Page 297 - Encyclopedia of Philosophy of Language

In short, he distinguished between conditional prop- ositions and argument structures. Indeed, in later developments in this subject area of consequentiae, it came to be recognized that there was a close relation- ship between the validity of an argument and the necessary truth of the conditional connecting the con- joint premises and conclusion. Also, in the intricate debate surrounding this subject there was a no less lively appreciation of the material conditional than one finds in debates about this subject today.
See: Medieval Philosophy of Language.
5.3 The Renaissance up to the Eighteenth Century
The rise of what is known as 'humanism' in the Renaissance coincided with the new availability of ancient texts of Plato and Aristotle which had not been known in the west during the Middle Ages. This gave rise to new studies across a broader range of subjects than had been possible before, and included a new interest in the scientific study of the world, including mathematical study. The effect of these changes on logical studies was significant. On the one hand, there was a tendency to downgrade the import- ance of logic. The complexities of medieval discussions of logic were not seen as having produced any sig- nificant addition to knowledge, whereas the study of mathematics and science was seen as offering some hope in this direction. (Interestingly, it was not until the twentieth century that medieval studies came to be seen as having made a contribution to the phil- osophy of logic and language.) On the other hand, though there was criticism of logic, there was no real attempt to reform or change the subject in any impor- tant way. By and large, the logic syllabus in the uni- versities remained the same, whilst interest in the subject withered. At the end of the seventeenth century, it had almost become fashionable to show a sort of contempt for the study of logic as done in the universities. John Locke himself wrote (in his Essay Concerning Human Understanding): 'God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational.'
The attitude of the philosophers of these centuries to logical studies illustrates what has been a back- ground theme of this survey. They bitterly criticized the logic they had been forced to study at university, but did not see their own work as in any way con- tributing to change that study itself. Though there were no doubt complex social and institutional causes oftheseattitudes,theabsenceofacoherentviewabout the place of logic in the study of mind and language was certainly a contributing factor. By the seventeenth and eighteenth century, the detailed study of a very restricted form of inference (the syllogism) based on a narrow selection of sentence types (categoricals) sim- ply could not serve as the basis for incorporating
formal methods into the study of language and reasoning in a wider context.
In this connection something should be said about the famous Port Royal Logic of Pierre Nicole and Antoine Arnauld. This work, whose title was La Logique ou I 'Art de Penser, was a new style of textbook in logic published in the seventeenth century, and it had a considerable influence on logic for more than a century. Essentially what it did was to combine the formal logic of the syllogism with the then modern conception of reasoning which had its origins in the epistemological concerns of Descartes and his followers. Logic was understood as the art of directing thought so as to yield knowledge of the world, and the most novel part of the book contains interesting discussions of method and clear thinking. What should be stressed in the present context is how strange it now appears that the limited syllogistic should con- tinue to be the core of formal logical methods in a work whose subject matter is inquiry in general. The partnership between formal methods of logic, a gen- eral conception of reasoning, and a philosophy of language appropriate to these had yet to be made. Certain of the basic ingredients of philosophy of logic and language were around, but at this point, the for- mal methods available were both inadequate, and yet not fully seen to be so.
6. Logic and Mathematics
The period beginning with Leibniz (1646-1716) and leading to Frege's work at the end of the nineteenth century sees the development of formalisms of con- siderably more sophistication than the syllogistic. Moreover, since these formalisms by and large developed through various attempts to bring logic and mathematics together in certain ways, it is not unreasonable to think of the theme of the period as the 'mathematization' of logic.
6.1 Leibniz
G. W. Leibniz is an exceptional figure in the history of logic, philosophy, and mathematics. In each of these areas he produced work, often sketchy or incom- plete, which was both original and fundamental. Indeed, in some ways, his ideas suffered from the fact that there was little or no context into which they could be fitted. Aside from being one of the 'standard' philosophers in the present syllabus, he was (with Newton) an originator of the differential calculus, and a pioneer in work on probability theory. From the point of view of this survey, his most interesting work is that on the idea of a so-called 'universal character.'
Along with many writers at that time, Leibniz thought that language somehow obscured or ham- pered clear thinking about the world. The general opinion, which Leibniz shared, was that it should be
Logic: Historical Survey
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