In my understanding, logic is consequent on the nature of being, and all being is traceable to God. So, logic is posterior, not prior, to God. — Dfpolis

Right, so then God could presumably make anything He desired logically possible.

1

Yes, but since contradictions cannot be instantiated, (by the ontological principle of contradiction) they are not possible. So, the formulations mean the same thing. — Dfpolis

2

What is contradictory is outside the scope of being and so not a limit on being. — Dfpolis

3

The laws of nature, for example, act throughout the cosmos, but have no parts outside of parts. — Dfpolis

4

and an Infinite Being can do any possible act. — Dfpolis

5

Infinite being can act in all possible ways in all pos­sible places at all possible times. — Dfpolis

6

Nor is the universe God because it is constrained by the laws of nature, which are more restrictive than what is logically pos­sible. — Dfpolis

7

Thinking something does not make it exist. — Dfpolis

8

So, we can only prove God's existence if knowledge of it is implicit in experience. People with good intuition can see it directly, but may not be able to articulate it for others. — Dfpolis

9

If a being exists, its explanation must exist. — Dfpolis

10

If something exists, its existence is explained either by itself or by another. — Dfpolis

1) What does contradiction inhere in? Let's set aside once and for all apparent contradiction. Now, your #7 in mind, we have to ask if contradiction is merely something thought, an artifact of reason arising out of a cognitive juxtaposing of conceivable circumstances, that in juxtaposing them informs reason that the reality of the juxtaposition cannot be? The trouble with this is it's just a mental construct, a thought thing. By your #7, then, a something that does not exist by being thought.

Time for you to define existence and being, or to save you some trouble, to correct mine. Allow me to make a division into two classes: mental reality and extra-mental reality. Seven, for example, is a mental reality and not an extra-mental reality, as are all numbers, truth, justice, love, and the American way. I hold God to be a mental reality. A brick, on the other hand, possesses the quality of extra-mental reality. To know this extra-mental reality requires the application of practical knowledge - and it would be beyond tedious in this thread, although perhaps exciting in other contexts - to lay out how we can know anything about extra-mental reality if all we've got is mental reality. Practical knowledge, for present purpose, shall be the sword that cuts that particular Gordian knot.

So we have a real world and a world of thought, and we can mostly, and in theory always, tell the two apart. Contradiction, then, being of thought, is not reified by being thought. But that only tells us about our own thought and our own limitations on our own thoughts. Our suppositions about contradictions, then, remain exactly - merely - and only that. As such, this thinking must be silent on the capabilities of God.

That is the account of contradiction as a creature of reason, as such irrelevant to God. Or, contradiction is more than just a creature of reason - and God is, or is not, subject to constraint by that contradiction. That is, in the extra-mental world we inhabit, there are, plain and simple, things that cannot be and events that cannot happen. In which cases, God can either be and do them, thus doing contradictory things, or, God cannot, and thus God is neither fundamental nor primordial, but derives from a more basic set of rules that are not God.

----------------

I would leave this at one item, for practical reasons, and resume with others in other posts. But perhaps a possibility of resolution lies in your response to this question.

Your #s 9 and 10. I read these as a variation on Leibiz's "Nothing is without reason." And following your distinctions about "explanation," I take both reason and explanation to be in themselves reasoned verbal references to the facts that themselves account for the thing being explained. That is, references to extra-mental realities. It's easy to think in terms of cause, here, but "cause" is a very tricky word.

It seems to me that the extra-mental reality referenced by the explanation must be coterminous with the thing explained in both space and time. I do not mean this in any complicated way, only that for an explanation to be the explanation, there can be no other intermediate explanation. Rather the explanation must be im-mediate. E.g., my lighting the fuse is not the explanation of why the dynamite explodes.

This says that if one thing exists (extra-mentally), then other things must exist (extra-mentally) as explanation. But this "argument" is a mental construct - not necessarily conclusive with respect to extra-mental reality. The notorious and fatal infinite regress is thus a product of the argument and not necessarily a feature of extra-mental reality.

Thus reason seems limited by itself and its own limitations. And to make this very brief, but not so brief that you will miss the point, God would seem to stand entirely outside of what reason can know or itself reason in terms of extra-mental realities. What reason knows cannot be God. God, then, can only stand as a mutable mental reality/construct that in terms of extra-mental reality can only stand as the unreasoned answer to questions not yet answered, or that may be unanswerable. But that implies that God, as answer, cannot be knowable except in speculation or in terms of efficacy as an answer, in neither case as an extra-mental reality; as real, as being a being, but only as an idea - the power and efficacy of ideas being a whole other topic.

