Math Is Not A Language

Mathematics reduces down to logic, not the other way around, yet people in general still continually distinguish the two while treating mathematics as more fundamental or knowable, when it is logical axioms and logical truths as a whole that are more fundamental and still more easily accessible than numeric truths.  Rarely does a person make just one philosophical error with regard to an issue.  Where there is one delusion, contradiction, or assumption, others are typically embraced as well.  Because math so commonly gets erroneously thought of as separate from logic, it is in a sense natural for non-rationalists to leap into other falsities like the idea that mathematics is in any way a "language."  This wholly contradicts the actual nature of numerical truths.

The symbols and words used to communicate or, in some cases, simplify understanding of them are part of languages, yes.  Just as the experience of pain is not the word pain and a logical truth about friendship is not the words that could be used to express it, mathematical concepts and truths are not language.  The ideas words express transcend words and written numeric symbols alike.  The former can come to one's awareness by pure reason or through thoughts promoted by experiences and guided by reason, but one must contrive or hear about words to assign to various concepts.  Language is always a mere reaction to concepts that people have already thought about or that they could have already thought about beforehand.

The most abstract truths about the laws of logic can be understood perfectly without any words to prompt recognition or aid in it, but it would be extremely difficult to conceive of massive numbers like 5,000,000 or particularly random numbers like 709,836,912 without relying on a numeric symbol and imagining it.  This still only means that languages and the accompanying numeric symbols are used to facilitate thought or communication about mathematical facts and ideas.  Numbers and the logical truths that both extend beyond numbers and underpin all of mathematics are not a language, or a social construct of any other kind.  Epistemologically, one must understand them to even assign words to them.  Metaphysically, their nature goes far beyond the momentary epistemological convenience many people regard them as.

They are true whether or not any language exists to convey them--or whether or not any conscious beings exist to grasp them, including God, and whether or not any natural world exists to be confined by the necessary truths of mathematics.  The logical axioms and deductive chains that ground mathematical truths must be used to even doubt or reject them, so they cannot be false no matter what else is.  One of the more precise and grand ramifications of this is that logical truths, including mathematical truths, are not just true of other things like consciousness or matter as long as the latter things exist.  They are the only things, or aspects of the only thing (the collective laws of logic), that could not not exist.  They are a metaphysical thing that does not depend on the external world or on any mind, including God's, and they would continue to exist even if the natural world and God ceased to exist.  This is not true of any language, and thus this fact serves as another proof that mathematics could not possibly be a language.

The kind of person who mistakes mathematical truths for a language might also mistake music for language--but pure language communicates precise ideas through written or verbal words.  Even in terms of how the word "language," is commonly used, not every vocal sound, like grunts, is part of a language, and not everything that could be used to convey (or try to convey) a message from one person to another is linguistic.  Objects left out to communicate without words or physical motions, but that do not spell words, are not a language.  Physical gestures meant to communicate precise meanings are not language in the purest sense, although sign language is called sign language.  Even if these alternate attempts at communication were language, the ideas being communicated are not, and so numbers and logical truths about them are not a language by default.