:rofl:
When you're done scratching yourself, here's a little light reading for you:
It's from the School of Mathematics and Statistics University of St Andrews, Scotland.
William of Ockham's name is sometimes written William Occam. He is also known as the "More than Subtle Doctor" or the "Venerable Inceptor". Nothing is known of his parents or his early life before he entered the Franciscan order at the age of fourteen. His education was in a Franciscan convent and it was almost certainly the London convent since it acted as the educational centre for the area in which he lived. We do know that he was ordained a subdeacon by the archbishop of Canterbury in Southwark, London, in 1306 which certainly supports him being trained in London. After this some students were sent to Paris for further training, the rest taught at a convent. There is no direct evidence to support which of these alternatives Ockham followed but it must have one of them. He was then sent to Oxford to study for a theological degree.
At Oxford Ockham lectured on the Book of Sentences of Peter Lombard. Peter was a 12th century Italian theologian who had written the work to state clearly the position found in the Scriptures and that of the Church fathers on Christian doctrine. Peter Lombard, a conservative theologian, wrote the text as a reaction against some who at the time were applying Aristotle's logic to theology. It was required that every student working for a higher degree in theology would lecture and comment on the Book of Sentences which is what Ockham did at Oxford in 1317-1319. The text was used as a framework for students to develop their own original positions and to debate with their teachers and fellow students. In June 1318 Ockham was granted a licence to hear confessions and by 1320 he completed study for his bachelor's degree.
Ockham lectured on logic and natural philosophy in a Franciscan school from 1321 to 1324 while he waited to return to university to study for his doctorate. During these years he wrote many deep works on philosophy and logic. Corcoran writes:-
William of Ockham was certainly among the most imaginative, competent, and prolific of Medieval logicians. The scope of the apparently original concepts, problems, and results found in his works is impressive, if not astounding.
In particular Ockham wrote the monumental three-part Summa logicae during these four years which Corcoran says:-
... is probably the most comprehensive original logical treatise written in the period between Aristotle's "Organon" and Bolzano's "Wissenschaftslehre" (1837).
Ockham's opinions aroused strong opposition and he was summoned by the Franciscan provincial chapter <3>:-
... to explain his views on thirteen propositions derived from his teaching on the Aristotelian categories, especially the category of 'relation'.
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In terms of philosophy Ockham was strongly committed to the ideas of Aristotle. One of the main problems he contributed to was the problem of universals: is there anything in reality which corresponds to our general words and concepts, and if so, what is it like? Here there are strong connections to mathematics, for mathematical notions are not absolute terms for Ockham. He states mathematical terms in conditional form so that it was not necessary for him to suppose the real existence of such mathematical entities as points and lines in order to make useful use of them. Ockham takes a nominalist approach (indeed he is often called the father of nominalism) believing that points, lines, etc. are mere abstractions and do not really exist.
In his studies of mathematical logic Ockham made important contributions to it which are significant today. He considered a three valued logic where propositions can take one of three truth values. This became important for mathematics in the 20th century but it is remarkable that it was first studied by Ockham 600 years earlier. He also came very close to stating De Morgan's laws. In the Summa logicae Ockham defines a conjunctive proposition as a composite of two or more categorical propositions joined by 'and'. Similarly he defines a disjunctive proposition as a composite of two or more categorical propositions joined by 'or'. A conjunctive is true if and only if every conjunct is true and a disjunctive is true if and only if some disjunct is true. Ockham notes that a conjunctive implies, but is not necessarily implied by, each conjunct separately. He explicitly adds that if one conjunct implies the others it implies the whole conjunctive. Similarly, he notes that a disjunctive is implied by, but does not necessarily imply, each disjunct and that a disjunctive together with a negation of one of its disjuncts implies the disjunctive of the rest. He also notes that the contradictory of the conjunctive is the disjunctive of the contradictories of the conjuncts. He also states a similar statement for the contradictory of the disjunctive, with the obvious changes.
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Ockham.htmland when you're done with that, this is from the Stanford Encyclopedia of Philosophy:
3. Logic and Semantics
Ockham is rightly regarded as one of the most significant logicians of the Middle Ages. Nevertheless, his originality and influence should not be exaggerated. For all his deserved reputation, his logical views are sometimes completely derivative<11> and occasionally very idiosyncratic.<12>
Logic, for Ockham, is crucial to the advancement of knowledge. In the "Prefatory Letter" to his Summa of Logic, for example, he praises it in striking language:
For logic is the most useful tool of all the arts. Without it no science can be fully known. It is not worn out by repeated use, after the manner of material tools, but rather admits of continual growth through the diligent exercise of any other science. For just as a mechanic who lacks a complete knowledge of his tool gains a fuller by using it, so one who is educated in the firm principles of logic, while he painstakingly devotes his labor to the other sciences, acquires at the same time a greater skill at this art.
