The phrase "a non logical" is not correct in standard English; it should be "illogical" or "non-logical." You can use it when describing something that does not follow logical reasoning or is not based on sound reasoning.
Example: "His argument was a non logical conclusion that failed to consider the evidence presented."
Alternatives: "irrational" or "illogical reasoning".
Warmbrod and Tharp even explore the possibility of taking truth-functional logic to be the whole of logic and viewing quantification theory as a non-logical theory (Warmbrod 1999, 525; Tharp 1975, 18), though both reject this idea on pragmatic grounds.
The tenability of logicism been disputed on multiple grounds, the most prominent of which has been that the notion of membership fundamental to the theory of sets is not a logical notion but rather a symbol that must be added to first-order logic to formalize what is properly understood as a non-logical theory.
The top scorer in the Chilean league with Colo-Colo last season, he moved to the United Arab Emirates for £2.5m in the summer (I'm surprised there weren't other takers), a move that I can only assume was a non-logical stepping stone on the way to European football.
The symbol "=", for identity, is not a non-logical symbol.
Begging the question fits under the heading of a non-logical, material fallacy in which a premise has been unduly assumed, and ignoratio elenchi is a non-logical, material fallacy in which an irrelevant conclusion has been reached.
This is not a fully realistic requirement, since actual agents are known to have beliefs of a non-logical nature that nothing can bring them to give up.
The warrant for this claim can only be the language relativity of identity when treated as a non-logical notion (see §1).
Intuition can be a process of arriving at an idea with a non-logical feeling for the significance of the idea and is a personal capability.
That this is what Geach has in mind is clear from some approving remarks he makes in his 1973 article about Quine's (1970) proposal to treat identity as a non-logical notion.
These results are again in agreement with actual usage, for example in the model theory of first-order set theory, where the membership predicate is taken as a non-logical constant.
As before, \(L^\) is the expanded language that results when a definition \(\mathcal{D}\) of a non-logical constant \(X\) is added to \(L\); hence, \(X\) may be a name, a predicate, or a function-symbol.
