Thought for the Evening: Convertibility of Signs and Principles
One of the most important aspects of human life consists of probable reasoning, by which I mean not 'reasoning with those quantities called probabilities' but reasoning that deals with the truth-like, the apparent, and the only partially proven, with signs rather than proofs. A significant part of any intellectual inquiry consists of pulling these signs together, first in a way that starts to make sense, and then in such a way that they serve as a foundation for claims about truth, and then in the development of what is effectively a proof (although not always a strict demonstration). The key issue governing proof by signs is convertibility of evidential signs with actual principles and causes.
Following (somewhat loosely) St. Albert the Great in his discussion of signs of verisimilitude (Topicorum 1.1.2), we can organize these evidential signs in something like the following way.
(1) Evidential signs that are immediate phenomena, 'on the surface'. These are typically sensible qualities or immediately experienced features of the world which have a connection with deeper things. Thus, the whiteness of snow gives us a clue about its internal structure, but there is a significant gap of inquiry in the two, because the whiteness of snow is immediately recognizable but the internal structure to which it is a clue takes a considerable amount of investigation to reach.
(2) Evidential signs intermediate between the immediate phenomena and underlying principles. Albert takes the intermediate level of signs of truthlikeness to be the ones that are recognizable to many with only a little reasoning. His example is the pole star as a sign of the movement of the earth; the former shows the latter with a little reasoning that is of the sort that closely connects with things that most people don't have a difficulty understanding, if they put an effort into understanding the reasoning.
(3) Evidential signs convertible with the underlying principles. 'Convertibility' here means that they have an immediate connection such that they go together. Albert's example is the eclipse and the relative motion of the moon. These signs can only be recognized by considerable reasoning and investigation, and so are only apparent 'to the wise', but when you recognize them, it is practically like recognizing that of which they are signs. These signs themselves have three grades:
(3a) Convertible so as to be recognizable by reflection on experience. These are are cases in which the actual convertibility is something we can sense.
(3b) Convertible so as to be recognizable given relevant competency. The actual convertibility requires at least a general kind of skill to recognize.
(3c) Convertible so as to be recognizable with great experience and familiarity. The actual convertibility requires what we call relevant expertise to recognize.
However, we can take complexes and patterns of evidential signs together, and interlink them in various ways to get new signs, and because of this we can embed a superficial sign in a context of signs that gets us to (2) or (3). We can also strengthen signs by ruling out possibilities, and so we can transform a type (1) or type (2) sign into a type (3) sign by ruling out all connections but one between the sign and the underlying principles of which it is evidence.
Historically, people seem to have worked out at least four kinds of methods for transforming signs so that they are convertible with principles -- at least, methods that can be seen as such. The earliest, which we find forming in Plato's account of dialectic and developed in Aristotle's Topics and commentary on it, consists of maximal propositions and commonplaces (topoi or loci communes) and topical differentiae, which are principles for how to construct arguments given various starting points. An example of a maximal proposition would be, 'When a material is lacking, what is made from the material is lacking', whose differentia is 'from a material cause'. Suppose you were inquiring into whether a society had swords, but you don't have any direct information about it. To answer, "Does this society have swords?", you can apply the maximal proposition from material causes by recognizing that effective swords require certain kinds of materials -- bronze, iron, steel -- and then you can see if you have evidence that rules out each kind of material being commonly available. The more completely you can rule out the materials needed to make the swords, the tighter connection you create between your evidence and the actual causes and features of the situation. Another maximal proposition is, "It is not right to contradict what seems to be the case to everyone or the many or the wise." This differs from the previous one by being the maximal proposition for an 'extrinsic' topic, and the way you would approach convertibility would be by looking at the reasons why it seems true to everyone or the many or the wise, since, if something seems true to all or to many or to the intelligently informed, then even if it were strictly speaking wrong, there would have to be a reason why it seemed true to them.
A second method people have worked out to get convertibility of signs and principles is Nyaya, the systematic logical approach developed around the 2nd century by (it is thought) Aksapada Gautama in the Nyaya-sutra, and which, in the roiling turmoil of Indian intellectual thought, where massive numbers of different intellectual positions were put into argumentative competition, was raised to a high degree of sophistication, taking various forms in different Indian philosophical schools but perhaps reaching its most thorough form in the Nyaya-Vaisheshika school. The term that approximates what we are calling 'convertibility' here is in Nyaya called vyapti, or 'pervasion/concomitance'. The Nyaya approach identifies various pramanas, or ways of knowledge -- like perception, inference, and testimony -- which allow conclusions to have a connection to what is true, and an elaborate, and sometimes remarkably clever, apparatus was developed for analyzing ways in which such connections can go wrong and right. The result is encapsulated in what has popularly become known as the 'Nyaya syllogism', roughly: "There is fire on the hill? There is smoke on the hill. Wherever there is smoke, there is fire (i.e., pervasion between smoke and fire) as with a kitchen hearth (example of another actual case where the same pervasion is found) but unlike a steaming lake. This hill is smoky in that way. So there is fire on the hill." Or another example: "Atoms and karma have to be given direction by a conscious agent before they can function? They are insentient like an axe. Insentient things come to function only when directed by a conscious agent as a cause, as axes cut only when directed by an axeman. So atoms and karma also have to be given direction by a conscious agent as a cause."