Ockham's main logical writings consist of a series of commentaries (or “expositions”) on Aristotle's and Porphyry's own logical works, plus his own Summa of Logic, his major work in the field. His Treatise on Predestination contains an influential theory on the logic of future contingent propositions, and other works as well include occasional discussions of logical topics, notably his Quodlibets.
3.1 The Summa of Logic
Ockham's Summa of Logic is divided into three parts, with the third part subdivided into four subparts. Part I divides language, in accordance with Aristotle's On Interpretation (1, 16a3-8, influenced by Boethius's interpretation), into written, spoken and mental language, with the written kind dependent on the spoken, and the spoken on mental language. Mental language, the language of thought, is thus the most primitive and basic level of language. Part I goes on to lay out a fairly detailed theory of terms, including the distinctions between (a) categorematic and syncategorematic terms, (b) abstract and concrete terms, and (c) absolute and connotative terms. Part I then concludes with a discussion of the five “predicables” from Porphyry's Isagoge, and of each of Aristotle's categories.
While Part I is about terms, Part II is about “propositions,” which are made up of terms. Part II gives a systematic and nuanced theory of truth conditions for the four traditional kinds of assertoric categorical propositions on the “Square of Opposition,” and then goes on to tensed, modal and more complicated categorical propositions, as well as a variety of “hypothetical” (molecular<13>) propositions. The vehicle for this account of truth conditions is the semantic theory of “supposition,” which will be treated below.
If Part I is about terms and Part II about propositions made up of terms, Part III is about arguments, which are in turn made up of propositions made up of terms. As mentioned, Part III is divided into four subparts. Part III.1 treats syllogisms, including a complete theory of modal syllogistic.<14> Part III.2 concerns demonstrative syllogisms in particular. Part III.3 is in effect Ockham's theory of consequence, although it also includes discussions of semantic paradoxes like the Liar (the so called insolubilia) and of the still little-understood disputation form known as “obligation.” Part III.4 is a discussion of fallacies.
Thus, while the Summa of Logic is not in any sense a “commentary” on Aristotle's logical writings, it nevertheless covers the traditional ground: Porphyry's Isagoge and Aristotle's Categories in Part I, On Interpretation in Part II, Prior Analytics in Part III.1, Posterior Analytics in Part III.2, Topics (and much else) in Part III.3, and finally Sophistic Refutations in Part III.4.
3.2 Signification, Connotation, Supposition
Part I of the Summa of Logic also introduces a number of semantic notions that play an important role throughout much of Ockham's philosophy. None of these notions is original with Ockham, although he develops them with great sophistication and employs them with skill.
The most basic such notion is “signification.” For the Middle Ages, a term “signifies” what it makes us think of. This notion of signification was unanimously accepted; although there was great dispute over what terms signified, there was agreement over the criterion.<15> Ockham, unlike many (but no means all) other medieval logicians, held that terms do not in general signify thought, but can signify anything at all (including things not presently existing). The function of language, therefore, is not so much to communicate thoughts from one mind to another, but to convey information about the world.<16>
In Summa of Logic I.33, Ockham acknowledges four different kinds of signification, although the third and fourth kinds are not clearly distinguished. In his first sense, a term signifies whatever things it is truly predicable of by means of a present-tensed, assertoric copula. That is, a term t signifies a thing x if and only if ‘This is a t’ is true, pointing to x. In the second sense, t signifies x if and only if ‘This is (or was, or will be, or can be) a t’ is true, pointing to x. <17> These first two senses of signification are together called “primary" signification.
