Considering that molecular biology depends on things like electron orbits and the Pauli exclusion principle for molecular bonds at a very fundamental level, and these things are fundamentally mathematical, there can be no truth that includes molecular biology that excludes mathematics. On Mon, Apr 2, 2018 at 12:27 PM, Brent Meeker <meekerdb@verizon.net> wrote:
In my view they instantiate quite different meanings of "truth" and "real".
In mathematics and logic "2+2=4 is true." means something like "Given the Peano axioms and rules of inference '2+2=4' follows." "True" is an attribute that is conserved by the rules of inference; so if the axioms are true the theorems are true. But "true" is just a marker like "t" in a programming language.
In science "true" is almost never used. Theories are "accepted" when they entail the observations and nothing to the contrary. Then they are provisionally thought to correspond to facts. This is always hypothetical and provisional because one can never be sure of the facts and because other theories might entail the same observations.
So my personal view is that mathematics exists in a different domain. The declarative part of all possible language = Platonia. Observations, perceptions, exist and from them we formulate theories of physical reality, which are (so far) always provisoinal and incomplete.
Brent As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. -- Albert Einstein
On 4/2/2018 9:42 AM, Dan Asimov wrote:
If this common discussion subject among mathematicians has come up in math-fun previously, it must have been a while ago:
Is mathematical truth real? I was reminded of this question when I happened to sit next to an esteemed molecular biologist who has strong opinions on the matter: He thinks math is "all in the brain" of humans who think about it. I could not convince him that math has any kind of independent existence — though I certainly believe it myself.
What do other think about this? I would say that mathematical truth is *at least* as real of a thing as physical truth.
—Dan
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