The problem with this is that if you allow one brute face, one exception to the need for adequate dynamics, one thing with no intelligible explanation, then there is no reason not to allow others -- and once you do that, your entire line of reasoning breaks down. If one arbitrary finite being can have no explanation why can't any arbitrary finite being have none, be a brute fact? So I see your reasoning self-refuting. — Dfpolis

I do not see more than one brute fact as a problem; all that is required is a brute fact to act as the first cause for causality/time. It maybe that God and matter/energy are both brute facts and God injected the matter/energy into time with the BB. I cannot rule out the possibility of more than one timeless being - all I seek to justify is the cause of the universe - which I believe is the timeless being I refer to as God.

I see no reason to accept this definition. Information is the reduction of possibility, while every new existent makes more acts possible. I agree that finite beings have an intelligible/informative essence that specifies what they can do, but the essence of infinite being does not limit possibility, and so is utterly uninformative. (This is confirmed by trans-cultural reports of mystical experience -- see W. T. Stace's works.) — Dfpolis

I think we have a very different conception of what God is. I have a pseudo-materialist outlook on the world. God has to play by certain common sense axioms - he exists in reality (possibly an unfamiliar / non-material reality) and reality follows certain common sense axioms - so must God. I cannot imagine anything that is not composed of information.

I think we are not likely to agree on this or the remaining points.

But thanks for the discussion and peace to you also!

The genius of Aquinas's insight that God's essence is His existence is that it gives us an intelligible reason why God requires no extrinsic explanation. — Dfpolis

You might think it genius but as you said in the OP, thinking something does not make it exist. So too, for the same reason, one cannot define something into existence . Aristotle saw that the cause of being cannot be a being. Aquinas, in line with the belief in a Creator, avoids the problem by simply declaring that there is an uncaused being that is the cause of other beings. A being that is (existence) because to be is what it is (essence).

You are attempting to put old wine that has turned to vinegar into new bottles. Once again:

You use the term explanation to mean:

the fact(s) that make some state of affairs be as it is. (We may or may not know these.) This is the sense I am using.
— Dfpolis

You avoid Aristotle's causal language but do not side-step the problem. What distinction do you make between the fact(s) and some state of affairs? You said:

Proofs show us how to assemble facts we already know to see something we may not have noticed.
— Dfpolis

Your argument is that there are these facts because of some other fact(s). There are finite beings because there is an infinite being, that the infinite being is the "explanation" of finite beings, and that the infinite being needs no explanation because it is infinite. In Scholastic terms you make the distinction between contingent beings and a necessary being. A first cause. An uncaused cause.

The same tired old argument. — Fooloso4

The zero energy universe hypothesis (which I don't necessarily buy) has some sort of 'seed' causing a chain reaction that then generates the rest of the matter/energy in the universe in exchange for negative gravitational energy. So I agree something permanent must exist (at least a seed, maybe all matter/energy if the hypothesis does not hold). But permanent existence is only possible outside of time so whatever existed permanently has its origin outside of time. — Devans99

You have some particular (unprovable) ontology in mind, and dismissing other possibilities because they are inconsistent with the (unprovable) assumptions of your ontology. For example, the notion that something with causal efficacy can exist "outside of time" is pure assumption - there's no basis for thinking such a thing can exist. If such a thing can exist, then your scenario is fine. But if it can't exist, then we're stuck with the sort of scenario I've described - along with the assumptions it entails. We've been down this road before, so there's no point in going down it again. Thanks for the discussion.

You avoid Aristotle's causal language but do not side-step the problem. What distinction do you make between the fact(s) and some state of affairs? — Fooloso4

I avoided "cause" because I'm not writing in ancient Greece. Modern philsophy ignores essential causality and takes "causality" to mean Kant's "time sequence by rule." as I am not speaking of temporally prior events, but of concurrent agency, I carefully avoided the term "cause." I am perfectley happy with either "fact" or "state" of affairs as long as no confussion arises.

Your argument is ... and that the infinite being needs no explanation because it is infinite. — Fooloso4

That is a complete misstatement of my position that everything that is, has some underlying dynamics/explanation. It you are going to criticize, criticize what I actually say.

