P1: Mathematics is the substrate upon which all natural phenomena occur and necessarily governs phenomena in the physical world.
P2: One can experience something that is not mathematically commensurate.
C: Therefore, such an experience can be real.

Rationale: I know that according to the Sapir-Wharf Hypothesis, one can only think in the words they know, but perhaps the hypothesis is likened to phenomenology that is experienced to the resolution of the mathematics one understands. And in that case, the natural world will reveal more of itself when one understands more mathematics the same way, according to the Hypothesis, one can formulate mathematically more specific ideas and phrases when they have a greater vocabulary in multiple languages.

Does the following argument about the ontological nature related to math exhibit specific fallacies? Which philosophers and philosophical disciplines are related to evaluating such an argument?

[edit] thanks for all the help on formulating my question!

  • 3
    The Sapir-Whorf hypothesis in global form has been abandoned by most linguists long time ago, and how is "mathematics the substrate upon which all natural phenomena occur"? On most conceptions it is a causally inert abstraction upon which nothing real can occur. Do you have something like Tegmark's mathematical universe in mind?
    – Conifold
    Oct 26, 2020 at 17:52
  • I was beginning with the assumption of Tegmark's. Consider it a rationalization of the hyper platonistic position. Oct 26, 2020 at 21:06
  • your a priori statement - 'mathematics is the substrate upon which all natural phenomena occur' - is not true. Oct 27, 2020 at 3:13
  • @Conifold- This 'causally inert abstraction' is credited with 'proving' all of the hypotheses in advanced physics which cannot be observed or measured. How does that square up?
    – user37981
    Oct 27, 2020 at 3:55
  • @CharlesMSaunders As I read it, 'causally inert abstraction' implies a metaphysical presupposition that rejects downward causation.
    – J D
    Oct 27, 2020 at 17:32

1 Answer 1


"If one experiences something that is not mathematically commensurate, is it not a real experience?"

No, number theory can not express or explain everything.

From Wikipedia: Examples of undecidable statements

The combined work of Gödel and Paul Cohen has given two concrete examples of undecidable statements (in the first sense of the term): The continuum hypothesis can neither be proved nor refuted in ZFC (the standard axiomatization of set theory), and the axiom of choice can neither be proved nor refuted in ZF (which is all the ZFC axioms except the axiom of choice).
These results do not require the incompleteness theorem. Gödel proved in 1940 that neither of these statements could be disproved in ZF or ZFC set theory.
In the 1960s, Cohen proved that neither is provable from ZF, and the continuum hypothesis cannot be proven from ZFC.

The above answers your question better than Whorf's explanation that the number of Inuit words for "snow" confers a greater understanding of the substance than that of the standard average European.

A Theory of Everything has yet to be derived.

Things can be real, or not, without the ability to be explained or proven.

If our existence, or love, can not be explained mathematically is it not real.

  • 1
    Your argument only shows axiomatic mathematical systems can not always answer decide the truth-value of every statement about the mathematical objects they describe, it doesn't necessarily disprove the platonist view that such statements are definitely true or false (statements about arithmetic might be decidable by an oracle machine which can decide non-computable questions, for example). And it certainly has no bearing on whether or not experiences like love are producible by mathematical algorithms.
    – Hypnosifl
    Oct 27, 2020 at 3:55
  • @Hypnosifl, you might want to reread that; Sets are one of the best ways to approach this.
    – Rob
    Oct 27, 2020 at 9:38
  • "number theory can not express or explain everything." Explain... maybe, but express: a lot of "facts" about numbers. Oct 27, 2020 at 9:56
  • 1
    Approach what, exactly? Set theory doesn't tell you there are areas of reality that are non-mathematical, and a mathematical platonist about set theory can still believe there is a definite mathematical truth about the continuum hypothesis. Alternately, some mathematical platonists may believe that some areas of mathematics like arithmetic have objective platonic reality but others like the math of higher transfinite numbers do not (and the Lowenheim-Skolem theorem shows that any formal system which can be interpreted in terms of transfinite sets also has a countable interp.)
    – Hypnosifl
    Oct 27, 2020 at 15:09

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