SFOLStandard First Order Logic
SFOLStrike Fighter On Line (US Navy)
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What a SFOL should provide in the case of an individual constant such as 's' is a tripartite structure as described before.
So far we have criticized the practice of presenting SFOL by means of TS on the grounds that it is besieged by difficulties.
Rather, our target is the practice of teaching SFOL by means of NL.
Moreover, since the purpose is to explain SFOL, the advocate assumes that the referent of the expression 'x has the property of being human', given to it by its use in natural language, is a set in the mathematical sense.
There is no escape to the conclusion that the advocate of TS is projecting the properties of the mathematical tools underwriting SFOL onto thereferents of natural language expressions, and that he does not provide any justification to do so (and the burden of proof certainly falls on him).
The belief that NL has properties (i)-(iv) is an implicit foundational belief in the practice of using a TS in the explanation of SFOL.
There is an aspect to this hypothesis that is even more problematic, namely, that it confuses two different kinds of study: the study of SFOL and that of SNL.
Now, even if SNL and SFOL were structurally identical--and thus the hypothesis were true-, the discovery of such a truth requires two different studies: the empirical study of natural language and the mathematical study of Model Theory.