Friday, December 11, 2020

Reducing "Symbolic Logic" To Pure Logic

One is unlikely to encounter references to "symbolic logic" outside of academia, but rationalists can benefit from familiarity with the symbols that can be substituted for written words when making an argument.  Depending on what is being communicated, symbolic logic is nothing more than an alternate way of writing truths like "If X, then Y; X is true; therefore Y is true."  It may have the appearance of something far more esoteric, but that is only the symbols themselves, not the logical truths or conceptual analyses that the symbols are meant to convey.  The former is contrived and must be learned from others if one does not devise a set of symbols oneself; the latter is fixed and immediately accessible to anyone.

Language can be used to communicate truths about logic, and symbols of many kinds could be used as a language even without words to accompany them.  Symbolic logic can therefore communicate logical facts, even if the name misleadingly implies that logic is a language of sorts, when it is actually a set of necessary truths that one must already grasp to even construct or understand a language to begin with.  Rather, language, of the symbolic kind or more traditional kind (yes, one could think of letters as "symbols," but they are distinct from those used in symbolic logic), precedes all things.

There is nothing special about symbolic logic, as if it requires a higher level of intelligence to wield than "ordinary" logic.  Everyone can reason out logical truths with intentionality, even though some logical truths might take more effort to arrive at.  All one needs to do is reflect on what necessarily does and does not follow from a given idea.  No one needs a system of symbols to know that some things follow from others, that to deny reason is to embrace a self-defeating impossibility, or that consciousness is the ability to perceive, to list only a small handful of examples.

Symbols and words alike are arbitrary, while logic is not.  Any person with the desire to do so can directly access at least the most foundational necessary truths, or axioms--those few logical facts which plunge one into utter contradiction upon denying the fact that they could not have been any other way--and work their way to the web of more complex logical truths with effort.  Contriving a language of symbols is wholly unnecessary to understand reason and the concepts reason illuminates.  There is no difficulty in understanding symbols or lack of awareness of symbols that can separate someone from understanding the laws of logic.

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