolf", he actually believed that man was indeed a wolf.
Turbayne selects three cases of sort-trespassing where Descartes does not seem to comprehend the full implications of his arguments.
The first case of sort-trespassing "is that of the deductive relation with the relation between events. The former relation belongs to procedure […] The latter relation belongs to the process going on in nature" (Ibid., 46). Making use of deduction, Descartes was able to work with the theorems which were deduced from principles. "Principle and theorem were necessarily connected" (Ibid., 46). Supposing the principles were true, and because the mathematical method was employed, as in a chain of reasoning, it would be expected for the theorems to be true and therefore to be put at work in the process of explaining the world. Which brings us to the next issue. "The principle of procedure that starts a demonstration is repeated in the ‘active principle’ that starts the causal process" (Ibid., 46). Thus, what Turbayne argues is that when Descartes thought about the fact that "physical causes produce the existence of their effects, and that the effects necessarily follow from the causes" (Ibid., 47) he was applying the procedural algorithm to the physical world or, as Turbayne metaphorically puts it "a prominent page of the recipe was mixed in with the stew" (Ibid., 47). This act of shifting what was found in one domain into the other, or of associating them until they became "necessarily connected" gave enough grounds for Descartes to affirm that nature can be subjected to the deductive method. Which, Turbayne considers, is a clear example of taking a metaphor literally.
The second case of the sort-trespassing detected by Turbayne in Descartes’ system of thought is "the inadvertent identification of explanation with physical explanation and this with causal explanation, that is, the reduction of one to the other" (Ibid., 47). This means simply that Descartes thought the main preoccupation of physics to be that of discovering the laws governing the movement of the bodies and then, using these laws to account for their motion. And this explanation was nothing other than a causal explanation which implies that events were actually caused by the "physical laws". One should not forget Descartes was determined to make use only of distinct and clear ideas as opposed to "obscure notions". In this case, the clear and distinct ideas were offered by entities such as: "bodies moving", "bodies at rest" and "external causes" or "resistance", where the former ones are nothing but the effects of the causes expressed by the latter ones. All along Descartes’ explanation the word "principle" was used to designate both "the premise or statement of the law in the procedure and the active principle , the supposed cause in the process" (Ibid., 48). Thus, Descartes failed to see the difference between the physical explanation of phenomena and their theoretical explanation. The concept of force, used in theoretical explanations, is fallaciously ascribed to objects. "Something that belongs to persons or living things is ascribed to matter", Turbayne considers.
The third case of sort-trespassing involves the
unwarranted identification of deduction with computation or calculation or any other form of metrical reckoning or counting […] Because mathematical computation is constantly used in science, we must not regard it as a defining property. Because lines and angles are used to enormous advantage in optical demonstration […] we must not therefore succumb to the tendency to think that explanation by means of lines and angles exhaust optical explanation. We might just as well say that mechanical explanations exhaust science or that we cannot set up a deductive system without using differential equations. (Ibid., 49-50)
In Turbayne’s view, the Mathesis Universalis need not be geometrical. What is to be taken and used from the method itself is the demonstration feature and not "the nature of the terms used in it". The "geometrical method" is valuable inasmuch as it uses demonstration, not inasmuch as it is geometrical. It does not matter if the terms pertain to the area of geometry or not, as long as the algorithm followed is the one of demonstration.
Turbayne concludes that: "If we are victimized, then we confuse devices of procedure with the actual process of nature, and thus, unknowingly insinuate metaphysics"(Ibid., 56).