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

Mathematical physics is still physics. It is not axiomatic. It will ultimately still be experimentally tested. 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.

The difference between physics and mathematics is not that one is about nature and the other not — Dfpolis

That is exactly the difference.

Math is about nature as quantifiable — Dfpolis

Mathematics is not number theory. Most mathematical theorems are not about numbers or quantities.

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

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. The function will not manage to return a result, simply because it never stops running. That is how the problem appears when it is modeled in software. The way automated systems behave, is unrelated to physical-world problems that they would mirror, because they often don't, and in this case, they certainly don't.

All you're doing is ruling out obvious nonsense, leaving open the possibility that all mathematics may be obscure nonsense, — Dfpolis

Only category theory is termed general abstract nonsense.

In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, “abstract nonsense” may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself.

Not all mathematics is abstract nonsense, but the very best stuff certainly is.

It strikes me that the only possible act that God engages in directly is the act of creation ex nihilo. — Theorem

Creatio ex nihillo was in the past. One an ongoing basis God engages in creatio continuo -- mainting conteinfent beings in existence.

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 primarily maintains His own being. Thus, Aristotle called Him, "Self-Thinking Thought." This is an immanent activity -- directed to self-perfection as opposed to a transient activity, which is directed to others. So, God's immanent activity is contingent on nothing else.

The necessity of God upon the universe is not ontological, but epistemological. Knowing the universe is sufficient to lead us to know that God exists by necessity.

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

I eat sandwiches for God, and so do all the other sandwich eaters. We can only eat because we exist, and we only exist because we are divine activities.

What is "contradictory' cannot be the same as the possible and not-possible, beacuse the latter is mutable, changes over time. — tim wood

As I discussed in my thread on the analogy of necessity, there are different kinds necessity and possibility depending on the contextualizing basis. What is physically possible can change over time, as the initial conditions do. It could also be different in other universes with different laws. What is ontologically possible is not like that. Ontological possibility is only limited by the ontological principle of contradiction. If a fully specified A is, then it cannot not-be That never changes.

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

That is why we need to be very careful with out definitions.

In any case, we've devolved this notion of "God" from an omnipotent and infinite being to one who cannot do anything! — tim wood

False. God can do anything. The problem is that contractions cannot be things

I like ham, but can you do pastrami? — tim wood

I'm an omnivore..

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

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.

I skipped a number of points as they did not address my argument in a substantive way, and so need no response.

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

This is false. I explained, discursively, why God's essence (what He is) entails that He is.

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

This is false.

There is no point in spending more time responding to you when you do not understand and respond to what I actually write. Two false claims are enough.

sandwiches — Dfpolis

Perhaps you missed my post; from my view it is at the end of the previous page.

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

You are missing the point. Deductions are only sound if the premises are true and the logic valid. According to you, no mathematical proposition is true. So any argument a scientist makes using a mathematical premise is necessarily unsound.

The difference between physics and mathematics is not that one is about nature and the other not — Dfpolis

That is exactly the difference. — alcontali

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.

Math is about nature as quantifiable — Dfpolis

Mathematics is not number theory. Most mathematical theorems are not about numbers or quantities. — alcontali

I did not say it was number theory. This is not the first time you have twisted my claim, saying I was talking about number theory when I did not mention it. This is not honorable. I named other areas of math, and explained how set theory was based on nature as quantifiable.

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

Again, doing so leads to a contradiction precisely because proceeding in this way makes assumptions that are not based on abstraction.

Since you did not respond the main argument of my last post, there is no point in continuing. I am simply wasting my time.

Yes, I did miss it. It did not appear in my email notifications. Thank you for your thoughtful reply.

Let me say that, while I am Cristian, I don't think that we can have proof that God acts in a Christian way - that we have no proof of a "Christian God," or a Jewish or Moselim God for that matter. Belief in such a God is a matter of faith. It may be justified internally by some more or less intimate relation. Knowing that relation (an I-Thou) points to a Thou, making faith a genuine, but incommunicable, kind of knowledge. It may be justified externally, not by empirical knowledge, but by the worthiness of the commitment it calls for.

