Yet, mathematical physics is one of the most successful sciences. Your theory can't explain this success. On it, what mathematical physicists do is completely unjustifiable. — Dfpolis
The difference between physics and mathematics is not that one is about nature and the other not — Dfpolis
Math is about nature as quantifiable — Dfpolis
The reason for Russell's paradox is not some formal problem that requires a theory of types (though a theory of types avoids the problem). The reason for it is that there is nothing in reality from which we can abstract the concept of the set of all sets that do not include themselves, just as there is nothing in reality from which we can abstract the parallel postulate or the axiom of choice. — Dfpolis
All you're doing is ruling out obvious nonsense, leaving open the possibility that all mathematics may be obscure nonsense, — Dfpolis
It strikes me that the only possible act that God engages in directly is the act of creation ex nihilo. — Theorem
it would imply that God's existence and the existence of some logically possible universe are mutually dependent. In other words, if God exists only when he is exercising some capacity, and if the only capacity he has is for creation ex nihilo, then God exists iff some logically possible universe of his own creation exists. — Theorem
God, then, is limited to the possible, the which He cannot instantiate himself - like eating a sandwich - so he acts through agents - demi-urges? Demons? Lesser deities? is there a problem with the divine/common interface here? — tim wood
What is "contradictory' cannot be the same as the possible and not-possible, beacuse the latter is mutable, changes over time. — tim wood
There are some very appealing and intuitively obvious answers, but those cannot be our criteria - if for no other reason than the question relates to the capabilities of "infinite" beings — tim wood
In any case, we've devolved this notion of "God" from an omnipotent and infinite being to one who cannot do anything! — tim wood
I like ham, but can you do pastrami? — tim wood
So, the order of precedence here is God -> created being (including humans) -> logic (created by humans). — Dfpolis
So if logic is simply something created by humans to think about reality, then God would not in any way be constrained by logical possibility, right? — Terrapin Station
Third, in my proof infinite being does not stand as unexplained, but as self-explaining and precisely because it is infinite being, so that what it is entails that it is. — Dfpolis
This is an equivocation. Either you can explain the existence of God, that is provide a discursive explanation or you cannot. You have not. — Fooloso4
You claim that there is an:
Infinite being [who] can act in all possible ways in all possible places at all possible times. — Dfpolis
and build your discursive explanation based on that assertion. — Fooloso4
sandwiches — Dfpolis
The amount of mathematics used by physics does not change its fundamental nature. It certainly does not turn physics into mathematics. It just makes sure that it is incredibly consistent. It is its consistency that explains its success. — alcontali
The difference between physics and mathematics is not that one is about nature and the other not — Dfpolis
That is exactly the difference. — alcontali
Math is about nature as quantifiable — Dfpolis
Mathematics is not number theory. Most mathematical theorems are not about numbers or quantities. — alcontali
You can represent a set by its membership functions and disregard what elements it contains. From there on, the paradox becomes a problem with these membership functions. — alcontali
Logic is as it is because, to be salve veritate (truth preserving), it has to reflect the nature of being. Being is not a constraint, because being only excludes non-being -- which is to say being excludes nothing. What excludes nothing is not a constraint. — Dfpolis
What determines the nature of being--God, or.something else? — Terrapin Station
Being is some way(s) rather than other ways, no? — Terrapin Station
Deductions are only sound if the premises are true and the logic valid. According to you, no mathematical proposition is true. — Dfpolis
If you are only going to repeat you faith claims, and not try to justify them there is no point in posting on a philosophy forum. — Dfpolis
The page in Britannica is good starting point to answer your objections:
Axiomatic method, in logic, a procedure by which an entire system (e.g., a science) is generated in accordance with specified rules by logical deduction from certain basic propositions (axioms or postulates), which in turn are constructed from a few terms taken as primitive. These terms and axioms may either be arbitrarily defined and constructed or else be conceived according to a model in which some intuitive warrant for their truth is felt to exist. — alcontali
So re those three statements, are they the case because God willed it so, or are they prior to God so that God has no choice in them, either? — Terrapin Station
But then God could have willed being so that it's other than it is, right? — Terrapin Station
Clearly, many mathematicians are concerned the justifying their axioms. I am also concerned about this issue. You seem not to be. So, we do not share a common interest. — Dfpolis
You are attacking Platonism, which I do not hold. — Dfpolis
So there is no point in our continuing to dialogue on this topic. — Dfpolis
If you justify the axioms, then the justifications will become the new axioms. — alcontali
As Aristotle wrote: If nothing is assumed, nothing can be concluded. — alcontali
I subscribe to mathematical Platonism. However, for practical reasons, I do not make use of the possible link between the real, physical world and the abstract, Platonic world of mathematics. I rather leave this link unspecified. In fact, so does everybody else. — alcontali
Citation? — Dfpolis
A secondary source is not a citation from Aristotle. — Dfpolis
While he says we cannot deduce everything, he is convinced that we can justify axioms non-deductively and does so in a number of instances. — Dfpolis
If God willed "something" other than being, God would will no-thing. — Dfpolis
If God willed "something" other than being, God would will no-thing. — Dfpolis
What makes this the case, God or something else? — Terrapin Station
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