User talk:JCGonzales/logic

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See Wikipedia:Stub types for deletion/Log/2007/July regarding an archived discussion on a closed recommendation to delete or rename this stub category, resulting in a decision to keep this stub and also have a general logic stub.

A member of the WikiProject Logic has raised significant points on the use of terminology by philisophers and non-mathematical logicians compared the usage of the same terms by mathematical logicians. In Gregbard's analysis, the sentence arose: "The notion expressed more than once here is that 'mathematical logic' isn't logic."

• I will assume ordinarily reasonable people will generally agree that the above statement implies "logic isn't mathematical logic." In some cases it does have this meaning, but in some cases it does not. Ackowledging this point should be no problem for most if not all philosophical and mathematical logicians.

• I will further assume that there are two points of view here; a mathematical point of view that uses the terms "logic" and "mathematical logic" as equivalent out of our implicit desire to represent concepts as the shortest written form possible to still maintain universal recognition among mathematicians, and a separate point of view that uses "logic" as equivalent to the phrase "all instances of forms of logic" or "that which is always and generally applicable as logic."

• By the precise term "point of view", I refer to that which is acceptable in given socially recognized and socially valid spheres and NOT in any way to be construed in a class that would be a violation of WP:POV; otherwise there would exist a glaring contradiction of the concept that the Wikipedia was involved of the censorship of ideas at such a fundamental level as to render the Wikipedia worthless for open discussion. As it is not our purpose to render the Wikipedia as worthless, the view of the Wikipedia must allow for the existence of those two legitimate points of view as implicit in the wiki structure.

• The points of view appear to be separate by their separate graphical representations as sets. Mathematics has a restrictive view on what constitutes mathematical logic, and with apologies to everyone else, when a mathematician uses the term "logic", he or she is referring to "that which is mathematical logic", and because mathematicians speak in those terms, we should be forgiven for stating anything like "philosophical logic is not logical" when we really mean that "philosophical logic permits arguments to be constructed in ways that have been deprecated in mathemataical logic" as a statement of fact between mathematicians. These mathematicians nearly all accept this statement of fact as true and therefore openly communicate to and with other mathematicians in this way. This is bith sociologically real and valid in its reality. Computer science can be and is mathematically seen as an extension of mathematical logic because first-order formal logics can be used to conveniently express concepts of computability, complexity, and other measures of algorithmic behavior and performance, and so here we are on the Internet. For computer science types who approach that science from a mathematical standpoint, philosophical logic is more art than science in a fuzzy logic sort of way, and it is algorithmically difficult and many times impossible to encode philosophically valid arguments into fragments of functional programs. This statement means that mathematicians either know, are aware of, or are capable of discoverying in the literature, proofs of that difficulty or impossibility where the proofs have mathematical rigor and precision in logic. A value judgement that some things just are not worth even contemplating arises when the impossibility of some entire class of concepts is a fact known with mathematical certainty.

None of this detracts from the philosophical validity of arguments allowed in philosophical logic, which is sociologically valid for many more people than there are of mathematical logicians, but hopefully it will explain the entrenchment of sides in the above-linked discussion in a place, the Wikipedia, where more of those mathematical logicians might tend to congregate and edit. (This is WP:OR and should be deleted as such except for the facts that (1) it is documented in "stable" do-not-edit form available by hypertext transfer protocol (HTTP) at the Wikipedia, at the above link and (2) it is true. If this is deleted, it is already available elsewhere at academia.wikia.com in the Wiki Journal. The necessity for deletion points to a Wikipedia policy paradox wherein it must be true that WP:FAIL for a living system with inter-communicating (Internet) components.)