Still, I think the logic of arguments such as those of Aristotle, ibn Sina and Aquinas (and the one I posted here) is sound. Just because what logic tells us is limited, and perhaps even inadequate to a well=lived life, does not mean that it is false. So, I think we must agree to disagree. I think that we can prove that there exists a timeless Power maintaining the universe in being.

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?

What determines the nature of being--God, or.something else? — Terrapin Station

i think the question involves a category error. Being is in indeterminate, not determinate. As what essences limit and so determine, existence is not itself determinate. It is the indeterminate power to act.

Being is some way(s) rather than other ways, no?

Being is some way(s) rather than other ways, no? — Terrapin Station

I'm not sure what you mean. Surely anything that can act in any way must be, and nothing can be unless it can act in some way -- for it it could not, it would be indistinguishable from no-thing.

Well, for example, you said that "Logic is as it is because, to be salve veritate (truth preserving), it has to reflect the nature of being." So you think that there's some way that the nature of being is--the nature of being has such and such set of characteristics, and not this and such set of characteristics, that are reflected by logic, right?

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.

In my opinion, the premises in mathematics should be thought of as arbitrarily defined. Axioms are indeed not correspondence-theory "true":

In epistemology, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.

The possibility that these premises would be conceived according to a model in which some intuitive warrant for their truth is felt to exist harks back to the core philosophy of mathematics, which is Platonism.

In Plato's Theory of Forms, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations.

Just like in Plato's Allegory of the Cave, there may indeed be some further unspecified link between both the real, physical worlds and the abstract, Platonic world of mathematics.

I am not necessarily opposed to this view, but I think that it is, for all practical purposes, unusable.

This unspecified link is certainly not correspondence-theory "true". Therefore, for all practical purposes, it is safer to consider mathematical axioms to be arbitrarily defined, rather than somehow esoterically linked to the real, physical world.

So, yes, I maintain my position that axioms are not correspondence-theory "true".

The dominant philosophy in mathematics is Platonism, and most mathematicians subscribe to it:

A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.

The reason why you criticize this view is because you are not a mathematician while you insist that mathematicians should think about mathematics like you do, i.e. as some kind of theory that is isomorphic with the real, physical world. Your views are completely rejected in mainstream mathematics. It is not me who would be "repeating faith claims", but it is you who are deeply mired in your false, pagan beliefs and other heresies.

:lol: I feel like that should end with “burn!” or “bazinga!” or “and your mama’s fat, too!”

No. In all seriousness, if I had the energy I had in high school, then I might be tempted to learn about these things. As it stands now, most of my time is spent trying to figure out if everyone around me is lying to me or whether I am really delusional.

Yes. (1) Whatever is, is, and whatever is not, is not. (2) Something must either be or not be. And, (3) nothing can be and not be in one and the same way at one and the same time. These are reflected in the kinds of assertions that can be true.

Still, these are not constraints, because they exclude no-thing.

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

Defining a method is not an argument justifying the application of the method. 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.

You continue to make unargued claims. You are attacking Platonism, which I do not hold. You are attacking my claims, not by offering a substantive critique, but by the ad hominem that I am unqualified to comment, despite having studied advanced math and its history. So there is no point in our continuing to dialogue on this topic.

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?

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

Neither.

Nothing is prior to God, because if something were, God would be dependent on it, and so not self-explaining, Further, statements are the expression of discursive (time-sequenced) thinking, and as God is unchanging, God does not engage in discursive thinking.

The statements are the result of finite, discursive minds expressing a partial understanding of being. As all being is willed by God, His will makes the statements possible in two ways: (1) by creating intelligible being to be understood and (2) by creating discursive minds to understand it.

In sum, God wills being, and the statements are the result of humans grasping part of the intelligibility of being.

