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Logic will here be defined as formal semiotic. A definition of asign will be given which no more refers to human thought than does thedefinition of a line as the place which a particle occupies, part bypart, during a lapse of time. Namely, a sign is something, A, whichbrings something, B, its interpretant sign determined or created byit, into the same sort of correspondence with something, C, itsobject, as that in which itself stands to C. It is from thisdefinition, together with a definition of "formal", that I deducemathematically the principles of logic. I also make a historicalreview of all the definitions and conceptions of logic and show notmerely that my definition is no novelty, but that my non-psychologicalconception of logic has virtually been quite generally held, thoughnot generally recognized.
By an application of categoric, I show that the primary divisionof logic should be into stechiology, critic, and methodeutic. Thereis a cross-division into the doctrines of terms, propositions, andarguments, to which three kinds of signs, however, stechiology,critic, and methodeutic are quite differently related. The varioushistorical divisions of logic are considered.
I shall here show that no less than thirteen different methodsof establishing logical truth are in current use today, and mostlywithout any principle of choice and in a deplorably uncritical manner.
I shall show that the majority of these methods are quiteinadmissible, and that of the remainder all but one should berestricted to one department of logic. The one universally validmethod is that of mathematical demonstration; and this is the only onewhich is commonly avoided by logicians as fallacious. I shall show inthe clearest manner that this notion is due to a confusion of thought,which I shall endeavor to trace through all its metamorphoses. I hopeto give this its quietus.
The methods of discovering logical truth can naturally not benumerous when discovery is pretty nearly at a standstill. I explainmy own method.
