Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'Toward a Philosophy of History' and 'The Boundary Stones of Thought'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

4 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
18815 Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]
     Full Idea: On the conception of logic recommended here, logical laws are higher-order laws that can be applied to expand the range of any deductive principles.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3)
     A reaction: You need the concept of a 'deductive principle' to get this going, but I take it that might be directly known, rather than derived from a law.
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18804 The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
     Full Idea: I think it is a strategic mistake to rest the case for classical logic on the Principle of Bivalence: the soundness of the classical logic rules is far more compelling than the truth of Bivalence.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
     A reaction: The 'rules' to which he is referring are those of 'natural deduction', which make very few assumptions, and are intended to be intuitively appealing.
18805 Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
     Full Idea: There is not the slightest prospect of proving that the rules of classical logic are sound. ….All that the defender of classical logic can do is scrutinize particular attacks and try to repel them.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
     A reaction: This is the agenda for Rumfitt's book.
18827 If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
     Full Idea: If we specify the senses of the connectives by way of the standard truth-tables, then we must justify classical logic only by appeal to the Principle of Bivalence.
     From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7)
     A reaction: Rumfitt proposes to avoid the truth-tables, and hence not to rely on Bivalence for his support of classical logic. He accepts that Bivalence is doubtful, citing the undecidability of the Continuum Hypothesis as a problem instance.