The arts course: signs, induction, mathematics, experientia
5.1. In the second part of this review of the art course, I pass to instruments of thought which in some cases are less exalted and in others more specialised. Because of its importance in diagnosis and prognosis, sign theory is a particular concern to university teachers of medicine, as are analogy (in identifying illnesses and treatments) and induction (in reasoning from limited data). In different ways, issues of quantification (of humours and doses), of probability (of one construction of evidence against another), and empirical knowledge (including that acquired indirectly through the experience of others) also arise . I shall look at these issues in turn.
It is pertinent first to consider the doctrine of signs, which, together with topical argument and the theory of forensic oratory, was enriched after the discovery in the early fifteenth century of certain rhetorical works by Cicero and Quintilian1 . The ‘signum’ is recognised to be of importance to linguistics and to logic; in medicine, where it is also known as ‘nota’, ‘indicium’, ‘connotans’ and ‘indicans’, it is also of importance, and is recognised to be, according to a formula with which we are now familiar, a ‘latius nomen quam in logicis’2. Argenterio says it is broader because it is latent and plural3; but as well as being broader, it is also a looser term, belonging to Aristotelian language theory, syllogistic logic, conjectural arts and rhetoric, and not only to Aristotelian but also to stoic logic. It will be helpful first to set out the relevant parts of the Aristotelian doctrine before considering the debate among Renaissance doctors about the status of the sign and their uptake of the sign theory of the stoics.
5.1.1 Aristotelian signs Signs appear in a number of Aristotelian contexts4. We have already met the designation of the linguistic sign (the name) in the De interpretatione, i (16a 4ff.) as bearing no more than a conventional relationship to that which it signifies (above 4.2.1). In Prior Analytics, ii.2, (70a 5ff.), a general term (sēmeion) is introduced, and distinguished from a probability (eikos):
A probability is not the same as a sign. The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability, e.g. that the envious are malevolent or that those who are loved are affectionate. A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.
Aristotle goes on to discuss enthymemes which are syllogisms involving eikota and sēmeia, consisting only in a proposition and a conclusion, and shows that there are three ways of including signs in syllogisms which correspond to the three figures of the syllogism. As a sign is singular, the syllogisms derived from it have a limited validity, and indeed are only valid if in the first figure (DARII):
All who have milk are pregnant
this woman has milk
therefore she is pregnant.
In the third figure (IIA), the argument is clearly fallacious:
(2) Pittacus is good
Pittacus is wise
Therefore all wise men are good
The same applies to this less obviously fallacious version (AII):
All who are pregnant are sallow
This woman is sallow
Therefore this woman is pregnant5.
These Aristotelian examples are cited by doctors and by those writing as natural philosophers6. Frölich calls the sign in the example cited above a ‘rhetorical’, as opposed to ‘logical’ sign’; the fallacy with which it is associated is the fallacy of the consequent (if all A is B, then all B is A: see De sophisticis elenchis, vii, 169b 7f.); it is the one most to be avoided in medicine7. To extricate themselves from this fallacy, logicians have, according to Donald Morrison (citing Philoponus), to be Platonists (i.e. to take universals to be prior to particulars) and hence to unite ‘prior in nature’ with ‘prior to us’8. Otherwise the paralogisms in De sophisticis elenchis (167b 10ff.) apply: not only the fallacy of the man being hot having a fever, but also the paralogism (associated with a syndrome of signs) of a well-dressed man roaming the streets at night being the adulterer (see below 5.2.2; 8.4.2).
A further discussion in Prior Analytics ii.27 (70b 12ff.) relates signs to physiognomy:
[Supposing that] one grants that body and soul change together in all natural affections [...] and also that there is one sign of one affection, and that we can recognise the affection and the sign proper to each class of creatures, we shall able to judge character from physical appearance [...] in the first figure, provided that the middle term is convertible with the first extreme, but is wider in extension that the third term and not convertible with it: e.g. if A stands for courage, B for large extremities and C for lion. Then B applies to all of that to which C applies, and also to others, whereas A applies to all that to which B applies, and to no more, but is convertible with B. Otherwise there will not be one sign of one affection9.
These passages may be linked to discussion of signs in rhetoric: Rhetoric to Alexander, xii (1430b 30ff.) develops some of the distinctions mentioned above:
One thing is a sign of another - not any casual thing of any other casual thing, nor everything whatever of everything whatever, but only a thing that normally precedes or accompanies or follows a thing. Something happening may be a sign not only of something happening but also of something not happening, and something that has not happened may be a sign not only that something is not a fact but also that something is a fact. A sign may produce either opinion of full knowledge; the best kind of sign is one that produces knowledge, but one that causes an extremely probable opinion is the second best kind10.