An uncaused cause. — Fooloso4

Thank you for illustrating why I did not use "cause" -- by misstating of my position.

I avoided "cause" because I'm not writing in ancient Greece. — Dfpolis

Aquinas did not write in ancient Greece

I am perfectley happy with either "fact" or "state" of affairs as long as no confussion arises. — Dfpolis

The point is you are using the term in two fundamentally different ways - (1) fact(s) that are not dependent (God/infinite being) and (2) all other facts which are dependent on (1).

Your argument is ... and that the infinite being needs no explanation because it is infinite.
— Fooloso4

That is a complete misstatement of my position that everything that is, has some underlying dynamics/explanation. It you are going to criticize, criticize what I actually say. — Dfpolis

What you said is that God, i,e., the infinite being is self-explaining.

An uncaused cause.
— Fooloso4

Thank you for illustrating why I did not use "cause" -- by misstating of my position. — Dfpolis

How does your argument for a self-explaining God differ from Aquinas' first cause, an efficient cause, an uncaused cause?

Thanks for the conversation too. One parting point:

Imagine an eternal god who has always been counting - what number would he be on? Forever has no start, so the god could not have even started counting - so the lack of an initial state invalidates all subsequent states - 'forever' is impossible.

What is self-explaining (meaning 1) but cannot be explained (meaning 2) is a conjuring act. — Fooloso4

I have no idea what you're talking about. I said precisely how God is self-explaining. Please read what I posted.

All that is actual is possible, and our concern is with what is actual, that is, the universe as it is, was, and will be. — Fooloso4

First, you are begging the question by assuming that all reality is part of the universe. Most cosmologists, even though they are naturalists, believe that there may be other universes, with other laws (the multiverse). Second, you are confusing logical possibility with physical possibility. The laws of nature restrict what is physically possible, but they do not restrict what is logically possible. Third, things that happened in the past are possible in virtue of having actually happened, but they are not actual because they no longer exist.

We cannot extrapolate from our limited acquaintance with limited things to a universe that is limited. — Fooloso4

Yes, we can. Because whatever changes has to be limited. If it were not, it would be all that it could be, and so there would be nothing for it to change into.

What is self-explaining (meaning 1) but cannot be explained (meaning 2) is a conjuring act.
— Fooloso4

I have no idea what you're talking about. I said precisely how God is self-explaining. Please read what I posted. — Dfpolis

It is really quite simple. You have not provided an explanation (2) for the existence of God, you simply assert that God is self-explaining (1). You are claiming that an explanation (1) is:

the fact(s) that make some state of affairs be as it is. — Dfpolis

and that in the case of God:

the explanation is the thing in question — Dfpolis

and:

So for an infinite being, what-it-is would be identical with that-it-is. — Dfpolis

This is not an explanation (2) it is an unsubstantiated claim, creatio ex nihilo, of an infinite being made to explain (2) what cannot be explained - being. It amounts to saying it must be because otherwise there is no explanation for what is (2).

First, you are begging the question by assuming that all reality is part of the universe. — Dfpolis

The question is whether the universe requires God. It seems evident to me that what is part of the universe is actual. If you are going to claim that there is something that is not that is the explanation for what is in the universe then the burden is on you to demonstrate its existence.

Most cosmologists, even though they are naturalists, believe that there may be other universes, with other laws (the multiverse). — Dfpolis

Is the multiverse infinite in the sense you are using the term? If not, then the same problem holds - it would not be self-explanatory. If the multiple universes are separate then the existence of one has no effect on the others.

The laws of nature restrict what is physically possible, but they do not restrict what is logically possible. — Dfpolis

And what do you think follows from that? If something is logically possible that does not mean that it is actual or has any bearing on what is actual.

Third, things that happened in the past are possible in virtue of having actually happened, but they are not actual because they no longer exist. — Dfpolis

This is muddled. If something were not possible it would not have happened. There are things that are possible that are not actual, but what is actual cannot be impossible.

We cannot extrapolate from our limited acquaintance with limited things to a universe that is limited.
— Fooloso4

Yes, we can. Because whatever changes has to be limited. If it were not, it would be all that it could be, and so there would be nothing for it to change into. — Dfpolis

The inability to change is a limit.

