- Ockham’s world and future
- Ockham’s world and future Arthur Gibson PHILOSOPHICAL BIOGRAPHY Ockham was born in about 1285, certainly before 1290, probably in the village of Ockham, Surrey, near London. If his epitaph is accurate, he died on 10 April 1347. Yet Conrad of Megenberg, when writing to experts in the know, appears to assign to Ockham a piece written after November 1347, so perhaps the epitaph was doctored. It has been affirmed that he died in Munich, possibly of the Black Death, though perhaps the Plague had not yet reached Germany or Bohemia by that date (see [14.55] 27–8). Whatever the correct view, the beginning and end of his biography are subject to some uncertainty. Ockham’s intellectual life is replete with confident redefinition of contemporary philosophical concepts, often drawing on, or sharing in, the work of other theologians doing philosophy. This redefinition was not a source of pleasure to the powers that be. Medieval Christian philosophy was the manifestation of complex axioms, the restatement of which was a constant attraction as well as a risky endeavour. Arriving at Oxford in 1309, the Franciscan Ockham was eventually perceived by the Chancellor of the university and secular theologian, John Lutterel, to have fallen from grace. This was partly because Ockham did not accept this Chancellor’s own Thomistic doctrines. Lutterel was fighting a rather lonely rearguard defence of Aquinas, since Ockham’s philosophy was preoccupying most of the English scholars in his subject.1 Ockham had studied under the previous Oxford Chancellor, Henry Harclay (who died in 1317),2 and he had embraced the latter’s criticism of Duns Scotus on universals. In about 1315 we find Peter Aureoli developing similar criticism. Ockham was not, then, the sole dissenting original thinker in a burgeoning trend of new reflection, which was stimulated in part by the unexpected revival, and modification, of concepts of supposition (denotation) theory. Scotus’s work acted as both a major focus for and influence upon scholars at Oxford. He had reformulated aspects of recently past scholarship in ways that attracted Ockham’s debt, often through disagreement. Moving to London, after a less than peaceful time at Oxford, Ockham continued undeterred to compose his philosophy until 1324, even though in the previous year John Lutterel had already attempted to procure from the Pope in Avignon a judgement of heresy on fiftysix of Ockham’s theses. The papal legal process was commenced in spring 1327, and, even in June 1328, after a year’s work of the inquisition on Ockham, it had not yet managed to furnish a case against him using Lutterel’s evidence.3 Francis of Meyronnes counselled that Franciscan scholars in the interim should eschew public and unqualified determinationes of their traditional position (see [14.55] 57–9). Ockham’s conscience, leading him to open dispute, aggravated the situation. When at Oxford Ockham was carefully listened to by a number of scholars, including Walter Chatton and Adam Wodeham. Chatton was the most likely source of Lutterel’s indirect knowledge of Ockham’s views, though he did not purposely act as an inside-dealer against Ockham. Rather, Chatton was attentive to him because of his own interest in Ockham’s epistemology, which departed from the perspectivist theories with which he was familiar. The political conflict between Ockham’s Franciscan order and Pope John XXII (concerning the criterion of application for poverty) occupied a central place in his attention at Avignon, not least since he was asked to read the disputed papal bulls on this issue (see [14.11] xvii). By the time Ockham left Avignon he was a defendant in a heresy accusation concerning his earlier writings. But the principal reason Ockham departed was that he accused the Pope of heresy regarding his teaching on rights and poverty. Ockham departed from Avignon for the protection of the Holy Roman Emperor, Louis of Bavaria. Excommunicated, he thenceforth composed political philosophy for the rest of his life. A PRELIMINARY PICTURE OF OCKHAM’S WRITINGS AND PHILOSOPHY Ockham had finished writing his non-political philosophy by 1324. He had lectured on the Sentences at Oxford between 1317 and 1319. The next compositions were his Expositio aurea (‘Golden Exposition’, of Aristotle’s logic) and the Exposition of Aristotle’s ‘Physics’ (Books I–IV); all these were written during 1321–3. In addition to these, by 1324 he had produced his Summa logicae (Textbook of logic), the Quodlibets, the remainder of the Exposition of Aristotle’s ‘Physics’ (Books V–VII), and his two treatises on quantity. As well as a reportatio of his Oxford Sentences commentary, Books II–IV, there is a revised version of his lectures on Book I, an Ordinatio, probably dating from 1319–24. With the implicit reference to and condemnation of Ockham as a heretic by Pope John XXII (6 June 1328) in his bull Quia quorundam, Ockham’s work was disrupted. By 1332–4 Ockham commenced writing his, eventually very extensive, political philosophy, the first volume of which is Opus nonaginta dierum (Work of Ninety Days). Its extraordinary length and impartiality are amazing in view of his personal circumstances. Yet by late 1334 he had also composed and sent his Epistola ad Fratres Minores (Letter to the Franciscans), as well as having written I Dialogus, a very long neutral treatise on the concept of heresy and its application to papal authority, both now in English thanks to the fine editions of Stephen McGrade and John Kilcullen (see [14.11] and [14.7]). As with other medieval scholars, we should reckon on our possessing less than Ockham’s complete works. Non-extant writings and their detail, deemed to be obscure or of marginal significance, may not have been so regarded by Ockham or some of his contemporaries. It is possible that his lost writings, if rediscovered, would change topics in his philosophy. For example, Rega Wood draws attention to citations attributed to Ockham which do not occur anywhere in his extant writings ([14.102] 30–1; cf. her n. 25). These appear in the sole extant copy of John of Reading’s Sentences. This Reading, a Franciscan, typifies the lesser, yet ecclesiastically significant, type of figure who contributed to the battleground of dispute with Ockham. By 1323 Reading, interestingly a former student of Lutterel’s, was to be found as a consultant to the Pope at Avignon prior to Ockham’s arrival. Reading disputed Ockham’s view of intuitive cognition. He maintained that intuitive cognition of non-existents is possible ([14.2]). Although he was influenced by Duns Scotus, Reading here disagrees with him (see [14.93] 166–74), and he bases his case on God’s absolute power. God was central to Ockham’s philosophy. He was a theologian who did philosophy, with a penchant for logic. Although his researches in logic are detailed and widespread, they are not a formal system in our modern sense. Ockham was more explicitly interested in formal questions of logic than Aquinas, yet his instinct and understanding fall short of Aquinas’s. His fundamental principle for God and logic is simplicity. This is not a project about presentation—it is easy to think him ironic about simplicity when we view the often torturous complexities of his logic, though his writings betray no sense of whimsicality. His simplicity has its ideal in God: the unity, the necessity. ‘Ockham’s razor’ is a label for the philosophical counterpart of God: a principle to reduce, or keep, entities to a minimum. Just as a theologian views polytheism as a corruption threatening monotheism, so Ockham’s philosophy treated the multiplication of species as a corrosive infecting our perception of world-structure that mirrored God. Ockham’s programme relies on the reduction of ontological categories to just two, substance and quality—though he has no systematic logic worked out for implementing such a scheme. Ockham produced an extensive formal philosophy. Yet, rather like Bertrand Russell, he did not integrate his formal interests with his dialectical (for example, ethical) writings. This perspective is only slightly misleading, since Ockham’s dialectically presented political philosophy only obliquely embodies some of his other philosophical concerns. But Ockham sometimes makes an explicit, albeit unexpected, connection between the dialectic of obligationes and the logic in his Summa Logica. For example, Ockham’s philosophical logic there deals with the concept of ‘consequence’ and impossibility in its varying paradoxical forms under this general heading. In twentieth century terms, Ockham might be described as carrying out a thought experiment. Eleonore Stump illuminates the way Ockham connects the topics of ‘obligations’ and ‘insolubles’ (see [14.92] ch. 12). ‘Insolubles’ were forms of conundrums or paradoxes, and this linking of the two topics together was usual in Ockham’s lifetime. He attempted to show how impossible propositions might not, in disputations, obviously entail a contradiction. As Spade shows,4 Ockham permits self-reference in his logic. Ockham’s technique modifying Walter Burley’s, is to submerge the collisions in premisses concerning relevance to yield a possible world which both satisfies typical conditions of possibility, yet produces a state of affairs that unexpectedly reconfigures subjunctive conditional boundaries. This is not unlike Lewis’s [14.59] wider pluralising of worlds, increasing entities, not reducing them. Gensler has recently shown how one might discover such interconnections, more secure than Ockham’s ([14.39]). Although Ockham did not develop his work on obligations theory within his political philosophy, it seems clear that he was implicitly injecting the results of research into his political and ethical theory, in the way he combines canon law, logic and case-precedent technique, for example in his III Dialogus ([14.7]). Research on logic readily inclines a philosopher to give attention to the mental bedrock that facilitates the use of logic, and the perceptual spheres which are its media of operation. Although Ockham was committed to Aristotle’s maxim that ‘man is a rational animal’, he believed that this truth is often submerged by other psychological and dispositional tendencies, and certainly his political philosophy (see below) indicates that this is true of humanity. But unfortunately, Ockham’s own stress on the roles of the mind and universals provoked him too readily to internalize the grounds of knowing. A contemporary of Ockham’s, Durandus of Saint-Pourçain, stressed the person who observes—the agent, rather than the object known—as the ground for knowledge. Ockham was so impressed with this approach, that with the aid of divine intervention he supposed that one might have an intuitive cognition of a non-existent thing. But in usual circumstances, ‘intuitive cognition’ for Ockham marks the knowledge of a present singular individual with properties. This situation is partially causal and conjoins with one’s simultaneous abstractive cognition of the individual with properties. Abstractive cognition of this state of affairs lays the perceptual and prepositional mental grounds for repeating, and thus extending, the process and cognitions to like individuals. Memory is partly composed from such cognitions, and when there is a temporal lapse after intuitive cognition, there remains an imperfect intuitive cognition permitting the observer to infer the truth of the relevant past tense proposition representing a given experience (see [14.64] 186). These distinctions were the subject of extreme technical debate, bound into the science of the times. Adam Wodeham (see [14.93] ch. 10) was inclined to follow John Duns Scotus and dispute Aureoli’s view that intuitive cognition is understanding by means of which the individual is either present or appears to be. Wodeham nevertheless learnt from Aureoli that it would be possible for a perception to satisfy the same truth conditions if an absent entity were simulated, and so, on Ockham’s hypothesis, delude the observer by causing intuitive cognition. This is quite a different problem, Ockham thought, from having intuitive cognition by means of miracle. It is interesting to consider how the science and technology of a period affect philosophical theorizing: would televised individuals have been a convenient ‘presence’ for Wodeham with which to challenge Ockham? OUR DIFFICULTY IN DEFINING OCKHAM Controversy and misrepresentation attended Ockham’s philosophy in his own time and later. Philosophers of today display some qualified parallels with Ockham’s