SYLLOGIZING AD PROBABILEM IN PSEUDO-SCOTUS

This essay interprets Pseudo-Scotus’ treatise on induction, his seventh quaestio on Aristotle’s Analytica Priora. I will emphasize a relevance of this treatise, as already pointed out by Egbert Bos (1991), namely, a new emphasis given to the probable status of general natural principles as the conclusion of inductive syllogisms. This represents an alternative understanding of induction and inductive syllogisms as compared to classical Aristotelian accounts, but it also differs from other approaches to induction in the 14 century. In doing so, I am drawing attention for a thematic already explored before, mainly by E.P Bos (1993, 1991), and also by S. Psillos (2015), but I will seek a contribution on an underexplored topic so far, namely, the role of the notion of probability in this text regarding the justification of induction in later medieval logic and dialectics.


Aristotle on Induction
The first approach to the problem of how we get knowledge from reasons that are not conclusive is Aristotle's.In the Topics and the Priora Analytics he formulated a theory of induction (ἑπαγωγή), originally to give an account of how we arrive at general principles from experience, such as the principles of natural philosophy. 1 As discussed in the Analytica Priora, induction is the mechanism of how we get to general principles about the natural world.As it is known, in the Analytica Priora Aristotle developed the formal theory of the syllogism, which is complemented by the approach of the 'demonstrative syllogism' (συλλογισμὸς ἀποδεικτικός) that we find in the Analytica Posteriora, the latter focused on the type of reasoning which transmits knowledge from previously known and evident premises to the conclusion.The demonstrative type of reasoning characterizes infallible or certain knowledge, that is, what Aristotle takes to be epistêmê 'without qualification'.Aristotle builds his deductive system under the assumption that the validity of syllogistic forms (using forms in a rather loose way here) are principled by the inference schemata of perfect deductions or syllogisms.Every other valid possible combination of premises and conclusion is reduced to them; these are, so to speak, the principles of Aristotle's theory of the syllogism considered as an organized science of deductive logic.2 But an inductive argument seems to constitute no exception in his treatment of inductive logic, but rather its evaluation is carried forward with a view to the deductive schemata.Aristotle's example for this apparent reductive account of inductive inference to deductive schemata is treated in his developed account of induction, namely in his main account in the Analytica Priora, B 23, especially in 68b15-22.3 Aristotle claims in this passage that in an inductive argument the application of a middle term to a subject term is what is being proved in a conclusion, instead of a predicate term: that is, the standard syllogistic form is now rearranged and the original middle term is built into the placeholder of one of the extremes, namely the predicate.His famous example consists of the following inductive syllogism (APr.68b15; Hinttikka, 2004: 114): Horses, men and mule are long lived animals.
Horses, men, and mule are bileless animals.
Therefore, every bileless animal is long lived.
Interestingly, Aristotle said that induction proves the middle of an extreme (68b15ff.).We could make the following sense of that.If we take an instance of any normal Barbara scheme AaB, BaC, AaC, and switch the role of the placeholder for middle term by the placeholder for one of the extremes, we obtain a syllogism which does not give a "causal reason" as demonstrative syllogisms do.But the inductive schemata are somewhat derivative, for Aristotle, and they are supposed to establish a necessary conclusion (or an immediate premise for further deductions).Elsewhere in the APo., he describes inductive inference as a cognitive process of concept formation.7In this way, hardly the theory of induction proposes an unequivocal logical approach to the probability of general principles (or immediate premises), since for Aristotle generality builds a sure way to necessity, and those principles are, therefore, statements of necessity.
Aristotelian syllogistic underwent a considerable effort at systematization and unification in the medieval logic.Medieval philosophers inaugurated the approach to the syllogism in a general theory of consequence, especially in the later 13 th and 14 th centuries, which also encompasses propositional logic, virtually absent from Aristotle's Analytics.We can expect that the theory of inductive syllogism as understood along the lines of APr.B23 played a role within this project.Part of an influential rendering of induction in regimented Latin is adding an iterative cause in the premises, as exemplified by Peter of Spain (Psillos, 2015: 96): Socrates runs, Plato Runs, and so of all; therefore, all men run.