Number theory is not even Turing-Complete, and hence, considered to be a relatively weak and incomplete axiomatization. — alcontali

I did not confine my definition to number theory, which does not include geometry and its subdisciplines, topology, analysis, calculus, distribution theory, chaos theory, etc., etc.

Still, a sincere thank you for stating the role of set theory in the minds of contemporary mathematicians. I knew many in grad school and discussed these topics, so I should have included set-theoretic relations in my description of the subject matter of mathematics (defined as what mathematicians study).

If you take mathematics to mean what mathematicians study, then you can say metamathematics is part of mathematics. If you take the position that fields of study are defined by what is studied (their material object) and the aspect under which it is studied (their formal object), then metamathematics is not mathematics, even if we include set theory in mathematics.

It does not matter that one can represent meta-mathematical relations mathematically, for if it did, mathematical physics would be subalterned to mathematics, and it is not. The use of mathematical representations is a tool, and tools do not define the subject matter they are used on. The material object of mathematical physics is the dynamics of natural processes, and its formal object is being viewed from a mathematical perspective. Similarly, the material object of metamathematics is the fundamental structure of mathematics and its formal object is being viewed from a mathematical perspective. Who undertakes such studies, and whether they also study other things from other perspectives is completely immaterial.

Every Turing-complete axiomatization is capable of expressing all possible knowledge in its associated language. — alcontali

This is a sweeping, and over-reaching, claim. How would one express, without circularity that lavender is not orchid? Of course, one could say that L ≠ O, but will not adequately express this fact to one who does not already know what lavender and orchid are. Or did you mean that one can [inadequately] express all possible knowledge in a Turing-complete axiomatization's associated language?

This is not a fatuous observation, but points to critical issues. Natural languages are not purely formal systems. They are not merely sign-sets following syntactic rules. In order to function they need the power to instantiate meaning in other minds, and to do so they need reference, which relates signs to certain aspects of reality. Formal languages lack determinant reference, and in order to provide such reference, one must employ natural language. I have yet to see a mathematical proof not contextualized by natural language text.

So, your claim is either false, of vacuous. (It is vacuous if you mean that what is wholly indeterminate can receive any determination.)

No, mathematics has quantitative relations as its subject matter — Dfpolis

Mathematics, science, and history are not subject matters. — alcontali

Did I say they were????

They are epistemic domains, i.e. the sets of knowledge statements -- with knowledge a justified (true) belief (JtB) -- that you can legitimately justify using their associated epistemic justification methods. — alcontali

If you want to say "epistemic domains" instead of "fields of study," be my guest. They are not, however sets of knowledge statements. Why? Because:
(1) Sets are well-defined collections of distinct objects, while accepted science is indeterminate because it varies over time. Newtonian physics was unquestioned for centuries, but is now known to be inaccurate.
(2) The definition of a science cannot change with the discoveries it makes. When Aristotle, Archimedes, Jean Buridan and other early physicists applied mathematics to the study of natural processes they were as much physicists as those struggling today to find a theory of quantum gravity. Yet, in their day little of what we now accept was or could be justified. What defines a science is what is studied (its material object) and the approach to studying it (its formal object) -- not what is actually known at any time.
(3) Your definition suffers not only from indefiniteness, but from being closed. As sets have to be well-defined, they cannot adequately represent fields that are open to new data and theoretical revision.

Also, while I agree that scientific findings can be justified beliefs, in many cases we have no way to determine whether they are true in any absolute sense. So, your definition of knowledge cannot be applied to scientific findings in general.

There is no mathematical subject matter, nor a scientific subject matter, nor a historical subject matter. — alcontali

Unless you are willing to argue a case, this claim is to absurd to be worth rebutting.

Furthermore, these epistemic domains exclude each other. It is not possible that a proposition can be justified by one epistemic method and also by another. — alcontali

Why is that?

Physics uses mathematical formalisms to maintain consistency in its theories, but has actually nothing to do with mathematics. — alcontali

Physics is not subalterned to math, but that does not mean it has nothing to do with math. (1) Many mathematical concepts were discovered as part of physics before being formalized by mathematics. For example, medieval physicists developed the concept of instantaneous velocity, which is the basis of the concept of a derivative. The first examples of chaos theory were discovered by physicists. Dirac's delta function gave rise to distribution theory. (These examples also show that same finding can be discovered by diverse methods -- rebutting your claim above.) (2) Routinely, the observable implications of physical theories are mathematically deduced.

