We would have “true-and-I-can-prove-it” and “true-and-I-can’t-prove-it.” I’d be surprised if given those two categories there would be many people who wouldn’t elevate the testable statements above the untestable one in “truthiness.”
Where would mathematical statements fit in this classification of yours? They can be proven, but many of them can’t tested and even for the ones that can be tested the proof is generally considered better evidence than the test.
In fact, you are implicitly relying on a large untested (and mostly untestable) framework to describe the relationship between whatever sense input constitutes the result of one of your tests, and the proposition being tested.
There’s another category, necessary truths. The deductive inferences from premises are not susceptible to disproof.
Thus, the categories for this theory of truthful statements are: necessary truths, empirical truths (“i-can-prove-it”), and “truth-and-i-can’t-prove-it.”
Generally, this categorization scheme will put most contentious moral assertions into the third category.
This may be a situation where the modern world’s resources start to break down the formerly strong separation between mind and world.
These days, most if not all of the rules of math can be coded into a computer, and new propositions tested or evaluated by those systems. Once I’ve implemented floating point math, I can SHOW STATISTICALLY the commutative law, the associative law, that 2+2 never equals 5, that numbers have additive and multiplicative inverses and on and on and on.
These modern machines seem to render the statements within axiomatic mathematical systems as testable and falsifiable as any other physical facts.
These days, most if not all of the rules of math can be coded into a computer, and new propositions tested or evaluated by those systems. Once I’ve implemented floating point math, I can SHOW STATISTICALLY the commutative law, the associative law, that 2+2 never equals 5, that numbers have additive and multiplicative inverses and on and on and on.
Where would mathematical statements fit in this classification of yours? They can be proven, but many of them can’t tested and even for the ones that can be tested the proof is generally considered better evidence than the test.
In fact, you are implicitly relying on a large untested (and mostly untestable) framework to describe the relationship between whatever sense input constitutes the result of one of your tests, and the proposition being tested.
There’s another category, necessary truths. The deductive inferences from premises are not susceptible to disproof.
Thus, the categories for this theory of truthful statements are: necessary truths, empirical truths (“i-can-prove-it”), and “truth-and-i-can’t-prove-it.”
Generally, this categorization scheme will put most contentious moral assertions into the third category.
Agreed except for your non-conventional use of the word “prove” which is normal restricted to things in the first category.
This may be a situation where the modern world’s resources start to break down the formerly strong separation between mind and world.
These days, most if not all of the rules of math can be coded into a computer, and new propositions tested or evaluated by those systems. Once I’ve implemented floating point math, I can SHOW STATISTICALLY the commutative law, the associative law, that 2+2 never equals 5, that numbers have additive and multiplicative inverses and on and on and on.
These modern machines seem to render the statements within axiomatic mathematical systems as testable and falsifiable as any other physical facts.
How would you do this for something like the Poincare conjecture or the unaccountability of the reals?
Also how do you show that your implementation does in fact compute addition without using math?
Frankly the argument you’re trying to make is like arguing that we no longer need farms since we can get our food from supermarkets.
Edit: Also the most you can show STATISTICALLY is that the commutative law holds for most (or nearly all) examples of the size you try, whereas mathematical proofs can show that it always holds.