The central logical item here is the enumerative clause et sic de aliis singulis, (to be picked up later by Ps.-Scotus under the heading of "clausula communis").The picture suggests something equivalent or at least proximate to Aristotle's doctrine of complete induction, and furthermore makes it explicit that complete enumeration of individual instances is important for 'complete' inductive arguments.
may be seen as a figure of fallacious reasoning, the non distributio medii.2015).If a new perspective is generated in these two highly representative texts for later medieval logic, this perspective is closely connected with the view we find in Pseudo-Scotus.

The Probable Syllogism: Pseudo-Scotus' Approach
The commentary tradition on the Analytica Priora is vast, and for its hardest part, the theory of modal syllogisms, confronted several interpretative problems.Pseudo-Scotus has an important role on this tradition (see Lagerlund, 2000).Although the work of Pseudo-Scotus is hard to situate historically, it was probably written on the first half of the 14 th century.This text was for long regarded as one of Scotus' own works in the renaissance and modern editions.The text was formerly included in the Vivès edition (1891-1895) of Scotus' Opera Omnia, along with several other texts of dubious authenticityfor an overview the editorial history, see Wolter (1987) and E.P. Bos (1993), regarding the commentary to the Analytica Priora in special.
As normal with quaestio-commentaries, it does not have prefixed textual structure set out by the original text, and it does not have a merely exegetical intent, but it seeks to explore philosophical problems within the latter.A quaestio commentary is rather a collection of independent questions.His seventh quaestio is what we are calling here the 'treatise on induction'; it is mainly about the following It is also important to remark that Ps.-Scotus wants to know if inductive arguments are good without qualification (arguendo absolute).I think the arguendo absolute here contrasts with the 'qualified view' of induction as in Duns Scotus and Ockham, namely, where induction needs a meta-principle in order to be justified.But he is sensitive to the problems a justification of induction can bring about.
According to him, we could get to general statements in the conclusion by four mechanisms or inductive procedures (Pseudo-Scotus: 195a; E.P. Bos, 1991: 81): (1) inducting to all cases sub propria forma by their singular enumeration; (2) inducting to every singular instances by a common clause which says so and so of every instance of the predicated (et sic de singulis); (3) inducting to some singular instances sub propria forma; (4) inducting to some singular instances by a common clause.
He describes the method of inducing from every instance to a conclusion (1) by the way of observing each instance of particulars, enumerating them singularly (enummerando singulatim).But 9 We take here "inducere in" as "induct into", without using his word in any more technical sense.
10 "(…) si fiat inductio in aliquibus singularibus et non habetur evidentia, ut ratio, quoniam ita fir in aliis, oportet quod respondens concedat universalem inductam, vel quod det instantiam in aliquot singulari, vel quod assignet differentiam quare non est ita de aliis singularibus sicut de istis, vel erit reductus ad metam inopinabilem" (Pseudo-Scotus: 196b; E.P. Bos, 1991: 83).With Psillos (2015), could say that for him, as well as for J. Buridan, the intellect has a specific role in induction which differs from the one recognized by Aquinas' and Aristotle's.Also, what is sufficient for the goodness of inductive reasoning is does not conforms to same standards as deductive syllogisms do.In his definition, Ps.Scotus says that "induction is a progression from some singulars or from every singular instance sufficiently enumerated to the universal conclusion" (Pseudo-Scotus: 197b; E. P. Bos, 1991: 85).Regarding (2d), it is important to note that a positio or the assertion of a premise which is immune to counterexamples is undesirable in the course of inductive dialectical reasoning.To the contrary, induction does not have the purpose of demonstrating "evidently" the conclusion, but to make a probable opinion as a conclusion.This topic is of some importance for Ps.-Scotus conclusions.