With the term "method", I meant "epistemic method", i.e. knowledge-justification method, as in axiomatic "method", scientific "method", and historical "method". — alcontali

I do not see that there is an axiomatic method. There is deduction, which can be applied as much to deducing the consequences of axioms as those of hypotheses.

Axioms can be abstracted from reality, in which case abstraction is the method, or they can be hypothesized (like the parallel postulate or the axiom of choice), in which case we are dealing with an instance of the hypothetico-deductive method -- and one that it epistemically problematic, as unfalsifiable hypotheses are suspect. (Of course, we can confirm many consequences.)

Metaphysics does not establish the epistemic method for any area or research, including physics. It is epistemology that does that job. — alcontali

I did not say that metaphysics established the epistemic method for any area. I said "it deals with issues fundamental to all other areas of research." This means that it deals with foundational issues of logic and epistemology as well as physics.

Mathematics is what you can justify using the axiomatic method — alcontali

This is an absurd claim. How does the so-called "axiomatic method" justify its axioms? Clearly, it does not, for it takes them as given. Similarly, the scientific method takes takes observations and the logic involved in working out the implications of hypotheses as given, and provides no justification for either.

According to Karl Popper's 1963 "Science as Falsification", which has in the meanwhile become the dominant view in the philosophy of science, science consists of the theories that you can justify by experimental testing. — alcontali

You are equivocating. I said "science in the traditional sense," and you're discussing only sciences that use the hypothetico-deductive method. I have no problem with the concept of falsification in the context of the hypothetico-deductive method, but I hope we can agree that it is not the only method that can be applied to come to a rigorous systematic understanding. If it were, mathematics would not be scientific.

Furthermore, mathematics and science exclude each other. It is not possible to justify a theorem with both methods. — alcontali

This is obviously wrong. Newton did not develop fluxions in a rigorous, axiomatic way, but in a hypothetical way that was justified by its successful application to, and confirmation by, empirical findings. His empirically justified discovery was later "cleaned up" (axiomatically formalized) by mathematicians. The same is true of Dirac's discovery of the delta function and its later justification with the development of distribution theory. There are many other counterexamples I could cite.

It is absurd to think that any competent physicist would accept a proposed ToE absent rigorous experimental testing. — Dfpolis

According to the late Stephen Hawking, the problem will never even occur. According to him, there simply won't be anything to test — alcontali

First, this doesn't rebut my point, but only makes the claim that it's counterfactual. Second, it is an argumentum ab auctoritate from an unreliable source. Hawking, despite many admirable traits, has been wrong on fundamental matters much more central to his area of expertise. (See Leonard Susskind , The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics.)

Well, the ToE is an axiomatic system, and physicists seem to dream of finding it. — alcontali

While physics can be and has been axiomatized (e.g. quantum theory and quantum field theory), the axioms remain hypothetical, and so do not change the nature of the science. The justification for the axioms is that, so far, they seem to work. A ToE would be the same. Its axioms would not be deduced (or otherwise justified) on a priori grounds, but hypotheses that seem to work with respect to the available data.

Well, metaphysics seems to have very little influence nowadays on the practice of physics. This is not true for metamathematics, which thoroughly dominates the discourse in mathematics. — alcontali

I agree. Still, what is rational and what is in vogue are rarely the same. E.g., the interpretation of quantum theory is plagued by irrational and manifestly false beliefs.

If it is provable, then it is not about the real world. If it is about the real world, then it will not be provable. It harks back to the definition of the term "proof" as the derivation path between a theorem and its underlying axioms. Without axioms, no "proof". — alcontali

So, a bowl that holds only one apple and one pear cannot be proven to hold two pieces of fruit? Or, if Jane is actual, we can't conclude that Jane must be possible? You really believe that? I see such claims as in the same category as Daniel Dennett consciously denying that he is conscious.

A mathematical proof is an inferential argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed [Italics mine] statements, known as axioms, along with accepted rules of inference.

You can clearly see that this is not possible in science. — alcontali

Think logically, please! Scientists routinely assume statements to be true. Such assumed truths are called "hypotheses" (h) and they can yield conditional predictions (p) true about the real world, viz. h => p. Scientists also take observations to be true and deduce implicit facts from observed facts and "self-evident" "axioms."

Of course, no proposition is truly "self-evident." All truths derive from experience. It is just that some judgements can be seen to be universally true after a single experience.

