The Introduction To Logic
William's main work is a small logic manual, Introductiones in logicam. It survives in a single manuscript probably written in the late thirteenth century, headed 'Introductiones Magistri Guilli. De Shyreswode in Logicam', (Bibliothèque Nationale, Cod. Lat. 16617, formerly Codex Sorbonnensis 1797). It did not appear fully in print until 1937, in Grabman's Latin edition, and was not translated into English until 1966, by Kretzmann. No other works that are definitely by him have ever been printed.
The book consists of Six Chapters. Five of these are expositions of Aristotle's main logical works, as follows: 1. 'Statements', corresponding to De Interpretatione, 2. 'The Predicables', corresponding to Categories, 3. 'Syllogism', corresponding to Prior Analytics, 4. 'Dialectical Reasoning' corresponding to Topics, and 6. 'Sophistical Reasoning' corresponding to Sophistical Refutations. However, Chapter 5, 'Properties of Terms', contains material that is not in Aristotle, but is a distinctively medieval development, (Supposition theory) that deals with the semantics of propositions. The theory attempts to explain how the truth of simple sentences, expressed schematically, depend on how the terms 'supposit' or stand for certain extra-linguistic items, and tries to address the problem of sentential forms, like 'I promise you a horse', which do not appear to fit the standard syllogistic forms.
In this chapter William introduces what was to become a standard division of supposition into 'material', 'formal' and 'personal'. In material supposition, a term stands for itself, as when we say that 'Socrates' is a name (note that medieval Latin did not use quotation marks as in modern English). In formal supposition, the word signifies its meaning, as in man is a species. Formal supposition is similar to what is indicated in modern philosophical logic by italicising a common noun, as when we refer to the concept horse. Personal supposition is approximately the relation we now call 'satisfied by', or 'denotes', as in 'the term 'man' denotes Socrates, Aristotle, &c'.
He discusses a number of problem cases. For example, the sentence 'every man sees a man' is true when there is a single man that every man sees (for example if 'every man sees Socrates' is true). But the sentence is also true when every man sees a different man, or when some men see a single man (such as Socrates), other men see another man, and innumerable cases in between. This is called 'confused' supposition. This instance of the problem of multiple generality, is now thought to be insoluble using the fixed schema of Aristotle's semantics.
William's work spurred a development of logic in the thirteenth century under the general designation De Proprietibus Terminorum. Those who engaged in this part of logic were called the Moderni, or Terministae. Its most detailed treatment is found in Ockham, and in the works of those who followed him.
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