relation to his, not always intended, deconstruction of elements in medieval philosophical traditions. His philosophy contributed to the medieval ‘new modernism’; this is a designation Stephen Nicholls employed to characterize French medieval cultural contexts (see [14.71]). One might extend the depiction of this ‘new modernism’ to Ockham, and to others, by describing it as a claim to return to the past whilst reinventing it as a new future for, and to dispute with, the present. Typical of this is Ockham’s break with the medieval world in his treatment of logical and metaphysical relations. As with post-Enlightenment French romantic modernists, however, Ockham wished to look back to past archetypes (such as Aristotle) whom he moulded in his own image for the future. Central to the assessment of Ockham is the problem of measuring our own sounding-boards. In the late nineteenth, and twentieth century, what can be termed modernist logic5 and its philosophy of language are often presupposed by philosophers, in differing ways and sometimes indirectly by contrast, as the correct or true frequencies for observing the quite different universe of Ockham. These modernist logic developments stem principally from the work of Gottlob Frege ([14.34]– [14.36]), though there have been many developments since his last publication in 1923.6 Conversely sometimes there is a romantic disposition to give the privileged status to Ockham’s logic as if it should remain unchallenged by our analytical philosophy’s research and logic. This priority has not entirely escaped the epoch-making study by Marilyn McCord Adams,7 to which the reader is referred as the principal research resource on Ockham. For example, Adams judges ‘Peter Geach [to be one] who writes from a Fregean bias’ ([14.12] 393 and n. 34). Geach criticized Ockham’s two-name theory of predication.8 Adams does not attempt to prove her curt partisan dismissal of Geach and Frege. The problem here is not a matter of local in-house debate. It is a dispute about the identity of logic; to what extent should a logician’s work be judged by timeless, absolute standards? To what extent must it be seen in the context of its times? Some fresh general considerations expressed here require more research, not least since the generality and boldness of Ockham’s theories lay claim to answers outside his, and sometimes our, logical ken. But as we now attempt to look back at him, a straight contrast between, say, twentieth-century philosophical logic and Ockham’s medieval world obscures, fails to account for, explore, or sufficiently query, complex interconnections and differences between Ockham’s own philosophical prehistory and our contemporary philosophy (cf. [14.80]). Assuming that there is such a thing as logical truth, however, or if we presuppose that humans have made some progress in understanding logic, it would be surprising to conclude that Ockham’s position did not need revision or development after over 600 years. For Ockham, the expression of language which is the soul-home of concepts and utterance is in the mind—the mental language (peculiarly like, but not quite identical to Latin)—as Paul Spade points out (see [14.89]). In Ockham the strongest version of meaning is an internal utterance within the mind. This mental model is accordingly psychologistic, and it is reductionist. Is the concept of a mental language that is not itself the intention with which one speaks credible? Could Ockham’s philosophy benefit from modern work which argues that all natural languages can be treated as manifestations of underlying neurophysiological genetic syntaxes or semantics? Even were there to be an affirmative answer to this question, do we yet possess the, or most of the, formal elements which would constitute understanding of the logical ingredients of such a map? Does the Latin of Ockham display relativity which is in tension against this purported universality? Is it proper to employ our modern formal logic ‘languages’ to symbolize (and thus to interpret) Ockham’s philosophical language and logic? Our contemporary logics are highly formalized and explicit, with their symbolically refined artificial functions and operators. These logic languages are partially alien to Ockham’s philosophical language. For example, as Spade remarked,9 Ockham’s significatio (signification) cannot be translated by Frege’s Sinn (sense) without distortion. This is not because of untranslatability, however; it is owing to their competing theses: Frege’s is semantic logic, whereas Ockham’s is based on mental understanding. The medieval Latin he used, a hybrid of oral and written forms evolved into a sort of formal—often obscure—technical ‘dialect’, falls far short of the explicit and technical symbolism of our own logics. So an upshot of these questions is another one: when a medievalist paraphrases philosophical Latin employing our logics, can synonymy be preserved between the medieval ambiguity, and our contemporary often complex razor-sharp logic? Geach has demonstrated how well Buridan initiated the resolution of problems in ‘quantification into opaque contexts’ which are still partly intractable in our current philosophical research (see [14.38] 161–3, then 129–38, 148). One of these topics is intentional identity, i.e. only seeming to refer to a referent by use of a quasi-name with intentional verbs, as in, ‘I believe that I am referring to a square-circle drawn on the ground.’ Could this sort of intentional approach unexpectedly be utilized to map Ockham’s own thesis that there is a ‘mental’ language to which he only intentionally refers? Is the mental language a non-existent intentional identity falsely invoked by a quasiname and quasi-language? Is it a conceptual fiction? Ockham’s supposition theory is itself so subject to equivocation that confusion over intentional verbs cannot be clarified. Ockham posits (in his actual Latin analytical language) his alleged mental language as a vehicle by which to override and secure his logic and reference. If his (linguistic) analytical language in Latin is itself an intentional medium of expression, then he cannot actually succeed in referring to his ideal mental language since it would be an intentional fictive object. On this account, Ockham’s mental language, and its two class domains, inhere solely as a myth: a complex abstract object of his imagination. Perhaps we should look synchronically at differences within our own contemporary philosophical traditions and controversies to gain a clearer sense of the diachronic problem for us of identifying Ockham’s philosophy. Difficulties of paraphrasing Ockham into modern philosophy are not like problems in (in the required sense and to the relevant degree) unexpectedly new developments of our analytical philosophy. For example Russell’s basic logic has been developed in directions of which, one would judge, he did not or would not approve. A case in point is David Lewis (see [14.59]); he is rather like an Ockham in reverse. Where Ockham wanted to reduce ontological plurality, Lewis goes forth and multiplies it. His theory is that we can ‘invent’ ontologies by making counterpart universes for other space-times. The universes he reproduces are modelled from our own indexicals of location (here/there), person (you/me), time (now/then), etc., that mirror our own world. I believe that Russell would have thought that this sort of subjunctive conditional philosophizing to be like confusing ‘fairy tales’ with real-life ontology.10 But we can derive Lewis’s logic from Russell’s (and thus choose to ignore the latter’s lifelong neglect of modal logic), even though some ingenuity is required. Yet we cannot derive Whitehead and Russell ([14.98]) from Ockham’s logic. This sort of enterprise, generalized, indicates that Ockham cannot consistently, in this arena, be paraphrased into modern analytical philosophy without inventing a logic and philosophy.11 In any case, what it is to be a criterion of logical possibility, as a basis for refining or transforming a concept, is obviously not the criterion to assess what Ockham thought. Beyond this issue is another one: if one classifies logic as a subset of scientific knowledge, then one is committed to admitting some type of invariance to allow for the increasing explanatory power of theory. But this presupposes a questionable form of individuation in the philosophy of history, and of originality. Can we properly offer an intellectual biography of Ockham that in some way does not consider non-scientific creative originality in Ockham’s philosophy?12 We may wish to direct such queries to the ethical and political domains of Ockham, but the interplay of logic as a discovery procedure for inference, and creative intuition, requires more attention in research, though it would take us too far to investigate this axis for tracing Ockham’s consciousness in his compositions.13 Impinging on attempts to access Ockham for us in our worldviews is the issue of the status of extending a concept beyond its framed origin. Using a ‘function’ to formulate a predicate and quantifier logic (as Russell did, following Frege [14.34]) has revolutionized the identity of inferences involving generalization. We should not underestimate the scope of this revolution, though problems remain (see [14.84]). The logical power of the predicate calculus also enables sentenceforming operators (‘and’, ‘or’, ‘if, etc.) and quantifiers (‘some’, ‘all’, ‘the’, ‘few’, ‘scarcely’) to be defined using logical predicates. This calculus has many other transforming roles, which contrast with Ockham’s doctrine of terms. These issues compound the simple problem of what it is for a modern logical concept to be ‘contained in Ockham’s general premisses’.14 Can there be a relation of inference between Ockham’s philosophy of logic and the achievements in logic research over 600 years later? When we consider our contemporary philosophical defence and criticism of Ockham, do they embody merely the sort of narrow-mindedness Russell might have displayed toward Lewis, and did show Ockham?15 Consideration of such questions will contribute to our assessing Ockham’s modernity, limitations and potential more clearly, while guarding against charges of anachronism or overestimation. OCKHAM AND REFERENCE Names are fundamental for Ockham. Adams mentions that Ockham adopts the traditional distinction (see [14.12] 71), inspired by Aristotle’s On Interpretation, that there are three kinds of names: spoken, written and mental.16 Ockham uses the word for ‘name’ that he employs to classify a subject and a predicate. Yet they are functionally different. For Ockham, the proposition ‘The Titanic is wrecked’ is composed of two names: one for the subject ‘The Titanic’; and the same ‘name’ for the quite differently functioning predicate ‘wrecked’. Logic should preserve differences of use in language; Ockham’s naming strategy destroys it: the subject and the predicate in the above proposition are actually asymmetric in use. ‘The Titanic’ refers to an object. The predicate ‘is wrecked’ is a state of affairs which is true of its subject (if or when true). Once wrecked, the Titanic has the contingently necessary property of ‘is wrecked’. This predicate is a self-inhering term, though before striking the iceberg it was not even a property of the Titanic. The notion of identity is bound into ‘the Titanic’ in a way in which it is not in ‘is wrecked’. And that is not preserved by using ‘name’ for both parts of the proposition ‘The Titanic is wrecked.’ If, before the Titanic sank, someone called out and named: ‘The Titanic!’, it could logically yield the question: ‘Where?’ and the answer: ‘There!’ But if someone called out: ‘is wrecked’, at most this peculiar response would attract the question: ‘What is?’ This latter question advertises the problem: with a predicate one does not know the identity of the thing of which the predicate is true (or false, as the case may be). Contrariwise, with the subject ‘Titanic’, the identity of the subject referred to is the self-contained sense which is the use of the term.17 This difference is fundamental in oral, written and the mental language accessible for us to test. Therefore it is basic to a knowledge of Ockham’s use of names to appreciate that his theory about ‘name’ is contradicted by the foregoing argument. His explanation does not work for linguistic use, and if a language were constructed according to his rules, we could not communicate when using a large portion of it (witness, ‘I name this ship “is wrecked”’). Although he regarded Aristotle as his general inspiration, Ockham’s application of names to propositions is quite contrary to Aristotle’s concept of the asymmetry of subject and predicate in On Interpretation, as Geach observes ([14.38] 290–1).18 In claiming to retrieve Aristotle’s teaching, Ockham followed medieval contemporary tradition which reinterpreted some aspects of Aristotle’s later doctrine of terms. Ockham uses ‘name’ to represent two allegedly identical mental universals which constitute a proposition: the subject and the predicate. These are often translated nowadays into the letter-names: ‘N’ and ‘P’. For Ockham, there is here no naming difference between a subject and predicate. But in the above work by Aristotle, the subject and predicate are asymmetrical in functions, even though in the Prior Analytics Aristotle later dropped the scheme in favour of a doctrine of terms. (Although Plato’s Sophist was not available to Ockham, it is worth noting that elements of Aristotle’s asymmetry conception parallel distinctions in the Sophist, though for Plato the verb is classified in relation to its extension, whereas for Aristotle it is as a function in a statement. It is true that the distinction between name and predicate (or verb) in Aristotle is not as explicitly and exclusively defined as it is in our contemporary logic; but the central ingredients are there.) Now one would therefore think that Ockham was, in principle, in a position to choose to adopt the distinction of the functional asymmetry identities of logical subject and predicate, especially with his devotion to Aristotle. Yet he did not. Did it dawn on him that this asymmetry was in Aristotle, citing as he did from the same work in which this doctrine appears? It might be replied that since the doctrine of terms appears later in Aristotle, it is not surprising that Ockham, in any case, chose this instead of the concept of asymmetry between logical subject and predicate. Even so, for those who wish to ‘modernize’ Ockham’s logic, or paraphrase it into our logics, Ockham’s not choosing Aristotle’s asymmetry distinction, fundamental to most modern logics, implies a judgement against Ockham’s instinct for the deeper foundations of logic as they have been developed long after Aristotle’s, and then subsequent to his, lifetime. For Frege, for Russell, and most analytical philosophers, the predicate has no reference of its own because it is incomplete. It is like a function. On this interpretation, a predicate has to be linked to a logical name, which refers. By the mediation of the logical subject the predicate is attached to the name that refers, and is thereby true (or false) of the name’s referent; it has an ascriptive function to create its link with the refrent. There are issues to be addressed in these areas, such as the need to concentrate on the role of quantified general terms, rather than Russell’s own views of ‘definite descriptions’, and the effect it has had on interpretation of the predicate calculus. But, after all this is assessed, the difference between the enormous capabilities of the predicate calculus, as against the two-name theory with its supposition doctrine, is like contrasting alchemy with nuclear physics with regard to the transformation of metals. Ockham had absorbed the common doctrine of terms (in which a proposition is made up of names). The enormous grip that this doctrine, together with supposition theory, had on Ockham, and much of the medieval world, is hardly to be explained by this, less than ideal, at points implausible, interpretation of Aristotle and its amalgam of supposition. Why did Ockham adopt this position? One answer, apart from it being a trend at the time, is that a doctrine of terms, or names, enables one to play more freely with imaginative possibility. A reason for this is that the doctrine of terms helps one evade the features of the actual relations required by language to represent the external world, while pretending a logical guarantee of true meaning. In other words, it is a covert theory of equivocation which subverts the relations between semantics, ontology and mental understanding. Ockham’s two-name theory is undermined by two other considerations which reflect thinking by Dummett ([14.30] 223–4, 294). The target of the two concepts is the relation of a predicate to the mental realm, as they go proxy for parts of the external world. Dummett’s research has explored some hitherto ill-defined areas of reference. First, if predicates were to have the sort of name-reference Ockham ascribes to them and their mental and ontological counterparts, then to what does this commit Ockham? We would have to admit quantification over the referents of these predicates.19 Ockham opposed Aquinas’s view that ‘matter, already understood under corporeity and dimensions, can be understood as distinct in different parts’.20 For Ockham, the referents would need to be the indivisible ‘essence’ or ‘substance’ which is prior to quantification. But second, even if quantification over predicate-referents were compatible with Ockham’s philosophy, then this would commit him to an impossible position. That is to say, if we presuppose with Ockham that predicates refer—as his subjects do—they cannot refer to a complete entity. For if a predicate refers, its referent would have to be incomplete (i.e. ‘is wrecked’ is a semantic mirror of its ontology: there is no subject in it by which to refer to pick out this ontological subject). This is exactly the opposite of what Ockham needs. He requires a nominal universal in the mental realm to be referred to, which would have to be complete. Ockham could hardly allow an incomplete entity referred to by supposition. Ockham’s theory of naming is rather like one’s pointing to a ship-wreck in thick fog, or down through deep water; the ‘name’ does not locate its own object, and it locates a wrong position because it has no knowledge of the effect of refraction on perception. The conflation of subjects with predicates, we have seen above, is triggered by Ockham’s use of a ‘name’ category for subject and for predicate. Ockham absorbed the common doctrine of terms. He and Walter Burley, with some differences, embraced the theory of supposition, which had been strangely restored from near-oblivion. Yet Aquinas, before Ockham, employed applicatives (quantifiers) such as ‘some’, ‘every’, ‘only’ to explain that a predicate does not itself refer but indicates a nature.21 Ockham attempted to avoid the problem, created through his failure to recognize the asymmetry of subject and predicate, by looking to his idea of mental language. Ockham viewed mental language as a phenomenon that mediated us directly to the world it represents. Shortcomings when trying to implement his two-name theory in oral and written language provoke him to download the elusive mental language.22 How did Ockham suppose that the theory of supposition, linked to naming, connects with the mind? He supplied the connection through a theory of signification. An important study by Spade exposes aspects of the relation. Spade cites Buridan and Augustine to indicate concepts of signification which were influential in Ockham’s time ([14.87] 215). According to them, signification establishes the understanding of a thing, and that signs are causal lexemes which produce mental effects beyond the impression the thing makes on the senses. As Spade notes ([14.87] 218), the stress on mentality reflects, minus the sense-impression element, Aristotle’s On Interpretation (I, 16a3f): ‘Spoken words are the symbols of mental experience.’ Stated very roughly, the later medieval trend is to treat supposition theory as a semantic hypothesis (proposing connections between a term’s referring and its referent). In contrast, signification is an epistemological theory, concerned with understanding. The conjunction of these two approaches targets the conditions for knowing and learning in the medium of language. Ockham claimed to have direct knowledge of individuals. A term deployed in simple supposition in this perspective goes proxy for the concept to which it is subject. As Spade explains ([14.87] 222), by contrast, Burley’s view is that terms stand in simple supposition for what they signify. This involves a social view of language as a tool to communicate with others. Ockham proposed, in other contexts,23 that there is a triangular relation in some acts of assent between mental language, spoken language and the referent. In these contexts he argued that the consequence of such a relation is that a person may know something which is the product of it (for example, that one entity is not another), yet (to express it in a way Ockham does not) the person may not possess the recognitional capacity for having a concept of that concept (see [14.61]). Ockham’s main emphasis is on the grounds of a person’s own knowledge, not social interaction, and on the causal efficacy of signification for mental states, together with the denial of natures. From various twentieth-century philosophical standpoints, Ockham’s causal theory of understanding is not well grounded in its own or our terms. Two contemporary views on the philosophy of mind are first, that of the theory-theorists (see [14.58]) (i.e. those who maintain that to speak of the mind at all we have (at least implicitly) to have a theory of it); second, that of the simulationists ([14.48]) (i.e. those disposed to argue that we have no adequate theory of the mental, and in any case we simulate the mental states of others in our mental activity without presupposing a theory). Both could be partially integrated by utilizing the function of ‘implicit’ in the theory-theory view. This could mark an innate mental capacity tantamount to a theory, along the lines of Fodor (see [14.33]), which is partially activated by a simulationist model. Each of these approaches is concerned with the role of collective social learning in the way Ockham was not, and as such they complement Burley’s attitude.24 As the simulationist Heal points out ([14.48]), justification or epistemic status is a holistic notion, and the notion of relevance is extraordinarily complex and undetermined. These points count against Ockham’s signification. His signification is a semantics which naïvely causes mental language effects. Or, more precisely, mental states (thoughts, etc.) cause linguistic (spoken, written) signification. Ockham had no grasp of the instantiation of relevance theory, complexity theory, or simulation of others’ states. In relation to these issues, we now have fairly firm grounds for accepting the instability of linguistic signs, and their frequent indeterminacy relating to mental and oral uses, originally from research by Saussure into written Latin (and its interpretation by Starobinski, see [14.91]) and work by Jakobson (see [14.54]) as well as Anscombe’s rather different work on intention and mental causality in the contexts of their expression (see [14.16], [14.17]). We also have the latter author’s study on the difficulties of classifying the first pronoun (in agreement with Kant). To this one can add, for example, Chomsky’s more recent theories on indeterminacy in mind and orality in relation to the abstract identities of concrete entities. As Chomsky remarks, ‘the abstract character of London is crucial to its individuation’ ([14.24] 21). These have generally been taken to have fractured and dismantled the almost mechanistic symmetry that the Ockham scenario presupposes between spoken, written and mental terms. Even if there are criteria of identity appropriate to each, it does not follow that for each there is a fixed content to the criterion of identity (Moses’ identity may be fixed in varying ways (see [14.99] §§20–110)). One cannot sustain the view that there is a mapping criterion for which there is an equivalence of the relevant sort between Ockham’s supposition in respect of spoken, written and mental terms. Ockham had a naïve realist view about the way terms fix to referents. Adams speaks of Ockham’s view that the division between personal, material and simple supposition applies equally to spoken, written and mental terms.25 This has been criticized by Spade (see [14.89] XIII). He judged that it follows from Ockham’s way of relating concept, thought, personal supposition and signification, that, with mental terms which may have personal or material supposition, we do not always know what we are asserting. Spade’s view has been countered by Adams supposing that the issue is not really whether or not one of our thoughts could be about something (in the sense of a