It has occurred to me that, just because you use terms such as "modus ponens", it just might not be the case that you understand them. So, I am going to go into more detail on these arguments.
Russell E. Rierson said:
Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.
Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".
Ergo, it follows that your statement: "observation is not a mathematical process" is false.
It does not follow. Let's see why, formally.
The fundamental statements of the argument are these:
p: Mathematical existence is equivalent to physical existence.
q: Physical existence is free from contradiction.
r: Observation is free from contradiction.
s: Observation is not a mathematical process.
Your argument proceeds as follows:
1.) p-->q (Premise)
2.) q-->r (Premise)
3.) Therefore, ~s (Conlcusion)
That this is a non-sequitir is obvious to anyone with any familiarity with logic. The basic statements of the premises do not even appear in the conclusion, which makes the conclusion totally unconnected to the statements cited to support it. Furthermore, it is a simple fact that conclusions of valid arguments cannot contain statements that do not appear in the premises, but this argument does. You can test it for validity yourself by determining the truth table for the compound statement:
[p-->q]^[q-->r]-->(~s)
You will see that the statement is not tautological, and so the argument cannot be valid.
But perhaps you didn't mean to include a new term in the conclusion, and that it only looks like you did due to a poor choice of words?
[1.] Physics would not exist without an ability to describe phenomena.
OK, so formally this is an "if-then" statement:
If physics exists, then it has the ability to describe phenomena.
I'll contract it to:
p: Physics exists.
q: Physics has the ability to describe phenomena.
So we have:
1.) p-->q.
[2.] The description of phenomena must be logically consistent[free of contradiction].
Since this is not a compound statement, it will be denoted by a single logical variable:
2.) r
[3.] Mathematical existence is defined as freedom from contradiction.
Same here.
3.) s
[4.] Mathematics describes phenomena.
And here.
4.) t
Therefore
Physics would not exist without mathematics.
And this is equivalent to the "if-then" statement:
If physics exists, then mathematics exists.
The antecedent was already denoted as "p". Let the consequent be "u". So we have:
p-->u.
And your argument proceeds as follows:
1.) p-->q (Premise)
2.) r (Premise)
3.) s (Premise)
4.) t (Premise)
5.) Therefore, p-->u (Conclusion)
This argument has the same malady as the first one, though to a lesser extent (one logical variable from the premises actually occurs in the conclusion!). But this argument is not valid either, which you can verify using a truth table.
On to your next post:
You agree that physical observations must be non-contradictory.
You must also agree that descriptions of physical existence must be
non-contradictory since observations must be non-contradictory.
Yes.
We can drop the label "mathematical existence"
if it puts a burr in your saddle.
It puts a burr in my saddle because it is irrational.
In other words, you appear to be arguing semantics, not physics.
No, logic is not semantics. Furthermore,
you aren't even arguing physics. The position "physical existence is equivalent to mathematical existence" is a philosophical position, not a scientific or mathematical one.