Here mention is made not only of a hierarchy of certainty, to which I shall return, but also the possibility of signs bearing negative information, and of absence or omission being possibly a sign of something positive.
The term ‘eikos’, used for probability in the passage cited above, is used in Rhetoric, i.2 (1356b 1ff.) to mean sign and is described as a ‘protasis endoxos’, a likely or probable sign which occurs only generally (‘hos epi to polu’: ‘ut multum’, ‘ut plurimum’, ‘magna ex parte’); that is to say, even if generally accepted as having a certain sense , it is capable of having a different one. It is linked to a discussion of enthymeme, analogy and induction. Quintilian also refers to eikos and gives eikota three meanings: what usually happens (a judgement of frequency); what is highly probable (‘propensius’) and that against which nothing can be said. These meanings do not include the modal sense (what is possibly the case) or a mathematical sense (what is approximately the case) which we might expect to be mentioned in this context11.
A third Greek term for sign is tekmerion: in Aristotle (and according to some doctors, Hippocrates), a widely quoted distinction is made between tekmeria, which are necessary and can be used in the construction of a syllogism of the first figure, and sēmeia which, being no more than ‘probable’, cannot12.
Signs appear elsewhere in the Aristotelian corpus, with consequences for medical science. In the De divinatione per somnum, i (462b 27ff.), ii (463b 23ff.) it is pointed out that they may be empty of content, or may provide no information about causes, or may be insignificant if overtaken by signs of more powerful causes 13. And in the Physiognomica, which is a doctrine ‘wholly located in the discernment of sensory signs’14, a number of distinctions and theoretical points about signs are made, including the general rule that one sign is not sufficient to show a cause, but that a number of signs consistent with each other are required. The distinction between proper and common signs is upheld; the latter are only acceptable, according to Chiaramonte, in the second figure of the syllogism15. It is also argued both that there can be no inference from a proper sign (see above, 4.2.1), and that there can be no (scientific) demonstration from a single [common] sign, as the text of the Physiognomica points out ( ii, 806b 37ff.):
Generally speaking, it is foolish to puts one’s faith in any one of the signs; but when one finds several of the signs in agreement in one individual, one would probably have more justification for believing the inference true.
Giambattista della Porta quotes this text and expands on it16: he also makes the negative point about the proper sign:
Nor are proper signs of any use, for proper signs are proper of nothing other than that one thing, and correspond to nothing else, and signify their proper passion; and if they were to correspond to anything else, they would not be proper signs, and as no affect is proper to the animals from which we practice physiognomy, there would not be a peculiar sign either17.
Other points of doctrine in the Physiognomica decree that signs can demonstrate a negativo or a contrario18; that they can be both innate and acquired, and permanent and labile; that the same sign can indicate quite different mores, and can indicate an accident not a substantial feature19 L’Alemant’s summary of Aristotelian doctrine is as follows:
There are [three] sorts of demonstrations from signs. The first is inferred, when a cause unknown to us is proved from a manifest effect, as in this case: as often as these symptoms are seen, namely difficulty of breathing, a stabbing pain in the side and persistent fever, there will be inflammation of the intercostal membrane; but pleurisy has these symptoms; therefore pleurisy is an inflammation of the intercostal membrane. The second sort infers an effect hidden from us from a sign. Whenever stiffness follows on from an ardent fever, it causes the fever to go away. But when the bile inflaming the skin, is evacuated through sweat, stiffness occurs. Therefore when the bile inflaming the skin is evacuated through sweat, the ardent fever goes away. The third sort assumes a remote cause, as in this example: anything which is troubled by melancholy is an animal; a plant is not an animal; therefore a plant is not troubled by melancholy20.
We can see here three medical examples, including the standard medical example of a syndrome of signs (see below 8.4.2) accommodated to syllogistic structures.
These Aristotelian texts generate both areas of agreement and clear differences of opinion among Renaissance doctors. It is also universally accepted that this always involves a passage from the known to the unknown, which, in the case of a posteriori reasoning, is a conjectural passage21. But whether the sign is sensory or intelligible in nature, whether it is a pre-rational datum, or a middle term, or the minor proposition of a syllogism are matters of debate. This is still of particular interest, as some elements of the debate recur in present-day disagreements between analytic philosophers and linguistic semiologists such as Umberto Eco. In reviewing the latter’s work, Colin McGinn asks ‘what non-trivial theory can be derived from treating human languages and measle spots as both instances of interpretable signs?’ and claims that ‘the perceptual recognition of signs and other objects is not itself a process of semiotic inference’22. This position may be compared with that of Argenterio, who adopts a very radical stance. For him signs fall into two classes: things which signify something and things which indicate that something should be done23: the second is the indication, which will be examined below (8.7). Of the first, he says that he sees no need to make a distinction between sēmeion and tekmerion; he believes that the broader sense given to sign absolves him from distinguishing not only between necessary and probable signs, but also between modes of signification, whether by effect or in any other way. For him to signify is tacitly to indicate one thing by another; this tacit admonition occurs through the comparison of the signifer with the signified, which is simultaneously grasped by the intellect without an express act of reasoning. There is no inference involved; the sign is a substitute for its signified, as is smoke of fire (a standard example, given a new use here)24. This is consistent with the claim that signs simply stand for something else, as do tavern signs25. A substitutive sign of this kind is a particular discovered by sense; Vega says that it is what is submitted to sense, leading us to the knowledge of something hidden from our senses, as pallor indicates the excess of bile in the body; Fernel describes the sign as something evident to our senses which accompanies something hidden from them; Lucius declares that it can indicate both the latent and the manifest (‘apparens’)26 .
