Many Logics?

Dr. J. Oliver Buswell's book review of Cornelius Van Til's book,  Common Grace, makes a distinction that I myself made in my last post on Greg Bahnsen's contention that there are many "logics":

Professor Van Til in the book here reviewed does not make the distinction (a distinction which seems to me a mere quibble) between the “system” of unbelieving thought, and unbelieving thought not designated by the word “system”. If it is insisted, contrary to all common usage, that the word “system” can be used only to designate perfectly coherent integration of thought, without the slightest contradiction in it, it would still remain true that the atheistic proposition, “The material universe is uncreated”, would have certain intelligible elements in common with the contradictory Christian proposition, “The material universe is created”. No two propositions could be contradictory if they did not have certain terms and meanings in common. As a matter of fact, however, whenever we wish to indicate that a “system” of thought is perfectly consistent with itself, as the “system of doctrine” taught in the Scripture is, we are obliged to add adjectival elements. The Cartesian philosophy is a remarkable “system” but is not perfectly consistent. The “system of doctrine” taught in the infallible Word of God is perfectly consistent, not because it may be designated by the word “system” but because the Word of God itself is infallible.

From:  Endnote #1.  J. Oliver Buswell,  "The Fountainhead of Presuppositionalism."

See:  Dr. Greg Bahnsen's Rejection of Logic.