In the third and fourth senses, terms can also be said to signify certain things they are not truly predicable of, no matter the tense or modality of the copula. For instance, the word ‘brave’ not only makes us think of brave people (whether presently existing or not); it also makes us think of the bravery in virtue of which we call them “brave.” Thus, ‘brave’ signifies and is truly predicable of brave people, but also signifies bravery, even though it is not truly predicable of bravery. (Bravery is not brave.) This kind of signification is called “secondary” signification. To a first approximation, then, we can say that what a term secondarily signifies is exactly what it signifies but does not primarily signify. Again to a first approximation, we can say that a “connotative” term is just a term that has a secondary signification, and that such a connotative term “connotes” exactly what it secondarily signifies; in short, connotation is just secondary signification.<18>
The theory of supposition was the centerpiece of late medieval semantic theory. Supposition is not the same as signification. First of all, terms signify wherever we encounter them, whereas they have supposition only in the context of a proposition. But the differences go beyond that. Whereas signification is a psychological, cognitive relation, the theory of supposition is, at least in part, a theory of reference. For Ockham, there are three main kinds of supposition<19>:
* Personal supposition, in which a term supposits for (refers to) what it signifies (in either of the first two senses of signification described above). For example, in ‘Every dog is a mammal’, both ‘dog’ and ‘mammal’ have personal supposition.
* Simple supposition, in which a term supposits for a concept it does not signify. Thus, in ‘Dog is a species’ or ‘Dog is a universal’, the subject ‘dog’ has simple supposition. For Ockham the nominalist, the only real universals are universal concepts in the mind and, derivatively, universal spoken or written terms expressing those concepts.
* Material supposition, in which a term supposits for a spoken or written expression it does not signify. Thus, in ‘Dog has three letters’, the subject ‘dog’ has material supposition.<20>
Personal supposition, which was the main focus, was divided into various subkinds, distinguished in terms of a theory of “descent to singulars” and “ascent from singulars.” A quick example will give the flavor: In ‘Every dog is a mammal’, ‘dog’ is said to have “confused and distributive” personal supposition insofar as
* It is possible to “descend to singulars” as follows: “Every dog is a mammal; therefore, Fido is a mammal, and Rover is a mammal, and Bowser is a mammal …,” and so on for all dogs.
* It is not possible to “ascend from any one singular” as follows: “Fido is a mammal; therefore, every dog is a mammal.”
Although the mechanics of this part of supposition theory are well understood, in Ockham and in other authors, its exact purpose remains a mystery. Although at first the theory looks like an account of truth conditions for quantified propositions, it will not work for that purpose. And although the theory was sometimes used as an aid to spotting and analyzing fallacies, this was never done systematically and the theory is in any event ill suited for that purpose.<21>
3.3 Mental Language, Synonymy, and Connotation
Ockham was perhaps the first person to give not just lip service to the notion of “mental language” (because Aristotle and Boethius had mentioned it), but actually to develop the notion in some detail and to put it to work for him.<22> Written language for Ockham is “subordinated” to spoken language, and spoken language is “subordinated” to mental language. For Ockham, the terms of mental language are concepts; its propositions are mental judgments. Whereas the signification of terms in spoken and written language is purely conventional and can be changed (hence in English we say ‘dog’ whereas in Latin it is ‘canis’), the signification of terms (concepts) in mental language is established by nature once and for all. Concepts “naturally signify” what they are concepts of; this “natural signification” is thought of as a kind of representation relation, based on the fact that concepts are in some way “naturally similar” to their objects.
This arrangement provides an account of synonymy (both interlinguistic and intralinguistic) and equivocation in spoken and written language. Two terms (whether from the same or different spoken/written languages) are synonymous if and only if they are subordinated to the same concept; a single given term of spoken/written language is equivocal if and only if it is subordinated to more than one concept simultaneously.
This raises an obvious question: Is there synonymy or equivocation in mental language itself? (If there is, it will obviously have to be accounted for in some other way than for spoken/written language.) A great deal of modern secondary literature has been devoted to this question. Trentman <1970> was the first to argue that no, there is no synonymy or equivocation in mental language. On the contrary, mental language for Ockham is a kind of lean, stripped down, “canonical” language with no frills or inessentials, a little like the “ideal languages” postulated by logical atomists in the first part of the twentieth century. Spade <1980> likewise argued in greater detail, on both theoretical and textual grounds, that there is no synonymy or equivocation in mental language. More recently, Panaccio <1990>, Tweedale <1992> (both on largely textual grounds), and Chalmers <1999> (on mainly theoretical grounds) have argued the contrary case for synonymy, that Ockham did—or in any event should have — allowed for certain kinds of mental synonymy.
The situation is complicated, but it goes to the heart of much of what Ockham is up to. In order to see why, let us return briefly to the theory of connotation.<23> Connotation was described above in terms of primary and secondary signification. But in Summa of Logic I.10, Ockham himself draws the distinction between absolute and connotative terms by means of the theory of definition.
