First-Order Logic and Classical Theism : Toward Logical Reorientation
Abstract: This inquiry seeks an answer to the question whether classical theistic doctrines about the nature of God are amenable to formal analysis in terms of standard first-order logic. It is argued that due to the conceptual impact of classical theism’s doctrine of divine simplicity there is a good reason for answering this question in the negative. Part I of the inquiry offers a historico-philosophical survey of various views on the relation between theistic doctrines and formal logic found in the work of twentieth-century philosophers and logicians such as Bertrand Russell, W.V.O. Quine and Jόzef Bocheński, along with a philosophical interpretation of key logical notions such as inference, truth-bearer and logical validity. Part II offers an answer to the question whether classical theistic doctrines about the nature of God are amenable to first-order analysis. Two main claims are argued for in answer to this question, namely: that these doctrines fulfil defensible criteria for amenability to propositional first-order analysis; and that these doctrines fail to fulfil defensible criteria for amenability to quantificational first-order analysis due to the conceptual impact of the doctrine of divine simplicity, and hence fail to be amenable to first-order analysis in the full sense. Various objections to both claims are examined, but are deemed unsuccessful. In Part III various responses to the above claims are discussed. It is argued that some well-known alternatives to first-order logic are likewise inadequate for the formal analysis of the relevant doctrines, but that formal logics adequate for this purpose might be obtainable e.g. by supplying first-order logic with a non-standard semantics, or by revising standard first-order logic so as to have parts that apply to non-theistic subject-matter and parts that apply to theistic subject-matter, in line with the standpoint of logical pluralism.
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