Rather, I see it as a complex, intelligible whole from which we may abstract some universal truths. — Dfpolis


Well, these "truths" -- I would rather say experimentally-tested "theories" -- have only been tested at best against observations in the visible part of the universe. — alcontali

So, 2 objects and 2 more objects might not yield a total count of 4 objects outside the visible universe? Sehr interessiert!

To be continued...

Sets are well-defined collections of distinct objects, while accepted science is indeterminate because it varies over time. — Dfpolis

Science is a growing collection of theories that can be justified by the scientific method. At any point in time it is a set, but over time it is a changing collection. I concede that sets are immutable. In fact, I only wanted to refer to the fact that scientific theories are enumerable.

What defines a science is what is studied (its material object) and the approach to studying it (its formal object) — Dfpolis

That is probably true for "a science" but not for "science", which is simply any proposition that can be justified by experimental testing.

Also, while I agree that scientific findings can be justified beliefs, in many cases we have no way to determine whether they are true in any absolute sense. So, your definition of knowledge cannot be applied to scientific findings in general. — Dfpolis

Yes, agreed. I do not think that knowledge is necessarily a "true" belief, with the term "true" as in the correspondence theory of truth. Knowledge as a "justified belief" should be sufficient.

Why is that? — Dfpolis

Math justifies by axiomatic derivation, while science is does that by experimental testing. Experimental testing always occurs in the real, physical world, of which we do not have the axioms. Therefore, we cannot axiomatically derive that what can be experimentally tested. The converse is also true. If a proposition is derived axiomatically from a set of axioms that construct an abstract, Platonic world, you cannot experimentally test it, because that would require the objects to be part of the real world and not the Platonic world in which they have been constructed.

I do not see that there is an axiomatic method. — Dfpolis

The axiomatic method is defined and discussed in numerous places, such as here and here.

In mathematics, the axiomatic method originated in the works of the ancient Greeks on geometry. The most brilliant example of the application of the axiomatic method — which remained unique up to the 19th century — was the geometric system known as Euclid's Elements (ca. 300 B.C.).

After Euclid's Elements introduced the axiomatic method, Socrates got the idea that philosophy had to be approached in a similar manner. The approach did not entirely succeed, and it was not a good idea for science, as would later become clear from Aristotle's now outdated scientific publications, but it works for mathematics and morality.

Axioms can be abstracted from reality — Dfpolis

That is how axioms were originally understood:

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.

Nowadays, axioms are deemed to be arbitrarily defined. They are unrelated to the real, physical world. Axioms are not true nor false, in terms of the correspondence theory of truth. Axioms are the building bricks of a new, abstract, Platonic world.

How does the so-called "axiomatic method" justify its axioms? — Dfpolis

It doesn't. In fact, that is even forbidden, because in that case, they are not axioms. In a knowledge statement P => Q, you can see that Q is justified by P. We do not care how P is justified, or if this is even the case. It does not change anything to the fact that Q necessarily follows from P. The knowledge expressed by P => Q, as a justified belief, is not P nor Q, but the arrow between both.

Similarly, the scientific method takes takes observations and the logic involved in working out the implications of hypotheses as given, and provides no justification for either. — Dfpolis

In science, the observations are the P (justifying statement) and the theory (knowledge statement) is the Q, in P => Q:

(P) justifying statement => (Q) knowledge statement

There is no need to justify P, because the status of P does not affect the arrow, which is the real knowledge.

If it were, mathematics would not be scientific. — Dfpolis

Mathematics is not justified by experimental testing, and is therefore, not scientific.

Second, it is an argumentum ab auctoritate from an unreliable source. Hawking, despite many admirable traits, has been wrong on fundamental matters much more central to his area of expertise. — Dfpolis

In his lecture, Gödel and the End of Physics, Hawking spent quite a bit of effort justifying his views. For me, it works.

While physics can be and has been axiomatized (e.g. quantum theory and quantum field theory) — Dfpolis

If it is physics, it is about the real, physical world, and in that case, you can test it. Therefore, it will not be accepted, as a matter of principle, that it does not get tested.

The justification for the axioms is that, so far, they seem to work. — Dfpolis

If "they seem to work" is about what they observed in the real, physical world. That amounts to again to testing.

So, a bowl that holds only one apple and one pear cannot be proven to hold two pieces of fruit? — Dfpolis

No. It will undoubtedly be true, but it will not be provable. To cut a long story short, there are numerous articles in the search results that explain why not.