term’s standing for some particular) without our knowing it. Ockham allows that when I think ‘Every man is an animal’, the term ‘man’ supposits for lots of things without my knowing that it does, since I have no awareness of those particular men. Rather the question is whether on the above proposal anything would make it the case that the term was suppositing for these rather than those. (see [14.12] 351 n. 104) It is wrong to argue here that, ‘the term “man” supposits for lots of things without my knowing that it does, since I have no awareness of those particular men ’. If a person knows the meaning of the term ‘men’, that person will know from experience and cognition that it is true or false that there are men. So at the very least, for those terms for which that person holds concepts which supposit in the singular and have (even conjecturally) more than one referent, it is not possible that ‘the term “man” supposits for lots of things without [that person] knowing it does’. This advertises the problem that, in Ockham, equivocation and ignorance are functions of his failure, not only to possess a viable theory of reference in his signification, but also of his system’s inability to explain the complex presence and scope of relevance. His system does not explain introspection of pertinent contents in one’s own consciousness. The presence of equivocation in Ockham’s supposition and signification is a mask for his failure to explain mental choice and the invasive role of complex relevance conditions in holding, knowing as well as using concepts. A suppressed general premiss behind Ockham’s positions here is his misconception that if one conjoins the functioning mind to the world, then it will ‘read off’ the true interpretation of both regarding terms. Consequently, his need for equivocating between supposition and signification is hardly surprising in view of his principle of parsimony. In practice, however, Ockham’s procedure is sometimes the negation of simplicity, since he approaches a simple situation by multiplying entities. He invents mental classes to which the signifiers supposedly refer, though people using language seem strangely unaware that these classes exist. For Ockham, ‘Socrates is a man’ is an instance of a categorical proposition. But Ockham has no general account of what it is to be a proposition. Following Ockham, Marilyn Adams paraphrases this sort of proposition as: ‘N is P if and only if N has P-ness or P-ness inheres in N.’26 This contravenes Ockham’s razor, since it multiplies entities for ‘N is P’ (and the technique requires increasingly complex ad hoc devices). The paraphrase mediates on behalf of ‘N is P’, intervening allegedly to make explicit the mental-language contract with the simple statement. This is at the centre of the two-class theory. In Ockham’s two-name theory ‘man’ is a mental sign, a nominal or conceptualistnominalist supposition that inheres not only in Socrates but other male humans. So, in the term ‘man’ employed of Socrates, it also denotes all humans. Aquinas would have had none of this,27 since he did not allow that a general term, such as ‘nature’, had direct reference, for it is true of individuals—ascribed, not referring to an identity. The appeal to ‘Pness’ invents a class that is not derivable from P, without the addition of a new entity: abstractions of the mind. Since ‘Socrates’ is symmetric in logical form to ‘man’ (in ‘N is Socrates’), we should be able to redistribute its ‘Socrates’-ness over other men. Obviously Ockham wanted to construe ‘Socrates’ as a uniquely suppositing term, with ‘is a man’ differently represented as a class name term. Yet he classifies them as names, which Adams formalizes identically. So here their representation in logic is uniform. But their interpretation as to function is distinct; that is inconsistent. We should here insist on that to which Ockham commits himself. Symmetry of syntactic formalization (the predicate has a unitary symbol, ‘P’, as has the subject) is the identity of its entities. No doubt we will be told Ockham did not intend this by his depicting the predicatename as a complete entity. Quite so; but that is the problem: intentionality. Intentions do not rule words. Can the two-name theory of Ockham be salvaged? It appears not. But imagine Ockham reading the foregoing with the foresight of (and disagreements in) our contemporary analytical philosophy. Ockham might respond: ‘I see the explanatory power of a logical singular term which presupposes a criterion of identity. It strikes a fundamental distinction with the logical predicate which I did not understand, and I admit that it is more accurate to represent the predicate as a function, asymmetric in role to the logical subject, along the lines of Fn. Despite these concessions, it seems that their scopes have been overstated. Your predicate calculus is correct, and my formalism crude, and I consider that supposition might be replaced with the following strategy, which I think achieves the same results. I restore something parallel with my two-name theory as follows, using your philosophical logic. ‘I want to disturb your confidence by exposing some weaknesses in twentieth-century analytical philosophy and logic, to make space for my own use of your distinctions. First, Frege used the analogy of a logical name to craft part of his concept of a logical predicate. And I understand that this analogy collapsed in a messy way ([14.29]). I can reconstruct my two names by taking the analogy, though I am unclear whether or not I was incorrect in degree or type to use “name” of the predicate. Second, twentieth-century philosophers when pushed have some difficulty making definitively explicit what they mean by “referring”. There is the “pointing” origin of the word for “reference” (German Bedeutung) in Frege.28 Many twentieth-century philosophers sympathetic to Frege do not seem able precisely to inform me what “referring” semantically is, except to say that it is what a singular term does: it picks out a single referent, by acting to implement one of the subject’s criteria of identity. Well, I wish to come back to this concession of ignorance. Why can this singular ability be achieved only by your logical name? I agree that my use of “name” was itself foggy, but I was aiming at a label for a particular, not the narrower sense later ascribed to me. I am willing to drop, for my predicates, what you term “referring”, and Geach’s analyses have convinced me that supposition theory is best eliminated completely, including from logically proper names. But I would like to conclude, with Recanati ([14.77] 401), that the differences between indexicals and proper names is largely pragmatic. ‘Now here is my original move. You have developed a logic of indexicals: “here”, “there”, “me”, “you”, “past”, “present” (David Lewis builds a whole universe from them). But I understand that you have a problem with the first person pronoun “I”. Logicians often deem that the first person “‘I” can be replaced by the person’s proper name. But of course that will not do, it fails some truth-conditions, including the third person proper name contexts when you substitute it with a proper name. And if Kant and Anscombe ([14.16]) are right to affirm that “I” does not refer, we have an indexical particular. It is more like a unique (categorial) predicate. It picks out a person in particular context. Now why may I not generalize this over large sets of indexicals? I can paraphrase my predicate-name scheme into an indexical programme. If I may borrow an expression from Heal, this procedure can be called ‘indexical predication’.29 I appreciate that this leads to complex semantic analysis, and a proposal to analyse propositions according to a deep structure which I cannot describe within my own terms. But for any abstract form such as “the property of whiteness” there is a paraphrase back to the surface form, e.g. “The donkey is white”.30 So a two-name theory can be replaced with something that is almost parallel, yet it satisfies the notion of asymmetry between the subject and predicate. Although we had no refined quantifier logic in the medieval world that treated quantifiers as predicates in the Frege manner, I see no reason why indexical predication cannot be extended to general terms and variables. As for the mental language, I shall have to exchange it for the Fregean metalanguage according to which object-languages are its manifestation. All this does not augur well for my principle of parsimony, but I may have to resort to the larger questions of cosmology to re-state it.’ OCKHAM’S RAZORS When Ockham was a young man, his fellow Franciscan Roger Bacon (1220–92) had only recently died. Ockham’s razor (as his principle of parsimony was later to be termed) is to some degree a reaction against Bacon’s theory of the multiplication of species. Bacon broke with other perspectivists (though their influence was less pervasive than Aristotle’s theory of knowledge)31 to argue that, for example, light multiplies in time, though this thesis was not, in his view, a matter of observation ([14.93] 16–26). Bacon’s notion of multiplication of entities has some concurrence in a modern logician such as Arthur Prior, with Prior’s counter-maxim: Entia non sunt subtrahenda praeter necessitate. ([14.75] 31) (Entities should not be subtracted unless it is necessary). Later in Bacon’s career (On Signs, 1267, and his final work, the Compendium of Theology, 1292), he began to restore and re-state aspects of the confused doctrines of supposition, while intending to remove some of its confusions, rejecting the notion of univocal supposition. It was left to the young Ockham to mull over the relation of his aversion to Bacon’s multiplication sum, and his attraction to Bacon’s late change of heart on supposition. Ockham was averse to Platonism, and conceived Aristotle as a champion of this dislike. Everything in the world was singular, and there was no principle of individuation. Real universals do not exist. Ockham believed that the grammar of propositions might bewitch us into thinking that their complexity mirrored structures in the world, but below this semantic surface the universe’s ontology has a proclivity for singularity, and so does our mental structure. He was convinced that we must therefore reduce the number of entities appropriate to these circumstances. Semantic expressions can be universal, as can mental concepts. Ockham’s synthesis of these hypotheses comprised an original, not to say problematic, equation of semantics and ontology, not least when Ockham conferred his unexpected gaze on a similar tradition or the fragmentarily parallel views of his peers. In practice ‘the’ parsimonious razor, which is the emblem of the perceived influence of Ockham, is often applied piecemeal, and episodically, by his successors, which in effect falsifies it as a universal principle. There was also contemporary opposition from writers such as Walter Chatton, who asserted a rule contravening Ockham’s: ‘If three things are not sufficient to verify an affirmative proposition about things, a fourth must be added, and so on.’32 ‘Ockham’s razor’ simplifies the quite various attempts by Ockham to formulate a principle of parsimony. This state of affairs could be evidence that Ockham did not succeed in specifying the vaunted singular razor. The popularizing aphorism, ‘do not multiply entities beyond necessity’, does not occur in Ockham. It arises from a number of sources, mediated, for example, by the editor John Ponce of Cork, in a 1639 note added to Duns Scotus.33 This aphorism is usually taken to echo the spirit of Ockham’s ontology, however. In the form just given, one might be excused for giving it short shrift, by remarking that the only entity which exists by necessity is God, so according to this maxim nothing else exists. Therefore is it not false? But the razor is resonant with Aristotle’s maxim, according to which a single means, rather than plurality, is favoured by nature and transcendent power.34 In this form Aristotle has no use for ‘necessity’, though his ‘plurality’ is akin to one of Ockham’s versions: ‘Plurality is not to be assumed without necessity.’35 Quite what ‘necessity’ has supposedly to entail according to Ockham is not, by him, definitively or consistently specified, though he does seem aware of some of the variety of different modal necessities. Perhaps intuitively sensitive to some counter-intuitive modal complexities, Ockham in some contexts excises ‘necessity’ and, for example, introduces us instead to: ‘No plurality is to be