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IUSS Philosophy Seminars - eMath Project


23 giu

11:00 AM

June 23rd, 2020, 11-13

IUSS Philosophy Seminars
eMath Project
Epistemology of Mathematics and Logic


Suki Finn (Royal Holloway University of London)

In this talk I will argue that Modus Ponens and Universal Instantiation govern the most fundamental patterns of inference that they underwrite the application of any logical rule, including themselves. As such, they both govern their own application. This is because logical rules of inference are, very generally speaking, universals and conditionals in their structure. To be of a universal structure is to apply in all cases of a certain kind. To be conditional in structure is to say what to do if in a case of a certain kind. Logical rules of inference take us from premises to a conclusion via a conditional, and are universal so that they apply in all cases when the antecedent of that conditional is satisfied. The antecedent of the conditional will name a situation when the rule is applicable, and the consequent of the conditional will name what one should do when faced with an instance of that situation. But if all logical rules of inference are universal and conditional in their structure, then those rules that govern or describe how to deal with universal or conditional structures (namely Universal Instantiation and Modus Ponens respectively) will face problems by being of the structure that they themselves govern. This talk will explore some of those problems.


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Organized by:
NEtS Center
PhD Program in Cognitive Neuroscience and Philosophy of Mind