Little is known of his life, but he is thought to have studied in Paris, was a master at Oxford in 1252, treasurer of Lincoln from 1254/1258 onwards, and a rector of Aylesbury.
He would have had a personal residence in the Cathedral close, would have employed a deputy and a large staff, and therefore could be absent as long as he performed those duties that could not be delegated.
It survives in a single manuscript probably written in the late thirteenth century, headed Introductiones Magistri Guilli de Shyreswode in Logicam.
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).
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.
William's work spurred a development of logic in the thirteenth century under the general designation De Proprietibus Terminorum.
Now, William is perhaps best known for a mnemonic poem to help students remember the names of the valid syllogistic forms: BARBARA, CELARENT, DARII, FERIOque prioris; CESARE, CAMESTRES, FESTINO, BAROCO secundae; tertia DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet; quarta insuper addit: BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON; This verse might not have originated with him, but it is the oldest known surviving version.