If being is willed by God, then "neither" isn't the answer. The answer would be God willed it so. But then God could have willed being so that it's other than it is, right?

God willed the being, Humans, not God, are the direct efficient causes of sentences by reflecting on the intelligibility of being. God is not the direct efficient cause of the sentences, and so did not will them, but their causes. i explained this in my last reply by saying God was the remote cause by willing both the known object and the knowing subject.

But then God could have willed being so that it's other than it is, right? — Terrapin Station

If God willed "something" other than being, God would will no-thing. That is the whole point of the ontological principle of excluded middle. Being is not the kind of thing that admits of intrinsic change.

"Being" is not a definable term, as it is intrinsically indeterminate. The only way to "change" it would be to make it what it is not, viz. either not-being or something determinate -- so replacing being simpliciter with a determinate kind of being.

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

If you justify the axioms, then the justifications will become the new axioms. Your strategy simply leads to infinite regress. That is why the axiomatic method does not allow this. As Aristotle wrote: If nothing is assumed, nothing can be concluded.

You are attacking Platonism, which I do not hold. — Dfpolis

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.

So there is no point in our continuing to dialogue on this topic. — Dfpolis

Well, in that case, don't.

If you justify the axioms, then the justifications will become the new axioms. — alcontali

Only if the justification is axiomatic. It is not. See my new thread on the foundations of math.

As Aristotle wrote: If nothing is assumed, nothing can be concluded. — alcontali

Citation? We need not assume what we know by experience.

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

Which is why this irrational belief continues to find adherents in mathematics.

Citation? — Dfpolis

I have found a reference here:

Aristotle also popularized the use of axioms (self-evident principles requiring no proof), claiming that nothing can be deduced if nothing is assumed.

Unfortunately, it does not say in which one of Aristotle's books he writes this. I suspect that it must be 'Metaphysics', but I am not sure about that.

A secondary source is not a citation from Aristotle. I've read his analysis of axiomatic foundations. 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.

A secondary source is not a citation from Aristotle. — Dfpolis

Well, if Aristotle said this -- I guess he did, and there are other links who say that he did -- he will most likely have done that somewhere in 'Metaphysics', probably, book gamma; but it could also be in 'Posterior Analytics'. So, if someone feels like scanning the text ...

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

Can you give an example of where Aristotle does that?

Yes, in the Metaphysics where he discusses the principle of contradiction.

If God willed "something" other than being, God would will no-thing. — Dfpolis

What makes this the case, God or something else?

If God willed "something" other than being, God would will no-thing. — Dfpolis

What makes this the case, God or something else? — Terrapin Station

The nature of being and God IS being.

1) You are just taking the word God and applying it to a concept. Problem is we can take any word and apply it to the same concept. That's why I feel the word God is useless in everyday arguments. When you say God, everyone is going to assume different things. It's ineffective. Usually when people create a word it is with the goal to have a specific definition different from other words so that when the word is used people understand what a person means. At this point, the word God has too many definitions, and by some people's standards it has no one specific definition.

2) There's no absolute proof that there is any entity separate from and outside of existence that acts upon it. It may be difficult for us to envision that existence itself has a life of its own. It may not fit our rules of logic. That doesn't mean it isn't possible. Also, there's problems with the argument that there has to be something or someone outside of and separate from existence that acts upon it because then it begs the question of who acted upon the original actor. The premise itself is contradictory. It says that a thing can only be acted upon by an external source and then goes on to say there's something that doesn't follow those rules. It's either one way or the other.

3) Saying that people whose intuition implies there's a God are more correct than those who have different intuitions is stepping outside of logic. It's unverifiable. You are going to have millions of people who say their intuition is correct at the same time conflicting with your intuition. All that really does is produce people who are so sure of themselves that they are willing to inflict pain on people with different perspectives. That is not productive at all. People that are more humble and aren't seduced by intuitions are generally more considerate of others and others values.