A system of predicate logic with transatomic units.
Richard Butrick · Notre Dame Journal of Formal Logic · 1987
Preliminary remarksThe original idea of introducing trans-atomic units into systems of formal logic was presented at the World Congress of Philosophy in 1983.Formal development of this concept at the truth-functional level was subsequently investigated in this journal [1].This paper extends the concept of transatomic (TA) units to Predicate Logic (PL). Motivation for investigating TA unitsThe concept of TA units allows the introduction of special connectives over and above the 16 limitation of standard two-valued logic without leaving the confines of a two-valued system.The one particular connective introduced in this paper has interesting possibilities as regards its use as a causal connective in the formulation of lawlike generalizations.Briefly, the difficulties with the Philonian (material) conditional in the formulation of lawlike generalizations concern its properties as regards confirmation and support:(1) (x)Gx (and consequently by the pair ((x)Gx,is supported by (1) Ga (and consequently by the pair (-Fa, Ga) (2) -Fa.There seems to be no escape from these difficulties.Even restricting evidence or support to instances of the corresponding conjunction, i.e., Fa & Ga, Fb & Gb, etc., is of no avail.Since (x) (Fx -• Gx) is logically equivalent to (x) (~Gx -* -Fx) the latter would be supported by -Fa & -Ga and hence the former also.The partial connective, *-c\ subsequently introduced avoids the