assumed except it be proved by reason, experience or infallible authority.’36 Ockham’s razor use of ‘proved by experience’ conflates practical reason with logical theory (as a logical axiom). In the required sense, logically necessity is not derivable from experience. That, in this type of rule, ‘experience’ should be taken as a criterion for logical uses of ‘plurality’ (elsewhere in Ockham guaranteed by ‘necessity’) is a category-error. Possibly such blemishes kept Ockham on the move to attempt other formulae to meet his taste for restricting plurality, or they reflect his confusion, despite his central logical motivation, i.e. his wish to follow a law of non-contradiction. Ockham does not prove his principle of parsimony. This inclination is compatible with an anti-realist position, and with the admission of truth-conditions for a minimal set of statements, which serve as the core for a theory of meaning (see [14.28]). But there is a problem with this approach and the various forms of Ockham’s principle of parsimony. As Wright argues in the context of late twentieth-century anti-realist versus realist debates (see [14.103] 120–4 etc.), there is no way anyone could possibly arrive at a conception of what it is for a verificationtranscendent state of affairs to be true as a result of training in the use of language. Ockham did not leave us with one principle. The plural occurrence of his parsimony itself reduces to a contradiction of the principle. And even if we allow this to pass by, it follows that we have no consistent criterion by which to identify the form or test the purported existence of the razor, and so on. Marilyn Adams claims that the principles Ockham states as versions of the razor are, ‘in the first instance, methodological principles, and it is not obvious how they are related to truth or probability’ ([14.12] 157). It is not formally evident what a ‘methodological principle’ is here, and anyway many cases of Ockham’s use of philosophical or logical terms in his formulations of the principle might be drawn upon to illustrate that Ockham is not in the first instance expressing what would normally be considered methodological principles. Let us consider the foregoing employment of ‘assumed’ (ponenda) in the form (also quoted by Adams): ‘plurality is not to be assumed without necessity’. This version seems to presuppose the negation of Adams’s view, since its terms are those employed in Ockham’s discussion of logic to express logic, in the first instance, not those of method or the logic of method. There are problems in mapping razor terminology on to our modern logics. For example, ‘assumed’ (ponenda) is rooted in the term for ‘possibility’, in its use here. Generally in medieval uses it has something to do with modally positing (what we would term) a prepositional function, whilst it does not fully comply with this latter type of modern usage.37 If one were to attempt an equation of it with terms in our predicate calculuses, it tends towards a premiss, whilst also partially contributing a function independently of that, of sharing a property of a presupposition, together with a weakened sense of the ‘assertion’ sign.38 In other words, there is a breakdown in an attempt to fit it uniformly and broadly, or narrowly, into the concepts attending our standard logical terminology. Nevertheless, this version of Ockham’s razor is no mere ‘methodological principle’, since it displaces space in logic otherwise occupied by different axioms and makes claims on the domain of logic and its putative ontology. If we draw on the traditions of ponenda on which Ockham rests, and attempt a partial alignment with our logics, we meet a complex hybrid of assumption, premiss, assertion and presupposition, bound into the conditional negation of ‘necessity’, generalization (‘plurality’), and axiom, applied with some confusion extensionally to ontology. It is thus apparent that Ockham is talking logic, not methodological principles. He is proposing a logic for ontology, not devising methodological principles, and is asserting reductionist logic rules of quantification, not methodological principles. One of the difficulties in aligning Ockham’s use of ‘assumption’ and other logical terms, including those in his razor versions, is that in typical cases he accepts generalized logical laws, whilst he deems that they have exceptions in theology (for example, in his view of the Trinity). His belief was that arguments of given general logical forms of syllogism are universally valid when applied to all matters in the world; but the same logical forms are invalid if applied to the Trinity, or need to be so interpreted through a nominalist or conceptualist supposition theory that they cannot ‘properly’ be so applied. As Geach makes clear,39 Ockham was confused about the relation of inference to ontology, and muddled about logical relations between first and second intention terms in logic. I leave aside here, as far as is practicable, other issues of ‘nominalism’ and doctrine, so as to isolate difficulties in his philosophy of logic. These exceptions are also ones often anticipated and rejected by, for example, Aquinas. So it is not self-evident that Ockham theologically needed to contravene the scope of logical laws, while it is clear that he held such collisions of his interpretations between logic and theology as a matter of sincere conviction. Consequently a reader of Ockham has to face a problem in Ockham’s examination of the Trinity. Where one might hope for a resolution of tension in the use of assumption and razor, there at the centre of the theological conception most important to him, Ockham admits that he has exceptions to logic. Unfortunately this is not a deployment of methodological principle. Clearly it is a contradictory exception involving accepting true premisses that imply false conclusions which, therefore, disprove his inferences, the razor rule, or his theological interpretation. This follows from Ockham’s own rule of non-contradiction. It was an embarrassment to Ockham that Chatton employed the law of noncontradiction to demonstrate the (alleged) truth of the anti-razor by considering the multiple components that constitute causal relations in an action (for example, wood burning) (see [14.66] 469f). Ockham attempts to head off a possible accusation of heresy by limiting the scope of his logic and introducing a nominal or conceptualist interpretation of abstract nouns into incarnation theology. So at this juncture he opts for semantic speculation to warrant rigging his logic, which is itself a violation of his ‘necessity’ and adoption of a law of non-contradiction. Ockham’s attempted justification of his failure to apply the razor in some doctrinal contexts appears in his extended version of the razor: ‘No plurality is to be assumed unless it can be proved…by some infallible authority’, in which, in addition to his appeal to Scripture, he adds ‘certain sayings of the saints and the determinations of the Church’.40 As Adams acknowledges: ‘Ockham always allows the claims of reason and experience to be defeated by contrary pronouncements of the Church, which should lead “every thought captive”.’41 But Ockham does not feel obliged to take the further step of embracing the fully general theory of which such ecclesiastical determinations are instances. Although he prizes generality as a desirable feature in theories, he is more committed to the maxim: a theory-maker should not multiply miracles, i.e. theses contrary to reason and experience, beyond necessity.42 There are deep fractures in these viewpoints. First, there is no logical or philosophical necessity at all to accept pronouncements of an institution, especially if they are contrary to reason. Second, there is a suppressed contrariety in his employment of the foregoing quotation, ‘every captive thought’. Ockham himself distinguishes between the authority of Scripture, which is infallible, and of the authority of the Church, which can on occasions— according to him—be wrong. But the quotation about ‘every captive thought’ comes from the New Testament, not from the Church’s pronouncements (which are clearly distinct from the New Testament in this context, on his own interpretation). It is wrong, then, on Ockham’s own terms, to use this quotation form as infallible authority, to underwrite the authority of an external institution which, he agrees, can be wrong in its judgements. Ockham deployed that guarantee to prevent himself allowing his razor its full generality. It is tragic, in the perspective of the medieval contemporary opposition to Ockham, to observe this internal inconsistency in Ockham’s philosophy: a sincere believer painfully doing his best, as he sees it, to pacify antagonistic inconsistent Church authorities by attempting artificially to manufacture agreement with them, when neither logic nor his razor demands it. Clearly we should position all this with problems any thinker has when living in a quasi-totalitarian regime in which the threat against life is not uncommon, as a device for achieving conformity in belief. In contrast, Ockham’s campaign, in the last twenty years of his life, to convict the Pope of heresy manifests a certain resilience and independence of mind. We stand outside the limitations of Ockham’s own life situation (but, as he would have done, have difficulty in standing outside our own) and are aware of the influence of our own times on our picture of Ockham. Nevertheless, could we attempt some damage-limitation or reconstruction of the fragments of Ockham’s philosophy criticized above? First, he could have dropped his nominalist analysis and reinterpretation of the Trinity. Second, one might argue, irrespective of his presentation of the razor’s exceptions, that Ockham should accept (what we would now term) deviant logics as having equal status to the bivalent one, and allow him subjunctive conditional certainty in a plural world. This of course would not leave him happy, since it would entail that his options are only possibly true. Third, someone could designate the Trinitarian doctrine itself as incorrect, and so the false conclusions thereby implied by the true antecedents simply identify a route on which Ockham did not continue (or of which he was not aware). This issue might be expressed as follows: in the foregoing discussion we have seen that Ockham used the Bible to develop some of his positions (as he did more extensively in his political philosophy, as the section below shows). Almost none of the defining terms of the Trinity occur in the Bible (nor do synonyms of them). So Ockham could have redefined the incarnation so as to avoid the troublesome terms which he judged require a restriction in the scope of his logic. Unfortunately, incarnation terminology in the Bible is not nominalist-conceptualist, and the propositions there do not fit the two-name theory. Fourth, one might utilize Alféri’s research (see [14.14]), and propose that a post-structuralist estimation of Ockham’s razor removes the need for the type of logical consistency which Ockham sought in formal theory. Fifth, one could transform hints in Ockham, and argue that his unconscious is ahead of his formal consciousness. One would thus propose that the solution to his formal logic problems is to dump his formal programme, and accept that, underneath his apparently ‘logical inferences’, at the crossroads where the collision occurs between inference using the razor and the incarnation, the answer to some of Ockham’s problems could be to metaphorize, as a ‘game’, areas of his whole logic. Although of course Wittgenstein did not suggest this type of enterprise,43 it might be envisaged as a possible upshot of his analyses of what it is ‘to follow a rule’ in his Philosophical Investigations.44 Of course, this is revolutionary even by our contemporary standards. Sixth, an Ockhamist could attempt to circumvent the foregoing and other criticisms by adopting the sort of paraconsistent logic that Priest devises,45 fragments of which occupied some medieval logicians. In a paraconsistent scenario, there are limits to cognition (in Ockham’s case the Trinity), and there are semantic closures smaller than the set of all propositions, yet which facilitate access to transcendence in part using set-theoretic reductionism. A paraconsistent approach has the drawback that it requires a given proposition to be (or that it could be) true and false. This would help support Ockham’s treatment of the Trinity, whilst eliminating his law of non-contradiction. A reason for mentioning some of these