But signs can also be described as mental objects, whether propositions discovered by reason or middle terms in a syllogism. Capivaccius is responsible for the prevalent definition of the sign as proposition:
Therefore the medical sign is a proposition, produced by the intellect from some sensory object or objects, revealing a posteriori something in the medical art which was unknown. From this it follows that every sign is to be sought either from what preceded the thing signified, or followed it; therefore, from the cause or from the effect27.
He here characterises medical signs (or rather their forms) as belonging to the order of the intellect (which is their efficient cause), and links their use with the Aristotelian doctrine of enthymeme28. At the same time however he stresses their necessary reference to objects perceived by the senses. In other passage, he derives from two Aristotelian loci (De interpretatione, i 16a 3f; Posterior analytics, i.6, 75a 28ff ) three distinct ways of looking at signs: the first involves looking at them either a priori (which can be done either by seeing the sign as a ‘causa essendi [simpliciter] or ‘causa inferendi’ [secundum quid])29; or a posteriori (as in the case of words which are signs of the passions of the soul); this latter mode can only be determined by inference. The second way involves looking at them formally (signifier and signified thereby become correlative, and are of the same nature); the third ‘fundamentally’, in the cases where the signified is posterior to the sign. His purpose here is to demonstrate that there are as many modes of sign as there are of things signified 30. Although this division appears in the writings of others and has the warrant of Galen, one may sense here a particularly Paduan predilection for scholastic logic, which leads to the slightly surprising allegation of a premonitory sign as a cause31.
Campilongo, although in some matters a declared disciple of Capivaccius, adopts a third position, which is to define the sign as a middle term and not a whole proposition. In the passage in which he speaks of non-prognostic signs, he cites the Aristotelian example from Prior Analytics, ii.27 (the pregnant woman having milk) and the standard Galenic example of the four signs of pleurisy, which taken together are ‘like a middle term’ (‘tamquam termin[us] medi[us]’), and then adds an appendix to his work justifying this claim against some unnamed opponents, who presumably include followers of Argenterio and Capivaccius. He engages in a technical logical and exegetical exercise both to save the text of Aristotle from inconsistency, and to establish that it is not correct to conclude from various loci that the Stagirite claims the sign to be a proposition; and finishes with a defence of the dual nature of signs as sensory and intelligible32. His position is modified in this last respect by Horst, who calls a sign ‘a certain mental concept, by which something in the operation of the medical art which is unknown is derived from existing knowledge’33. Part of the issue here is the status of indications, on which some doctors such as Argenterio and some faculties such as Montpellier place great weight, and which others (mainly Paduans) reduce in importance. In showing the role of the sign in the syllogism, the latter declare their explicit adherence to Aristotelian logic . The former, by concentrating on indications, stress the performative nature of the medical art. Among the medical logicians, therefore, there is a clear difference of opinion about the nature of the sign, whether proposition (conjunction of subject and predicate) or just middle term.
5.1.2 Stoic signs: epilogism and analogism As well as in Aristotle, signs play a role in stoic thought, which is mediated to the Renaissance in the work of Galen, who makes frequent reference to it. Signification is stressed in the pseudo-Galenic definition of signs as ‘all those things which signify something, or all those symptoms (‘accidentia’) which reveal something unknown and hidden’34. In his work may be found the same Aristotelian distinctions between tekmeria (which demonstrate unambiguous in a necessary way ) and sēmeia (which are not necessary, and which only signify ‘ut plurimum’)35, and between proper (inseparable, in Galen’s terms) and common (separable) signs; this latter distinction is extended by Cardano through combinatory logic to encompass signs which are proper and inseparable, proper and not inseparable, not proper and inseparable, and neither proper nor inseparable36. The most important part of stoic sign theory concerns the distinction between analogism and epilogism; the former (rejected by empirics) being an inference from an indicative sign which is unverifiable by experience, and which uses sensory phenomena to infer hidden conditions of the body; the latter, being an inference from a commemorative or hypomnestic [associative] sign, which is observed in conjunction with what it signifies, as is smoke with fire. This latter is accepted by empirics, who declare this to be verifiable empirically and able to be stored in the memory. The distinction clearly separates empirics from rational doctors who argue that just as geometry can show that there are only three types of triangle (this not being a matter of experience), so also the rational doctor can interpret combinations of signs beyond recalled individual cases37. As diseases have many manifestations, memory alone cannot lead to their identification, but rather a judgement about a range of symptoms and their strength and power. What is in question for rational doctors is not simple similarity but relevant or dominant similarity, used as a logical or interpretational tool38.
