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Suppose if we only regarded the concrete as real, and that abstraction is only a process of using the concrete to represent other concrete things. For example, a number is not a real thing, but it is the concrete object (mark, pixel, etc) that we use as a symbol that map to some configuration of other concrete objects, so that we can manipulate the symbols themselves to model and reason about the concrete.

Would this cause any contradictions with some first principles or common sense, or limit our ability to express or reason about the world?

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    The denial of abstract objects is called nominalism. Detailing its problems would take too much space to do here, please see online encyclopedias, e.g. IEP. – Conifold Jun 1 '19 at 18:08
  • @Conifold I believe OP is presenting a particular variation of Nominalism, therefore it is not necessarily broad. They are just inquiring if the said variation of Nominalism is problematic or not. – Bertrand Wittgenstein's Ghost Jun 2 '19 at 9:44
  • @BertrandWittgenstein'sGhost I do not see it, "abstraction is only a process of using the concrete to represent other concrete things" and "manipulate the symbols themselves to model and reason about the concrete" are as generic a description of nomina as it gets. – Conifold Jun 2 '19 at 9:51
  • @Conifold I do not necessarily disagree with you on that. However, I am disagreeing that the question is (necessarily) broad. I think tailoring a general critique of nominalism such that it deals with OP's description of it will be a sufficient enough answer to the question. Regards – Bertrand Wittgenstein's Ghost Jun 2 '19 at 9:59
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Suppose it is true that there are no abstract objects, and therefore every abstraction is just a nominal relational utility. That is, it is created solely to relate two distinct particular entity.

How exactly do you think it explains (-1)×(-1)=1? How many particular negatives do you have walking around the block? Well, can you pinpoint a negative number of negative entities?

After you find an answer for those two, then tell me how exactly it relates to a single potato.

Regards

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