ideas is to indicate that, taken together, Ockham’s philosophy of logic and his philosophy amount to a partial hybrid of competing logics. But brute forms of Ockham’s razor have been accepted and popular since his time, increasingly with the emergence of experimental science, though with exceptions. J.S.Mill is rightly regarded as a mediator of Ockham’s logic from the medieval world to modern philosophy ([14.69]). Nevertheless, in respect of parsimony, Mill was appalled by Ockham’s razor. In 1865 Mill attacked Sir William Hamilton for his use of a version of the razor ([14.70] 418–19). Hamilton’s own positions on logic were sometimes incompatible with Ockham’s. He was moving towards a quantification theory which, if it had any relation to Ockham, was one of contrast,46 in which there is a closer relation to Frege’s quantificational logic than the sort of Ockhamist logic that Mill (apart from the razor) had espoused. Later, Russell’s practice of eliminating, where possible, existential quantification, and Hans Reichenbach’s concern with simplicity evinced in his idea of logical empiricism, as Sober ([14.86]) notices have similarities with some uses of Ockham’s razor, though neither philosopher is generally compatible with Ockham. Dummett applies a restrained use of Ockham’s razor in mathematical theory, while he notes that denying a thought by the process of negation is intrinsically complex ([14.29] 38, 317). ANTI-REALISM’S TRUE RAZOR? The foregoing challenged Adams’s claim that the various versions of Ockham’s razor are ‘in the first instance, methodological principles, and it is not obvious how they are related to truth or probability’. Surely it is, in relevant respects, clear how Ockham relates at least some of them to truth. Adams’s view does not account for at least one version of Ockham’s razor, which she quotes: ‘When a proposition comes out true for things, if two things suffice for its truth, it is superfluous to assume a third.’47 The expression ‘comes out true’ (verificatur) and the word ‘truth’ are related to truth explicitly, by being the purported measure for true propositions in a thesis canvassing for a reductionist use of numerical principles as the basis for an austere ontology regulating generalization in logic. For Ockham, number relations are real. Such relational propositions have truth-conditions and substitution instances. They accord with a rough correspondence theory (not as well developed as those of Paul of Venice, and adopted without Duns Scotus’s full realism, while yet they are not minddependent). Of truth, Ockham states that, ‘truth, i.e. the concept truth, in addition to the proposition it signifies, connotes that things are such in reality as they are conveyed to be by means of the proposition’.48 Although Ockham’s theses are distinct from the semantics of Tarski- Davidson (in which to give the truth-conditions is a way of giving the meaning of a sentence),49 yet the various features of Ockham’s ‘correspondence’ presuppositions partially parallel these modern authors, principally because of the way he is attracted to anti-realism.50 Ockham’s ‘correspondence’ position was pressed by his anti-realism, a view which had some similarity with Peter Aureoli’s and Henry Harclay’s disposition to dismantle direct realism. Marenbon’s view appears to offer the most explanatory promise: Ockham’s rejection of essential essence realism, together with his acceptance of truth-conditions for the semantics of the external world, eventually imply that his adoption of a conceptual system for understanding the world in terms of species and genera is merely one possible system—whereas for his contemporary opponents it is a system which has to be used if one is to achieve a full understanding of reality. Any of these interpretations involve a use of truth which restores to it the role nor accorded it by Adams’s opinion that the above forms of the razor are methodological and that it is not obvious how they are related to truth.51 Indeed, the razor’s purported theory-generating informativeness seems to be its merit. But on occasions the razor is contradicted by the presence of informative complexity in a new more productive theory (as with fundamental physics and superstrings52 ), which is more informative than a previous simpler theory. Although scientists appeal to Ockham’s razor, their use of it often explicitly conflicts with Ockham’s own express claim that it should only be employed outside the scope of observation statements,53 which complies well with his desire to press demonstrative science into admission of uncertainty. Ockham was aiming at a reduction of individuation in ontology, and he denied that some relational states between propositions have to be distinct.54 Ockham’s use of a complex procedure using negation to achieve reduction of entities, is itself also a negation of parsimony, since its strategy is to acknowledge complex propositions while positing them as such, then negating them to achieve their elimination.55 Ockham’s desire to bring parsimony to ontology internalizes a tension between realism and epistemology. If one conceives that necessity in reason is a criterion of identity for restricting ontological plurality, then ontological contingencies may be unwarrantably censored (and this can cut against empirical productivity, as much as it can against semantics). Ockham’s way of meeting this tension is to internalize a version of anti-realism into his epistemological programme. But this ‘anti-realism’ is precariously positioned in relation to the traditions which he controverts, in particular if contrasted with twentieth-century opponents of realism. Ockham, after what appears to be an early position in which he agrees with Scotus, attacks Duns Scotus’s strong realism,56 though concurring with Duns Scotus that real relations are mind-independent.57 His aim is commendable, in his parsimonious wish to place limits on excessively strong claims about empiricism, and at a time when scientific mythology and ignorance falsely generalized local experience. We can concur with Goddu that this tendency is in keeping with our contemporary physics ([14.44] 208–31). Goddu furnishes us with the Quantum Mechanical Bell theorem’s scope, as an example to flesh out Ockham in current physics. This theorem is to the effect that, in universalizing realist claims in science, we must relinquish claims on locality or determinism respecting universal claims for empiricism. Clearly Ockham is a far cry from Bell. Ockham was concerned to argue that positing additional entities is not in principle a strategy for resolving realist problems in favour of a strong realism, just as the proposal that there are hidden variables in quantum mechanics does not resolve the issue of action at a distance without a medium. It seems clear that his view was being opposed by William of Crathorn, who lectured at Oxford in 1331 ([14.93] 255–74, etc.). Crathorn held that viewing was through a medium. He devised an original theory of knowledge that disagreed with Ockham (and Holcot, [14.93] 93). In particular, Crathorn, concerned with the purported uncertainty involved in intuitive cognition, affirms that incomplete objects in a prepositional context are complex, disputing Ockham’s reductionism and epistemological certainty. Although Crathorn’s theories are often uneven and cavalier in their attention to views of opponents, they illustrate that Ockham was part of a general trend of exploration in Oxford. Crathorn’s comprehension of prepositional complexity in the context of incomplete objects is an unexpected partial parallel with our modern concepts of the incompleteness of a logical predicate (to be attached to a subject term), which pulls against Ockham’s two-name theory. But while disagreeing with Crathorn and others, Ockham was impelled by the razors to admit incompleteness as a conceptual condition, so as to meet the restrictions of ignorance and yet adequacy according to empirical reductionism.58 FUTURE CONTINGENTS Looking from the present at the universe, Ockham was to some degree aware that we are observing its past. If psychoanalysis has any lesson to teach here ([14.22] 38–46), it is that analysis of the future is intentional, and the future is a sort of metonymy for present concerns, as well as a series of codes for covert absorption and transference of our pasts. No doubt such matters can be overstated. But with Ockham and his contemporaries, the most obvious constituent in their talk of future contingents, only slightly off stage, is their personal interest in that future. The study of God’s knowledge of the future is an understanding of how he deals with his people. The conditionality of present life requires guidance by instruction in the principles according to which God knows the future in relation to people in the present. In practice, however, the scholarly debates about such topics were often highly abstract technical affairs, and even used to feed earthly vendettas, networking through generations. Boethius refined the conception (cf. Chapter 1), which is followed by Peter the Lombard in his Sentences, that God is timeless and has present capacity to know from all eternity everything he knows in the present. Thomas Buckingham took up this thesis in his On the Contingency of the Future, and Free Will. His thesis was an attack on Thomas Bradwardine’s De causa Dei contra Pelagium (In God’s defence, against Pelagius). Bradwardine’s view was that humanity exercised freedom to choose, or not, to obey God’s will without the interference of preordination. As de la Torre has demonstrated ([14.94] ch. 5), Buckingham carefully refrains from explaining that Bradwardine accepted that the First Cause regiments people, yet they are able to act freely in secondary cause contexts. For Bradwardine, God, from all eternity, chose freely from the array of future contingents. Such contingency (contingentia ad utrumlibet) applies also to humans in the secondary cause contexts. A generation earlier Ockham had attempted to apply his sense of simplicity to reduce confusion. For him, duration was the foundation feature of time. God has knowledge of the future. Ockham was troubled by Aristotle’s On Interpretation. In accordance with the standard medieval view, Ockham took Aristotle to have argued that singular propositions about future affairs are not, prior to the time of which they speak, true or false. Since for Ockham this violates the doctrine that all propositions are true or false (to cut a long story short), there must never have been future contingents, or they are illogical.59 Ockham, then, interprets Aristotle as maintaining that God is, in a special sense, possibly ignorant of a future contingent. A reason for this is that—expressed that way—it is not an epistemological existent. That is to say, the future does not exist, thus future contingents do not instantiate, self-inhere, or obtain now, for the future, since it is not there nor here to refer to. But God’s absolute power, for Ockham, alters this bald state of affairs. Although in a narrow sense an individual, for Ockham and for Scotus, only intuition can deform this boundary for God ([14.64] 184–5), if and can only exercise intuitive cognition of an existing thing, the conjunction of God’s absolute power and if the law of non-contradiction is not violated. We should appreciate in this context that for Ockham logic is possibility for ontology as well as for propositions; this is partly why he was agreeable to ‘limiting’ God’s knowledge of future contingents: in a strict sense, they do not exist, do not supposit. Despite this, God’s omnipotence infinitely empowers his intuition, and God is also able, as well as willing, to make and implement promises about the future,60 which both inform his use of epistemological possibility and construct intuitive cognition. OCKHAM’S ETHICS AND POLITICAL PHILOSOPHY Ockham has waited over 600 years for the first publication in any modern language of his political philosophy.61 The castigation of Ockham by the ‘humble’ Christian Lutterel, with his complaint to the Pope at Avignon in 1323, embodied and generated an attitude to Ockham which outlawed him for some of his contemporary, and later, would-be readers. Lutterel was generally disliked and opposed at Oxford university. His appointment seems one of those conundrums that can attend an institution: the contrary of its identity is appointed to lead it. Possibly, since Ockham bore the brunt of Lutterel’s vehemence, as part of a tactic for the latter to ingratiate himself with the Pope’s power-base, this