The question that I pose is whether 1+1=2 because it makes sense, or whether our minds make sense because truths like 1+1=2 exist independently of all experience.

If it is the latter, then 1+1=2 stands in for a fundamental set of rules and relations for which consciousness serves to glorify, either accidentally or inevitably.

If it is the former, then that which ‘makes sense’ stands in for a perceptual acquaintance with qualities of undeniable coherence.

It is significant to notice that when we get down to elementary statements such as 1+1=2, we have slipped beneath the realm of logic and numbers without even realizing it. To say that one can be ‘added’ to one and that they are now equal to a group of two is entirely a matter of naming perceptions. There is no real arithmetic going on, we are saying only that when something is to be considered individually we call its individuality “one”, and when we want to consider the presence of one as being adjacent to one other, we call that adjacency “two”. The underlying properties which are being named are conceptually abstracted perceptions. There is no actual “information” named one or two, rather there is a language through which we generalize stereotypical features of our perception – particularly visual and tangible perception. Trying to apply mathematical models to perceptions like flavors and odors is less ‘informative’. They don’t really add up to be enumerable flavors as much as they involve us in a sensory experience in which flavors are both merged and independent.

Lemon + Lime does not necessarily equal two flavors, but can be just as easily thought of as Lemon-lime. Either lemon or lime could be broken down each into multiple flavors including sweet, sour, and citrus, but there remains an idiosyncratic note as well which identifies lemon as one flavor and lime as a different single flavor. Even if we isolate the compounds associated with these flavors, or synthesize artificial compounds with entirely different molecular profiles, there is a huge variation in our perception of any ‘one’ flavor. Lime jelly bean flavor is not the same as key lime pie flavor, yet in another sense, the similarity is self-evident, especially once we give it the name of ‘lime’. It is not a name that is arrived at through a computation or reasoning. Like ‘one’ and ‘equals’, lime is a subjective experience which we can point to but cannot define through a mathematical function.

Does it make more sense, given that the axioms of mathematics as well as physics are defined by subjective expectations (about objective conditions), that we should rule out the idea that all axioms are intrinsically perceptual? We might also ask, if mathematics and information were truly axiomatic, would it be possible to make errors? If our entire conscious experience were made of trillions of precise mathematical reflexes, why is the subject of mathematics even necessary to teach? Wouldn’t it make more sense that we would be able to perform comparatively simple algebras more easily than we can identify whether the flavor of a lime is natural or artificial?

  1. April 15, 2014 at 2:34 pm

    Very interesting matter indeed!
    You may want to read into Ferdinand de Saussure’s Course in General Linguistics. Perhaps not the first thing you would consider in this context, but it is actually very much related in a way — I think you may like it.

    • April 15, 2014 at 3:05 pm

      Thanks. I think you’re right…my influences all seem to come back to semiotics.

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