Dfpolis

I think the flaw is seeing the scientific method as the only acceptable means of inquiry. In its proper domain, the scientific method is fine.

No, I am not. I am arguing Aristotelian moderate realism. Experience is the data we have to work with. One can either work with experience, or one can...

You seem to have forgotten the OP, where I used it as an example of a hypothetical postulate. It is derived by assuming that our small-scale experienc...

You made a number of unargued claims I will not respond to. Intelligibility is a potential that exists prior to being actually known. So, it is not "d...

It is had to say without even knowing the area of research. I came up with it reflecting on Aristotle and Aquinas. Aristotle classes action as an acci...

The statement presumes that experience gives us access to reality -- which is an independent, not a recursive, assumption. Books have been written on ...

I do want to add that I was was unclear in discussing the relation of aleph-1 to the cardinality of the reals and that your point on that confusion wa...

This is a very confused statement. If a mathematical theory applies to reality accurately, it is instantiated in reality and the adequacy of the theor...

Thank you. If you read the context, I was arguing against the position that math need only be logically self consistent, not Russell's more extreme po...

Truth is not a value, but a relation between mental judgements and reality. Since it depends on judgements, it can't be prior in time to them. Only be...

I wasn't representing it. I was telling you why abstract numbers do not occur in nature, which is what we were discussing. Exactly! At last we agree. ...

I wasn't representing it. I was telling you why abstract numbers do not occur in nature, which is what we were discussing. Exactly! At last we agree. ...

You said you were not a mathematical Platonist. I was explaining to you why the abstract five is not actual until abstracted. No, it is not a mere ass...

Yes. No universal exists abstractly in nature. There is no actual humanity in nature. There are men and women with the intelligibility to engender the...

I am not denying that you have 5 fingers on your hand -- it is just that five fingers is not the abstract number 5 -- it is specific instance of five,...

Let's try this a different way. Surely the number does not inhere in the objects we count, for they can be grouped and counted in different ways to gi...

I understand the contrast, but not its point.

There are two potentials here. One is our potential to be informed, which belongs to us. The other is the set's potential to have its cardinality know...

But, what being is not, is nothing.

The degrees of abstraction have real differences which our definitions are based on. If "constituents" means preconditions, I have no objection to ide...

If numbers were objects in nature, you would be right, But they aren't objects in nature, they are the result of counting sets we chose to define. Why...

Thank you. Recall that David Hilbert's "program" (concept of math) was destroyed by Kurt Gödel. The Vienna Circle hardly deserves to have its name att...

Yes, the content of the Platonic realm is usually supposed to be prototypes of universal concepts, such as number and equality. Excuse my shorthand de...

Yes, as long as you do not take "nature" to entail limiting determinations.

I do agree that physicists tend to think more eclectically and in a less structured way than mathematicians. Still, I think logic is logic and the val...

The nature of being and God IS being.

First, thank you for posting Frege's argument. My comment is directly on point, and does not attack a straw man, but premise ii. It misstates the cond...

Which is why a consequent of formalism is that math, as a meaningless game, is of no intrinsic value. This view is incompatible both with our experien...

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

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...

This is just a verbal difference. Scientists certainly do, and that it my point: axioms need justification. The verbal difference is in how to define ...

Thank you. I will read it when I have time.

We seem to be converging. I see good history as the result of rigorous method, but not as explaining events from first principles. I have no problem w...

They have a degree of responsiveness that seems fully explainable neurophysiologically. We have no data implying such animals can actualize intelligib...

Only if the justification is axiomatic. It is not. See my new thread on the foundations of math. Citation? We need not assume what we know by experien...

Each field of math assumes its principles (its postulates and axioms), but that does not mean that the principles can't be investigated and justified ...

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 dire...

First, sciences do not establish their own principles, so it would be very surprising if math did. So, we agree on the first part. Second, I did not c...

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 exp...

And that relates to my OP how?

That is certainly the modern usage, but not the only one. Traditionally, scientia meant an organized body of knowledge -- organized in terms of explan...

Providing a purely mentalistic account is exactly what I am not doing. I am saying that our mathematical concepts have a foundation in reality. If the...

Defining a method is not an argument justifying the application of the method. Clearly, many mathematicians are concerned the justifying their axioms....

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 ...

It does not seem different enough to vitiate my point. In any lifetime, or finite number of lifetimes, we can only go through a finite number of axiom...

The Wikipedia provides a good discussion. It says "Informally put, the axiom of choice says that given any collection of bins, each containing at leas...

Thank you for your comments. I have no problem with the neoplatonic One Identified as God.

I am not positing that we're the only rational animals. I am saying that the principle of excluded middle reflects the nature of being and so is intel...

Yes, I am sure. Yes, to be instantiated is to be particular. We move from the particular to the universal by removing particularizing notes of compreh...

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, ...