For Ockham, there are two kinds of definitions: real definitions and nominal definitions. A real definition is somehow supposed to reveal the essential metaphysical structure of what it defines; nominal definitions do not do that. As Ockham sets it up, all connotative terms have nominal definitions, never real definitions, and absolute terms (although not all of them) have real definitions, never nominal definitions. (Some absolute terms have no definitions at all.<24>)
As an example of a real definition, consider: ‘Man is a rational animal’ or ‘Man is a substance composed of a body and an intellective soul’. Each of these traditional definitions is correct, and each in its own way expresses the essential metaphysical structure of a human being. But notice: the two definitions do not signify (make us think of) exactly the same things. The first one makes us think of all rational things (in virtue of the first word of the definiens) plus all animals (whether rational or not, in virtue of the second word of the definiens). The second definition makes us think of, among other things, all substances (in virtue of the word ‘substance’ in the definiens), whereas the first one does not. It follows therefore that an absolute term can have several distinct real definitions that don't always signify exactly the same things. They will primarily signify—be truly predicable of—exactly the same things, since they will primarily signify just what the term they define primarily signifies. But they can also (secondarily) signify other things as well.<25>
Nominal definitions, Ockham says, are different. Like real definitions, there can be several distinct nominal definitions of the same connotative term. But in the case of nominal definitions, all the definitions of a given term will signify exactly the same things in exactly the same ways. This is a very strong claim, and appears to mean that for Ockham all nominal definitions of a given connotative term are synonymous. Furthermore, Ockham seems to think of connotative terms as in effect a kind of shorthand abbreviation for their nominal definitions. If all this is so, then it means that not only are all the nominal definitions of a given connotative term synonymous with one another; they are also all synonymous with the term they define.
If, therefore, there is no synonymy in mental language, it follows that there will be no connotative terms in mental language either. Or, more carefully put, either there are no simple connotative terms in mental language, or else, if there are, then mental language does not have the wherewithal to formulate their (complex) nominal definitions. The latter hypothesis would seem to cripple mental language entirely. Hence the prevailing view until approximately 1990 was that for Ockham there are no simple connotative terms in mental language. There are connotative expressions there, but all of them are complex expressions that, if one wants to put it this way, can in a “degenerate” sense (as mathematicians speak of “degenerate” cases) be said to serve as their own nominal definitions. It remains that no two expressions of mental language are synonymous.
But in 1990 Claude Panaccio published a paper that showed once and for all that Ockham did hold that there are simple connotative terms in mental language. He says it explicitly and repeatedly, and in a variety of texts (just not the texts that had been previously focused on). Since that time the secondary literature seems to have gradually converged on the view that, for Ockham, there is no synonymy among simple terms in mental language, but that synonymy can occur there between simple terms and complex expressions, or between various complex expressions.
It should be emphasized that these matters are far from settled, and some of the claims above are controversial. Readers should nevertheless be aware of the issues. For much rests on them. This is because Ockham's use of connotation theory is crucial to his ontological enterprise.
For Ockham, absolute terms are a guide to ontology. Because Ockham thinks we get the absolute terms of our mental language from a direct experience of the things they signify, it follows that absolute terms are all truly predicable of (past or present) things. But connotative terms are not like that; we can and do have connotative terms for all sorts of things that have never existed — even for things that cannot exist, like (according to the medieval view) ‘chimera’ and ‘vacuum’.
Since simple connotative terms are in effect shorthand abbreviations for their nominal definitions, they can be systematically eliminated and replaced by those nominal definitions without loss of expressive power. If those nominal definitions in turn contain further connotative terms of their own, the latter can in turn be expanded into their own nominal definitions. And so on, until we arrive at a fully expanded nominal definition of the original, simple connotative term, a definition that consists only of absolute terms and of various syncategorematic expressions.
At least that seems to be the goal. What Ockham tries to do, then, is to eliminate the need for many putative entities by parsing away all talk of them via his theory of connotation. As we shall see, most of the Aristotelian categories, for example, are needless “extras” in a perfectly adequate ontology; we do not need any entities in those putative categories.
Thus the question whether there is synonymy in mental language is crucial to our understanding of the success of Ockham's overall ontological project. Since spoken or written language is semantically derivative on mental language, it is vital that we get the semantics of mental language to work out right for Ockham, or else the systematic coherence of much of what he has to say will be in jeopardy. The jury is still out.
http://plato.stanford.edu/entries/ockham/
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