Math but not Spirits (4)

Say you spend the first day of algebra learning about the nested hierarchies of numbers: naturals, wholes, integers, rationals, etc. and then you wonder if any other sorts of numbers exist. Later, when you find out about the complex numbers (or even the h and j numbers my students told me about today) you find out that the answer is yes.

In some other context (like a philosophy class) you’re talking about substances or the status of abstractions and someone asks whether numbers exist. No one is quite sure what to think, but since everyone agrees that a number isn’t something you could display in a zoo or spot in a telescope we guess that the answer is no.

And so we have two senses of exists that lead to totally different answers to the question of whether numbers exist. Exists (1) seems to belong to anything that can be an object of discourse, i.e. something with discoverable properties, unlike a the properties of fictional beings that can have no existence beyond what is actually given on the page. As BV points out somewhere, real objects differ objects like Hamlet because there is no fact of the matter whether Hamlet is, say, left-handed or green-eyed apart from what is already present in the text. Exists (2) is anything given by sense or the instruments of sense. At the beginning of De ente STA called existence (1) the truth of propositions while existence (2) is something in one of the ten categories.

The objects of metaphysics exist (1) and don’t exist (2).  No one is looking for God in a telescope or for the soul on an fMRI. These sorts of objects have a long history of being described as formal and no one seeks forms of any sort like this. But while no form depends on matter to be known, it some do depend on matter to exist. Not all forms can be of this kind.



  1. Johan Swart said,

    January 21, 2017 at 1:21 am

    //it some do depend on matter to exist.//

    Hi James, was this a typo, did you mean to say, it sometimes depends on matter or some forms depend on matter?

    Do you see a close parallel here with the concept of information?

    “Information philosophy agrees that “information is neither matter nor energy,” but it needs matter for its embodiment and energy for its communication.”

    • January 21, 2017 at 9:37 am

      That was a typo, but what is said does apply to information and energy, even if they don’t have the same dependence on the physical. STA uses that description to define mathematical things too, i.e. they are what he calls “formal abstraction” which results in something more intelligible than the form as it exists in sense.

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