Logic and Systems of Logic
One can construct nearly for every field of study a system of logic which is specific to this field. Many of these systems are extensions of first-order logic with identity (also known as classical logic). To list some of them, we have modal, epistemic, deontic, and tense logic. All of these are extensions of classical logic. But there are other systems that are not extensions of classical logic, like intutionist logic and quantum logic as some of the laws of classical logic do not hold in these systems. The applications of these systems in various branches of philosophy as well as science and mathematics are well known.
Alan Berger extensively discusses an important distinction Kripke had drawn in a graduate seminar he gave at Princeton in 1974. The distinction in a nutshell is between systems of logic, like the ones we have mentioned above, and logic itself. He raised the issue of whether we adopt a logic and likewise adopt an alternative logic. His conclusion is that the notion of “adopting a logic” is incoherent. His argument, which relies on an infinite regress, can be construed as follows. In order to investigate, understand or construct a new system of logic one would need an antecedent system of logic and so ad infinitum. Therefore logic itself cannot be one of the systems of logic. It is rather something that is presupposed by all presently constructed systems of logic or those that would be constructed in the future. Note that nothing else can be said for logic itself since once you attempt to explain what it is you already start constructing a new system of logic.
Perhaps the only way to stop the regress is to try to elucidate what logic is in non-logical terms. While recently reading Robert Hanna’s book Rationality and Logic published in 2006, I came across with an interesting division he made between “a single universal protologic” and “all classical and non-classical logical systems” we have mentioned above. He further claims that all logical systems are constructed by means of the protologic. Notice how this division is strikingly similar to Kripke’s contrast between logic and systems of logic.
In any case, Kripke touched upon an important issue about what logic is. I think it would be essential to have new studies on this subject.
Prof. Dr. Teo Grünberg
14 January 2020
Biography of Prof. Dr. Teo Grünberg
Teo Grünberg was born in Istanbul in 1927. He received his Ph.D. in Philosophy in 1964, Istanbul University. He became Assistant Professor in 1966, Associate Professor in 1970, and Professor in 1979 in the Middle East Technical University.
Teo Grünberg worked as faculty during 1962-66 in the Philosophy Department, Istanbul University, and during 1966-82 in the Humanities Department, Middle East Technical University as Chairman of which he was the founder. He retired in 1994 and worked in the same department as adjunct faculty during 1994-2002. He was also an adjunct faculty during 1968-79 in Philosophy Department, Ankara University, and during 1989-90 in the School of Engineering, Bilkent University.
Teo Grünberg in collaboration with his colleague Hüseyin Batuhan initiated the modern logic reform in high school teaching undertaken by the Ministry of Education, starting from 1966. He lectured during 1968-76 in the summer courses in modern logic for high school teachers organized by the Ministry. He initiated also the teaching of modern logic in various universities and contributed to the training of large number of faculties in this field.
He is the author of more than fifteen books and 35 articles, some of which published in international journals, in the fields of modern logic and analytic philosophy.