was a cause of the alienation Ockham increasingly experienced, though we ought to contend with his own sense of embodying the Oxford tradition which Lutterel dared to change. No doubt, alienation was nevertheless a growing component in Ockham’s identity, while yet it is only one thread in a complex fabric. Alienation is a property of ‘romantic modernism’, for example in French modernism, emerging in the early eighteenth century. Holland has identified schizoid behaviour in Baudelaire, induced by his alienation. In this case, narcissism encouraged by an elitist perspective was projected on to the society, which was challenged to conform to the writer’s perspective.62 Offler judged that Ockham was prisoner of his own elitism and had no interest in following the democratizing move to popularize scholasticism in the vernacular ([14.72] 341–2) such as Conrad of Megenberg displayed. Indeed, Offler mentions that the latter was fighting against the vogue of Ockhamist ‘modernism’. Fundamental to a modernism is individualism, and this held true for Ockham’s ethics and political action. As McGrade explains (see [14.62] 17ff.), there is a puzzling tension between Ockham’s individualism in practice (Ockham emphasizes not just individuality, but this property for sets of individuals) in contrast with the explicit abstractness, or impersonal style (even when writing of personal matters) of much of his writing on the topic. One could interpret this as a splitting of psychological identity along modernist lines. We do not know enough about his time at Avignon, nor of Lutterel’s, to understand what party politics made up the pressure on Ockham to provoke, or Lutterel act as foil for, his fracture with the Church. It was quite usual for a theologian of Ockham’s ilk to write political philosophy and ethics, not least if he were following Aristotle as the ideal. Offler observed that it looks as if Ockham seriously attended to Aristotle’s Politics and Ethics in 1339–40 ([14.72] 340), after he had written a considerable amount of the political philosophy. (See Ockham’s reference in III Dialogus, I, to Aristotle’s Politics V, 8.) It was some time later, in the 1340s, subsequent to more general compositions on political philosophy, that Ockham responded to the Pope’s assertion of supreme political authority and its relation to poverty, with his A Short Discourse on the Tyrannical Goverrnment: Over Things Divine and Human, but Especially the Empire and Those Subject to the Empire Usurped by Some Who Are Called Highest Pontiffs (see [14.11]). Hardly a basis for ecumenical rapprochement. In the convention of the time this title measures Ockham’s antagonism, individualism and pragmatism. It is a surprise if one is familiar only with the intellectual range circumscribed by his theoretical philosophy and logic. Consider for example Ockham’s intensive use of the Bible, for example in The Work of Ninety Days (in [14.7]). In his confrontation of the Pope’s extravagant riches, he sounds like a member of a theological underground of, say, Peter Waldo of Lyon in the twelfth century. He reminds the Pope that Jesus and the Apostles had no riches, concluding with the allegation that in such matters the Pope follows Constantine, not Peter ([14.7] 105). This policy-aim to contextualize the Bible does not expand to its internal limits, however, though one should not minimize its radical strategy. For example, it does not occur to Ockham to use the function of implication or dialectic within the New Testament narrative presuppositions to discover their own internal limiting parameters. (He uses the citations, instead, as checks for excesses in papal misuse of its rightful original position.) Ockham might, for example, have questioned, within the foregoing debate, how it is that the authority of Peter in Matthew 16 extends beyond the lifetime of Peter to others. Nevertheless his philosophical questioning about the relation of divine narratology to political institutions is bold and his new recognition of a repressed connection, in an atmosphere of intolerance, should not be underestimated.63 Ockham can be usefully placed by seeing him in relation to John of Paris,64 a Dominican who had supported Aquinas against Ockham’s order, the Franciscans. These two theologians, the former a disciple of the latter, spoke of law, discipline, and education as ruling functions of the state over the individual, though Aquinas stressed the natural law, in accordance with his view of Aristotle in his Nicomachean Ethics. Like Aristotle, John is interested in what it is to be human, rather than secular power-bases, whilst the state is the decision-maker and custodian of the common good. John’s synthesis, which was influential in the law of states, lays a foundation for fourteenth-century individualism and the state authority which denies it. So Ockham came at a time when there was a growing awareness of individualism and yet a lack of a counterpart discrimination in its corollary: the state should not obtrude on rights and liberty. Ockham argues that these come from God, instantiated in nature.65 Consequently papal authority should not usurp God’s power and provision by countermanding individualism. It is in the identity of a human experiencing this nature that general laws are derived from nature, and from revelation, on personal liberty and its collective form. There is some similarity on facets of individualism and freedom between Ockham and more recent philosophies of freedom.66 Holopainen has proposed that Ockham advanced a single theory of divine command ethics ([14.51] 133–49, etc.), which allows two moralities. Divine morality, transcendent with respect to cultural variables, supervenes on, and yet is manifest in, nature.67 But the relation between Ockham’s individualism and the logic of his various analyses is complex. The reader may with particular profit read Adams’s work on the extent of Ockham’s use or manifestation of individualisms (see [14.13]). She writes of the polyvalency of individualism, plausibly arguing that Ockham’s variety of individualisms are logically independent of each other, and warning against the seductive lure to integrate this variety into a singularity which can then easily be fitted into a grand historical sweep. These are important points, and ones which can be used to probe the extent and veracity of his parsimony. There are other considerations to complement such explorations. Logically, independence does not of course imply that separate individualisms cannot be consistent with each other, just as tokens are values of a single type. When we are attempting to assess a complex original figure such as Ockham, who also derives many of his patterns of thought from his contemporaries, it is problematic to develop connections, as Adams is aware. Given his sometimes original use of contemporary influences, Ockham can be elusive and difficult; he is a nuanced mirror of his era, which dislocates his period’s self-perception of continuity. NOTES Ockham is a central figure in fourteenth-century philosophy and his thought is discussed in a number of chapters. Readers may find the presentation of some of his main ideas in Chapters 15 and 17 below a useful introduction to the wider-ranging and more speculative discussion in the present chapter. [EDITOR] 1 At least, those of whom manuscripts are extant. See Courtenay [14.26]. 2 See Ockham [14.5] Ordinatio, I, d. 2, q. 7. 3 See Knysh [14.55] 25–6, who suggests that the liber suus of 1327 was a technical stumbling-block for the authorities. 4 Spade [14. 89] IV shows how Thomas Bradwardine’s research on insolubilia assisted him to craft a theory of signification that has correspondence-theory properties. 5 I propose that ‘modernist logic’ be used to mark philosophical trends that run contemporarily with the familiar use of the term ‘modernism’ for a general cultural context. There is a need for research on cross-currents between these contexts and philosophy in nineteenth-century European modernisms. 6 See Frege, ‘Compound logical thoughts’, in [14.36]; cf. Dummett [14.30]. 7 Adams [14.12]. Adams has only one brief reference to Frege (p. 388), and four to Russell (pp. 136–7, 150, 536, 797). 8 Adams [14.12] refers to the 1st edn (Ithaca, NY, 1962) of Geach’s book. There have in fact been two edns of the book since 1962. The 2nd in 1964, 3rd in 1980. Adams was published in 1987. In his 3rd edn, Geach ([14.37] 13), explains that he rewrote parts of the book, noting, ‘The sections most affected by these changes are sections 32, 34, and 35… The only major change in Chapter Three is in section 36.’ These include the main sections to which Adams refers. Adams ([14.12] 388), having only one brief reference to Frege, offers no presentation or proof of what the ‘Frege bias’ is supposed to be. 9 See Spade [14.87] 216, and the section below, ‘Ockham on reference’. 10 Russell was unable to judge that work. Smiley [14.84] assesses Russell on descriptions. 11 Adams ([14.12] 897–9) briefly refers to David Lewis in a taxonomical remark on Ockham, noting his indexical theory of actuality. She observes that Ockham’s ‘uniform assumption that temporal indicators cannot be eliminated in favour of an eternal-present show that he was not an Indexicalist’. 12 The relation between metaphoric language in scientific theory and logical space in philosophy is a facet of ‘logic as a work of art’. A starting point for this new area of research is the use in Wittgenstein [14.100] of a proposition as a projection in space, together with the role of space and geometry in Mallarmé [14.63]. For studies on this latter aspect, see Bowie [14.21], Gibson [14.42], Reynolds [14.79], Scott [14.83]. 13 Bowie [14.22] 37–42, 103–4, etc., relates logic to creativity. 14 Russell [14.98] regularly confuses premisses with assumptions. 15 Someone might wish to adapt Ockham’s theory of a ‘mental language’ by using the sort of innate syntaxes devised by Chomsky. Chomsky [14.24] proposed a thesis that incorporates indeterminacy into his theories of mind, however. According to Chomsky, our ordinary uses, not some ideal language, are nested innately. This would be the opposite of what Ockham needs. Chomsky’s generalization of indeterminacy is also alien to Ockham, and it destabilizes his nominal and causal relations. Russell’s misinterpretation of Ockham has been noted by Offler [14.72] 338 and n. 1. 16 Ockham [14.5] Summa logicae I, c. 1. 17 Dummett ([14.29] 59–62, etc.) offers valuable analysis of proper names and other subject/predicate differences. 18 See Aristotle On Interpretation 1–3, 10, 11. 19 This argument follows Quine’s work as presented by Dummett ([14.30] 223–4, 294). 20 Aquinas Summa theologiae I, q. 76, a. 6, ad 2. Cf. [14.12] 13–16, 679–997. 21 As Geach [14.37] 201–2. 22 On links between these ideas of Ockham’s and Wodeham and Rodington, see Tachau [14.93] 203–5. Walter Chatton attacked this aspect of Ockham’s thought. 23 As White [14.97] 173, referring to Ockham [14.5] Quodlibet III q. 8. 24 Kripke’s [14.56] approach amplifies in a different mould social and causal roles, for which, if adjusted, one could develop aspects of Burley’s approach. 25 As Adams ([14.12] 329) states it. On the different types of supposition see below, Chapter 17, pp. 412–14. 26 Adams [14.12] 387–8 mentions that Frege’s use of ‘is’ could be brought into the semantic analysis; but Frege’s approach to predication and the role of ‘is’ in such uses is the contrary of Ockham’s. 27 Aquinas, Summa, Ia, q. 13, art. 12. 28 Frege uses this one German term with the three senses of ‘referring’, ‘referent’ and the relation of ‘reference’. Dummett [14.29] maintains that Frege does not confuse these separate uses. So do we here have one term, also containing two polysemes, or a metaphor? 29 Suggested by Jane Heal. I should stress that this whole ‘Ockham’ reconstruction has nothing to do with Heal’s theory and is not suggested by her, though I am indebted to her reaction to my above idea. 30 A suggestion about paraphrasing (e.g. ‘she’s a right one’) indexicality, not in a referential role, not in an Ockham context, and without my generalizing thesis over whole general predicates, comes from Heal’s working paper delivered at the Cambridge Moral Sciences Club, 21 January 1997. I acknowledge her permission to mention it. 31 Marenbon [14.65], [14.64] 57 for Bacon’s Paris study and teaching of Aristotle. 32 See Walter Chatton [14.4] I, d. 30, q. 1, a. 4. 33 Duns Scotus, Opera omnia, ed. L.Wadding, J.Ponce et al., Duran, Lyons, 1639, vol. VII, p. 723. 34 Aristotle On the Heavens II, xii, 292a–b25. 