Retransmittability and Empirical Propositions

The standard dictionary definition of a formally valid argument in classical, bivalent, deductive logic proceeds as follows: An argument is valid if it is impossible for all its premises to be true and its conclusion to be false. A valid argument, unlike a sound one, can have false premises or it can have a mixture of true and false premises, but if all of its premises are true, then its conclusion must be true as well. This can also be expressed by saying that truth is transmitted from all of the premises of a valid argument to its conclusion and that falsity is retransmitted from the conclusion of a valid argument to at least one of its premises. The terminology of transmittability and retransmittability has its origins in the work of Popper and Lakatos. That truth is transmitted and that falsity is retransmitted are both mentioned in (Popper, 1974, 64), though Popper sees these as being properties of valid rules of inference rather than of arguments. Lakatos, in the course of developing his mathematical methodology of proofs and refutations, formulates a principle of the retransmission of falsity which states ‘that global counterexamples be also local: falsehood should be retransmitted from the naive conjecture to the lemmas, from the consequent of the theorem to its antecedent’ (Lakatos, 1976, 47). Two interesting questions to ask of valid arguments are whether anything other than truth is transmittable and whether anything other than falsity is retransmittable. Concerning transmittability, some unusual contenders have been proposed. For example, in (Gjertsen, 1989, 127) it is suggested that if the premises of a valid argument are ambiguous, obscure, uncertain or bland, then so must be its conclusion! In this paper I am interested in the questions whether the property of being an empirical proposition is transmittable and, especially, whether this property is retransmittable. I show that a valid deductive argument with consistent premises, all of which are empirical, can have a non-empirical conclusion which is not logically true. I also show that it is possible for a valid deductive argument with consistent premises to have an empirical conclusion and yet to have no empirical premises. (Note that in this paper I do not, as some philosophers do, distinguish between propositions and statements. These terms are used interchangeably.) My interest in problems relating to transmittability and retransmittability arose out of my interest in what is sometimes known as anti-justificationism. This term applies to a family of approaches to philosophical problems inspired by the work of