Epilogism allows you to say that something is so from its effect; (‘quod ita sit ab effectu’); but analogism can answer the question why it is causally so (‘cur ita sit a causis’)39. This reading of the distinction (by Cardano in the middle of the century) is somewhat different from that undertaken earlier by da Monte, for whom analogism is a ‘a sort of relation of the particular to the universal, permitting of a particular conclusion which takes the form that the major is a universal proposition, and an individual the subject of the minor’; and epilogism ‘a comparison of like with like, which is proper to empirics in the same way that analogism is proper to [rational] doctors’40. Da Monte here allows transgressively the middle term to be a particular, which he extends to the empirical individual41. After Cardano, Sanctorius rejects both analogism and epilogism on the authority of another Galenic text (Methodus medendi ii.6-7, K 10.115-56) and stresses the role of demonstrative division42. His chapter on this topic (xi.2) is entitled ‘Demonstration drawn from Aristotle and Galen that remedies can be investigated only by the method of division and never by experientia or analogism’43. For Sanctorius, particulars cannot belong to the sphere of knowledge; what is relevant is the cause or ‘indicans’, not similarities in the affected parts, diseases or palliatives (‘iuvantia’), and he uses paralogism (the fallacious forms of the syllogism) to demonstrate the failings of unconvertible particular propositions.44 Campilongo extends the discussion to the activity of the mind in accepting data; for him commemorative signs lead us to the knowledge of the disease, in which the intellect acquiesces; whereas there are there are signs of things which lead us to knowledge in which the intellect does not acquiesce; such counter-intuition has a role to play in indication (see below, 8.7)45. The smudging of the line between the order of the objective and the order of the psychological (subjective) is here again detectable.
There are other aspects of post-Aristotelian sign theory which are picked up by doctors; one of these is the developed version of the distinction between the common (koinon, commune, separabile) and proper (ideon, proprium, inseparabile) sign, found in Sextus Empiricus and Galen; another is Cicero’s and Quintilian’s discussion of signs and enthymemes and the signs peculiar to weather, dream interpretation and other conjectural arts46. In the end, a hybrid doctrine is evolved by which the medical art is admitted to be ‘defective in those parts which concern signs, more or less completely conjectural and hardly necessary or demonstrative at all’47. This defect arises from the enthymematic, inductive aspect of medical semiotics; it is merely resolutive in that it is inductive and proceed through sensory knowledge; it suffers the vice of ‘magna ex parte’ logic, and consists in the ‘artificiosa coniectura’ which Galen places between ‘exacta notitia’ and ‘omnifaria ignorantia’ (above, 4.3). The certain enthymemic reasoning using the necessary or unambiguous sign seems to be an asymptote, as there seem to be no sinbgle pathognomonic signs which are cited in these manuals (below, 8.4)48. Sanctorius insists that we must have a ‘convertibilis cognitio’ of any diagnostic conclusion, and that in nearly all cases (‘fere semper’ this will come from a syndrome of signs. The example he offers of this is pleurisy (for which he invokes a greater syndrome of signs than any other source). It is not clear whether he is arguing that all of these signs need to be present, or whether they constitute a polythetic class49; but he does concede that there is a fault in the logic of the syndrome of signs unless each sign is convertible with the disease, which, as they are common signs, they will not be50. So his ‘infallible [diagnostic] science’ of ‘six sources of information, no more, no less’, is not infallible, by his own admission:
For the rest, as common signs are more or less infinite in number, we have only agreed to include those which succeed the antecedent and subsequent causes, which we can carry over into our six sources51
The claim that six is a sufficient number is a mathematical, not a logical claim (he calls it at one point an ‘argument from the enumeration of a sufficient number of parts’52); it is symptomatic of the movement towards computation which is examined below (5.2).
For his part, Liddel introduces such words and formulae as ‘magna ex parte’ ‘pauca sunt...quae...’ and ‘plerumque’ at various points of his text to allow for exceptions which indicates, I believe, the same trend 53.