His conclusions give support for the idea that (3) and ( 4) are good candidates for an account of how induction works.We will go through the positive part of the treatise on induction.In the first conclusion, he indicates that induction is not valid in order to conclude of necessity, unless it would generalize over all singulars (what is impossible when they are infinite).Otherwise, we would admit a consequence with true premises and a false conclusion (Pseudo-Scotus: 195bf.;E.P. Bos, 1991: 82).The important aspect to note is that induction is not a consequence in the sense which deductive syllogisms are, but inductive syllogisms can nevertheless be good syllogisms.The second conclusion is related with the first one, and indicates that induction is not supposed to conclude evidently, unless the generalization is supported by a universal proposition among the premises.In this case, induction would not need any meta-principle or common clause, for it would be able to enumerate sufficiently and exhaustively.For an example, Ps.-Scotus picks the same one as Peter of Spain did, subtracting the common clause on the grounds of its non-propositionality (namely, the non-propositionality of "and so forth") and postulating a model which the premises exhaustwere "Socrates runs and Plato runs and Cicero runs; therefore, every man runs" to conclude necessarily and evidently, this would only be possible if there were only three men in the world, namely Socrates, Plato and Cicero. 14 The third conclusion is important.In this context, the notion of probability makes its appearance to qualify the status of the universal conclusion.He operates within the framework of the distinction of probable and closed induction as we see somehow in Albertus Magnus and Thomas Aquinas, as Egbert Bos pointed out, but it does not consider probable induction as a form of imperfect or derivative syllogism.Of particular interest is his III.3: In order to have a probable belief, creed or persuasion of a universal conclusion, it is sufficient to induce onto some singular cases, and permissible that it is not induced onto every singular case.And hence many inductions are good, arguing absolutely and E.P. Bos, 1991: 81 The notion of 'complete induction' is far from being unproblematic in medieval accounts of empirically based knowledge of general principles.Medieval authors were often engaged in discussion of the justification of induction by what Psillos has called the "induction dilemma" (2015: 98).For them, induction can be either perfect (based on a complete enumeration of cases) or imperfect (not based on a complete enumeration of cases but only on the observation of some).Typically, in the representative example of Aquinas, imperfect induction should be justified as creating knowledge by 'abstraction'; the intellect sees to it, on the experience of some cases or of a single case alone, that a predicate holds of other instances of the same subject, and then a connection between singular and general truths allows for the generalizing clause et sic de aliis singulis.8It is fair to say that the justification of induction was also pursued differently by John Duns Scotus Scotus and William of Ockham (Psillos, 2015), both of whom give it a metaphysical, rather than a cognitive, approach.In Scotus' Ord.I d.3 1.4, we see the use of a meta-principle drawn from the metaphysics of nature to justify induction, namely, the thesis unimpeded free causes yield always the same results(Wolter, 1987: 109).If this account is correct, things appear to have changed with the text we are considering, however, precisely when two texts are considered: our own treatise of Pseudo-Scotus, and also, proximately, John Buridan's Summulae de Dialectica (Psillos, : is it required for a good induction induct into 9 all singulars?Ps.-Scotus seems to refer here that induction is something different from establishing an evident and necessary consequent; it establishes a 'probable' principle or conclusion.A motivation plays a crucial role in evaluating inductive arguments, which replaces the generalizing abstraction model of Aquinas; namely, that inductive support is given not only as the premises give evidence for the conclusion, but by the absence of a counterexample (instantia) to the conclusion.Ps.-Scotus claims that, while seeking to object to an inductive argument, the "respondent" should then either give a counterexample, or introduce a distinction that explains why the predicate applies to some but not all singulars, or show a contradiction follows (meta inopinabile). 10This motivation plays a role in establishing inductive syllogisms in the quaestio.After all, the purpose of inductive argumentation is to establish a probable conclusion.For Ps.-Scotus, the status of the general principles which we aim at while construing induction is merely probable, and not necessary.Principles such as omnis ignis est calidus, if they are gained by experience, should then not be proved by any more general or more evident statements; to do so in argumentation would be to commit a fallacious move, if in the context induction should be a kind of ampliative reasoning or a progressio. problem It seems that Ps.-Scotus also took it that the intellect does not reach its target, namely general principles (or immediate premises for further deductions), by "generalizing abstraction".It rather reaches its goal by letting the conclusion survive the test of counterexamples.