A third method, which overlaps the first, is that of demonstrative regress. Some comments in passing in Aristotle's Posterior Analytics on demonstration in causal reasoning caused problems for commentators, because Aristotle seemed to attribute demonstrative status to a kind of argument that he elsewhere denies can be demonstrative. Early commentators interpreted him as using 'demonstration' (apodeixis) loosely, but in the Renaissance, commentators were not so sure and began to explore other possibilities, and this tradition, which perhaps can be said to begin with Agostino Nifo, reached its clearest form in the works of Giacomo Zabarella. Zabarella, pulling together ideas from prior commentators, argued that there is a kind of beneficial circular argument (regressus) in which you start by inferring the existence of a cause from the effect (Nifo calls this syllogismus conjecturalis, where 'conjecturalis' means not conjectural but non-necessary), and then by a business of understanding (negotiatio intellectus) or intelligent inspection (examen mentale) you make confused ideas more distinct; as you might expect, it consists of making distinctions and working out the implications of those distinctions until the whole field, so to speak, is well ordered, at which point you can prove the effect from the cause with a syllogism that has necessity ex condicione -- and thus you get a genuine demonstration for a conclusion, where certain conditions discovered in the negotiatio are respected. Cassirer noted that there were similarities between Galileo and Zabarella, and through the work of William Wallace and others it is by now established that Galileo knew the demonstrative regress and often makes use of its terminology, but he begins to rework the negotiatio to focus on geometry and experience rather than a priori distinctions, and as time goes on thinks less in terms of syllogisms than in terms of geometrical analysis. Wallace used this to show that many classical scientific discoveries could fairly easily be put into regressus demonstrativa form, even when the discoverers were not themselves thinking in those terms.
A fourth method we find developing with Francis Bacon's attempt to give an account of induction. Bacon suggested that we find the forma naturae of a given phenomenon by drawing up lists of what we found to happen with it in various circumstances and see what in these lists agrees and disagrees with what. This was put in a more rigorous form by John Stuart Mill in A System of Logic. Mill, looking over common patterns of inductive reasoning, condensed them into four or five 'methods' (depending on how they are counted) along the lines of Bacon's lists, which are summarized in the Canons of Induction: the Method of Agreement, the Method of Difference, the Joint Method of Agreement and Difference, the Method of Residue, and the Method of Concomitant Variations. For instance, in the Method of Agreement, you note that a phenomenon occurs in a number of different situations, which also share another phenomenon; from this you conclude that the two have a causal connection, and then you just keep applying the different methods until the causal connection becomes clear. Mill intended this to be a complete account of experimental reasoning; Whewell at the time pointed out that this is not how large portions of scientific inquiry works, but it had a great deal of influence in a number of scientific fields, for an extended period of time.
Various Links of Interest
* Ian J. Campbell & Gabriel Shapiro, Can You Deny the PNC? (Metaphysics Γ.3, 1005b11-34) (PDF)
* Nils Peterson, Goodbye Dorothy Parker, Apologies Edgar Guest, at "3 Quarks Daily"
* Mauricio Suárez, The Pragmatics of Scientific Representation (PDF)
* Marie Leborne Lucas, Neither One Nor Two. Philosophy of Pregnancy, at "Blog of the APA"
* Jeffrey Maynes, The method(s) of cases (PDF)
* Katja Crone, Foundations of a we-perspective
* Katie Ebner-Landy, David Hume vs literature, at "Aeon". This is an interesting argument, but I think things are slightly more complicated if we taken into view Hume's historical works, which certainly do use the character-sketch method as one of several methods.
Currently Reading
In Book
Walter Wangerin, Jr., The Book of the Dun Cow
Andrew Willard Jones, The Two Cities
Oliver O'Donovan, The Disappearance of Ethics
In Audiobook
Robert Jordan, The Eye of the World
Lois McMaster Bujold, The Vor Game
Lev Grossman, The Bright Sword