35 Ockham [14.5], Ordinatio I, d. 30, q. 2. 36 Ockham [14.5], Treatise on Quantity II i, q. 1. 37 Aspects of this use of ponenda are not unlike a notion that Dummett ([14.29] 309) pointed out in Gentzen’s use of ‘suppose’. Gentzen formalized inference to allow for a use similar to natural language reasoning, ‘Suppose that…’. If contradictory inferences follow from that use, one can withdraw the premisses which led to it. This complies well with Ockham’s desire for non-contradiction. 38 See Haack’s [14.46] treatment of Frege’s ‘presupposition’. For scrutiny of ‘assertion-sign’ see Dummett [14.29] 328–9. 39 Geach [14.38] 288–301. Adams [14.12] 989–90 quotes him ([14.38] 296–7), concerning Ockham’s use of humanitas and regarding Nestorianism. Although demurring from Geach’s view, Adams never attempts to fault Geach’s use of logic. 40 Ockham [14.5], Treatise on Quantity I, q. 1. 41 Adams [14.12] 1008–10. She is citing Ockham [14.5], Ordinatio I, d. 2. q. 1. 42 Adams [14.12] 1008–10 numbers this maxim 7. 43 White [14.97] serves as a framework for this suggestion. 44 This point could be applied with profit to any of Ockham’s logic. There is a profound treatment of the research in Boghassian [14.19]. 45 Priest [14.74]; cf. Smiley’s [14.85] criticisms. 46 Geach ([14.37] 27) points out that the expression ‘quantify’ and ‘quantification’ appear to derive from Hamilton. 47 Adams [14.12] 156: ‘Quando propositio verificatur pro rebus, si duae res sufficiunt ad eius veritatem, superfluum est ponere tertiam.’ Adams refers to its use in Ockham [14.5], Quodlibet IV, q. 24. 48 Ockham [14.5], Quodlibet VI, q. 29. 49 D.Davidson, ‘Truth and meaning’, in Inquiries into Truth and Interpretation, Oxford, 1984, pp. 24ff. 50 Boler ([14.20] 470; see Spade [14.87]) suggests that Ockham might be committed to adopting a sophisticated coherence theory of truth. Coherence theory (inadvertently) allows internal contradictions: they only have internally to cohere. 51 A response to defend this use of ‘methodological principle’ might be envisaged: does not Dummett [14.31] 164 employ the expression to describe an approach advocated by Wittgenstein [14.99], and is not criticism of Adams’s ‘methodological principles’ unwarranted? No, because Dummett is contrasting Frege’s (and others’) truth-conditional theory of meaning with Wittgenstein’s methodological principle concerning use, whereas Ockham’s ‘razors’ use logical terms to govern logic and its ontology, in which Ockham proposed truth-conditional logic. 52 See Gross [14.45], and resumption of this theme below in the section Anti-realism’s true razor? 53 Ockham [14.5], Reportatio II, q. 150. 54 Ockham [14.5], Ordinatio I, d. 30, q. 1. 55 Cf. Horst [14.52] 365–70 (from a perspective outside Ockham studies). 56 See Ockham [14.5], Ordinatio I, d. 30, q. 1, and Quodlibet VI, qq. 8–19, etc. 57 See Ockham [14.5], Ordinatio I, d. 30, q. 1. 58 An interesting extension of the principle of parsimony is provided by the astrophysical cosmology of the early universe, where some scientists seek a single equation functioning as the universal for the whole universe: see Rees [14.78], but cf. Hunt [14.53]. On the problems posed by such science (can its formulations be taken literally?), see Dallaporta [14.27] and Bell [14.18]. Perhaps Ockham, like these cosmologists, arrives at counter-intuitive consequences in his search for simplicity. On this whole question see Popper [14.73], Lewy [14.61] and Gibson [14.40]. 59 See Aristotle On Interpretation, IX, 1–16, 18–25. Few modern interpreters would accept this view. Cf. Anscombe [14.15] 53. See also Milbank [14.67] on Ockham’s confusion in this case. 60 Ockham [14.5], On Predestination q. 1. 61 McGrade [14.11] ix. As he points out (n. 1) E.Lewis [14.60] translated 23 chapters, and F.Oakley 4 chapters, in Lerner [14.57]. 62 This term is used in the sense of Holland [14.50]. In Gibson [14.42] Pt I, there is a comparative conception of ‘modernism’ complementary to the present study. 63 On the problems about connecting theoretical with political philosophy, and on criteria for difference and identity, see Milbank [14.68] chs. 7 and 8; Ward [14.96] 24–8, and also, more broadly, Dummett [14.29] 73–80. 64 John of Paris, On Royal and Papal Power. 65 On the Power of Emperors and Popes, in Ockham’s Opera Politics IV, ed. H.S. Offler, Oxford, British Academy, 1997, 278–355. Volumes I–III are edited by J.Sikes et al., Manchester, 1940–63. 66 Rawls [14.76], and with regard to Aristotle Ethics V; Dworkin [14.32] on inalienability of individual rights. 67 See Coleman ([14.25] 27) and generally for a concise valuable study on Ockham’s nature and rights. BIBLIOGRAPHY Original Language Editions and Manuscripts 14.1 Adam Wodeham Sentences 1, I, I, ed. G.Gál, in ‘Adam of Wodeham’s question on the “complexe significabile”…’, in Franciscan Studies 37 (1973): 66– 102. 14.2 John of Reading Sentences I, Florence, Biblioteca Nazionale Centrale, MS conventi soppressi D.IV.95. 14.3 Thomas Buckingham De contingentia futurorum et arbitrii libertate, in B.R. de la Torre, Thomas Buckingham [14.94]. 14.4 Walter Chatton Reportatio, Paris, Bibliothèque Nationale, lat. 15887. 14.5 William of Ockham Opera philosophica et theologica, 17 vols, St Bonaventure, NY, Franciscan Institute, 1967–88. Translations 14.6 William of Ockham ‘Five Questions on Universals’ (from the Ordinatio), in P.V.Spade (ed. and trans.) Five Texts on the Medieval Problem of Universals, Indianapolis, Ind., Hackett, 1994. 14.7 ——A Letter to the Friars Minor and Other Writings, ed. A.S.McGrade and J.Kilcullen, trans. J.Kilcullen, Cambridge, 1995. (Note: this is the volume announced before publication, in the Preface, p. ix, to A Short Discourse [14.11], as Selections from the Major Political Works.) 14.8 ——Philosophical Writings, trans., intro. and notes by P.Boehner, Latin text and trans. revised by S.F.Brown with new Foreword, Indianapolis, Ind., Hackett, 1990. 14.9 ——Predestination, God’s Foreknowledge and Future Contingents, 2nd edn, trans., intro., notes and appendices by M.M.Adams and N.Kretzmann, Indianapolis, Ind., Hackett, 1983. 14.10 ——Quodlibetal Questions, vols 1 and 2, trans. A.J.Freddoso and F.E. Kelley, New Haven, Conn., Yale University Press, 1991. 14.11 ——A Short Discourse on the Tyrannical Government, ed. A.S.McGrade, trans. J.Kilcullen, Cambridge, Cambridge University Press, 1992. Editor’s Bibliographical Note Since the ‘Studies’ section of Arthur Gibson’s bibliography is mainly occupied by details of the wide range of comparative material cited in his chapter, it may be useful to give a quick guide to the basic secondary bibliography on Ockham and his followers. Where the works are listed by Gibson below, just the author’s name and reference number are given. Biography L.Baudry, Guillaume d’Occam: sa vie, ses oeuvres, ses idées sociales et politiques, Paris, Vrin, 1949. Bibliography V.Heynck, ‘Ockham—Literatur: 1919–1949’, Franziskanische Studien 32 (1950): 164–83; J.Reilley, ‘Ockham bibliography, 1950–67’, Franciscan Studies 28 (1968): 19–214. General philosophical studies Adams [14.12] is fundamental. Other general studies include Alféri [14.14], L. Baudry, Lexique philosophique de Guillaume d’Occam: étude des notions fondamentales, Paris, Léthielleux, 1975; G.Leff, William of Ockham: the Metamorphosis of Scholastic Discourse, Manchester and Totowa, NJ, Manchester University Press/Rowman & Littlefield, 1975; and C.Panaccio, Les Mots, les concepts et les choses: la sémentique de Guillaume d’Occam et le nominalisme d’aujourd’hui (Analytiques 3), Montreal and Paris, Bellarmin/Vrin, 1991 (this compares Ockham’s semantics with modem Anglo-American discussions; a useful foil for the rather different comparison made in this chapter). P.Boehner’s important articles are collected as Collected Articles on Ockham, ed. E.Buytaert, St Bonaventure, NY, Louvain and Paderborn, Franciscan Institute, Nauwelaerts and Schöningh, 1958. Vossenkuhl [14.95] contains excellent articles by specialists on different aspects of Ockham’s work. Particular areas <b>Logic </b> E.Moody, The Logic of William of Ockham, London, Sheed & Ward, 1935, was groundbreaking but is now rather dated. Adams [14.12] covers this area thoroughly in volume I of her study; see also Chapter 17 below and bibliography there. <b>Epistemology </b> Tachau [14.93] places Ockham’s views in context and assesses their influence. <b>Ethics </b> Holopainen [14.51]. <b>Future contingents </b> A.Plantinga, ‘On Ockham’s way out’, Faith and Philosophy 3 (1986): 171–200, repr. in T.V.Morris (ed.) The Concept of God, Oxford, Oxford University Press, 1987; D.Perler, Prädestination, Zeit und Kontingenz: philosophischhistorische Untersuchungen zu Wilhelm van Ockhams ‘Tractatus de praedestinatione et de praescientia Dei respectu futurorum contingentium’ (Bochumer Studien zur Philosophie 12), Amsterdam, Grüner, 1988. <b>Political theory </b> McGrade [14.62] and J.Miethke, Ockhams Weg zur Sozialphilosophie, Berlin, De Gruyter, 1969. Contemporaries, followers and the next generation of Oxford philosophers Tachau [14.93] revises previous views about Ockham’s relation to his contemporaries and his influence; see also Chapters 15 and 16 below. Important general studies and collections include: J.Biard, Logique et théorie du signe au XIVe siècle; A.Hudson and M.Wilks (eds) From Ockham to Wyclif, Oxford, Blackwell Publishers, 1987; Z. Kaluza and P.Vignaux (eds) Preuve et raisons à l’Université de Paris: Logique, ontologie et théologie au XIVe siècle, Paris, Vrin, 1984. <b>Particular thinkers: Adam Wodeham </b> W.J.Courtenay, Adam Wodeham: an Introduction to his Life and Writings, Leiden, E.J.Brill, 1978; <b>Henry of Harclay </b> C.Balic, ‘Henricus de Harclay et Ioannes Duns Scotus’, Mélanges offerts à Etienne Gilson, Toronto, Pontifical Institute of Mediaeval Studies, 1959. <b>Oxford calculators (in general) </b> E.D.Sylla, ‘The Oxford Calculators’, ch. 27 in CHLMP, provides a good introduction; see also M.Clagett, The Science of Mechanics on the Middle Ages, Madison, Wis., University of Wisconsin Press, 1959; E.D.Sylla, ‘Medieval concepts of the latitude of forms: the Oxford Calculators’, Archives de l’histoire doctrinale et littéraire du moyen âge 40 (1973): 223–83. <b>Richard Swineshead </b> J.A.Weisheipl, ‘Roger Swyneshed, OSB, logician, natural philosopher and theologian’, in Oxford Studies Presented to Daniel Callus, Oxford, Oxford University Press, 1964. <b>Robert Holcot </b> F.Hoffmann, Die theologische Methode des Oxford Dominikanlehrers Robert Holcot (BGPTMA) (Münster, Aschendorff, 1972) (wider in scope than its title suggests). <b>Thomas Bradwardine </b> G.Leff, Bradwardine and the Pelagians, Cambridge, Cambridge University Press, 1957; H.A.Oberman, Archbishop Thomas Bradwardine: a Fourteenth-century Augustinian, Utrecht, Zemink and Zoon, 1957; E.W. Dolniowski, Thomas Bradwardine: a View of Time and a Vision of Eternity in Fourteenth-century Thought, Leiden, E.J.Brill, 1995. <b>Thomas Buckingham </b> J.-F.Genest, Prédétermination et liberté crée à Oxford au XIVe siècle: Buckingham contre Bradwardine (Etudes de philosophie médiévale 70), Paris, Vrin, 1992. <b>William Heytesbury </b> W.Curtis, William Heytesbury: Medieval Logic and the Rise of Mathematical Physics (University of Wisconsin Publications in Medieval Science 3), Madison, Wis., University of Wisconsin Press, 1956. Studies 14.12 Adams, M.M. William Ockham, 2 vols, Notre Dame, Ind., University of Notre Dame Press, 1987. 14.13 ——‘Ockham’s individualisms’, in [14.95]. 14.14 Alféri, P. Guillaume D’Ockham le singulier, Paris, Minuit, 1989. 14.15 Anscombe, G.E.M. ‘Aristotle and the sea battle’, in The Collected Philosophical Papers of G.E.M. Anscombe, vol. 1, Oxford, Blackwell Publishers, 1981. 14.16 ——‘The first person’, in The Collected Papers of G.E.M. Anscombe, Oxford, Blackwell Publishers, 1981. 14.17 ——Intention, Oxford, Blackwell Publishers, 1957. 14.18 Bell, J.S. Speakable and Unspeakable in Quantum Physics, Cambridge, Cambridge University Press, 1987. 14.19 Boghassian, P. ‘The rule-following consideration’, in Mind 98 (1989): 507–49. 14.20 Boler, J.F. ‘Intuitive and abstractive intuition’, in CHLMP. 14.21 Bowie, M. Mallarmé and the Art of Being Difficult, Cambridge, Cambridge University Press, 1978. 14.22 ——Psychoanalysis and the Future of Theory, Oxford, Blackwell Publishers, 1993. 14.23 Butler, C. Early Modernism, Oxford, Oxford University Press, 1994. 14.24 Chomsky, N. ‘Language and nature’, in Mind 104 (1995): 1–62. 14.25 Coleman, J. ‘The individual and the medieval state’, in J.Coleman (ed.) 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