All truths derive from experience. — Dfpolis

Yes, agreed, in the correspondence theory of truth, the real, physical world is the benchmark for truth.

So, 2 objects and 2 more objects might not yield a total count of 4 objects outside the visible universe? — Dfpolis

Doesn't matter, because you cannot observe it. Therefore, without observations in an experimental testing fashion, such claim about the non-visible universe is unscientific.

It does not matter that one can represent meta-mathematical relations mathematically, for if it did, mathematical physics would be subalterned to mathematics, and it is not — Dfpolis

Metamathematics is the axiomatic system about (other) axiomatic systems. It is an abstract, Platonic system that produces theorems about other abstract, Platonic systems. Mathematical physics, on the other hand, is still about the real, physical world. Therefore, it is not part of mathematics.

Mathematics requires you to painstakingly construct the world in which you will derive your mathematical theorems. We did not construct the real, physical world. Therefore, we are not allowed to derive mathematical theorems in it.

Continuing ...

At the simplest level, we understand being well enough to see that (1) Whatever is, is, (2) that a putative reality must either be or not be, and (3) that nothing can be and not be at one and the same time in one and the same way. — Dfpolis

Well, there seem to be physics theories that do not abide by this, such as Schrödinger's cat and the entire concept of entanglement. — alcontali

Yes, some irrational minds hold such views. That does not establish them as facts, or even good physics.

As I recall, Schrödinger proposed his thought experiment as a way of rebutting the Copenhagen Interpretation, not as a way of rebutting the foundations of logic. It should be clear to any physicist who approaches the collapse of the wave function at a fundamental level, that physics already accepts an understanding of bulk matter that entails the failure of superposition (e.g. the measurement problem, Schrödinger's cat, and the quantum-classical transition).

As I recently explained to David Hand on my YouTube channel, the wave function collapses because electron-electron interactions are nonlinear. Electrons interact via the electromagnetic field, represented by the 4-potential, A. The source of A is the 4-current j (charge density + current density), which is quadratic in the wave function, ψ. The interaction is represented by a jA term which is quartic (quadratic in two different ψs).

Superposition requires linearity. Before detection, we can treat a quantum as isolated, so its dynamics is linear to a good approximation. Once it starts to interact with a detector or any other form of bulk matter (which is bound by atomic electron-electron interactions) the system becomes nonlinear, and any superposition must collapse. So, Schrödinger's cat is physically impossible.

Turning to entanglement, Bell's theorem, spooky action-at-a-distance, etc., the issues raised attack neither the principles of being nor the foundations of logic, but a certain misunderstanding of physics. It is well-accepted that ERP/Aspect-type experiments imply no violation of the relativistic principle that no signal can travel faster than the speed of light. So, there is no violation of accepted physical principles, only a concern that a local, realistic, deterministic interpretation of quantum theory may not be possible. I assure you that is possible, as an assumption critical to Bell's proof (viz. detector independence) is false (it ignores accepted physics,i.e. the antisymmetry of multi-fermion wave functions under coordinate interchange aka the Pauli exclusion principle.)

The underlying error in most quantum mythology is Whitehead's fallacy of misplaced concreteness. It consists in treating abstractions as though they were actual, contextualized reality. The more formal and abstract, the more axiomatic, one's thinking, the more prone one is to this fallacy. One way of spotting such errors is that those making them are often forced to question fundamental metaphysical principles.

But then again, these theories are too physical-world to my taste. — alcontali

There's no point in being bound to reality.

I personally prefer the abstract, Platonic worlds of mathematics, for which you only need pen and paper. — alcontali

And the experience of being as quantifiable, from which to abstract the relevant concepts.

The mainstream view is that knowledge is a justified (true) belief: — alcontali

Ah! How powerful is the need for social acceptance! Still, I prefer to examine the foundations of "accepted" views, however common. Clearly, we may not believe (accept) what we know, which would be impossible if knowledge were a species of belief. As a historical example, Descartes knew he was in his chamber (an act of intellect = his awareness of present intelligibility), but chose to suspend belief that he was in his chamber (an act of will = the suspension of commitment to the truth of what was known).

Justified true belief is a definition of knowledge that gained approval during the Enlightenment, 'justified' standing in contrast to 'revealed'. There have been attempts to trace it back to Plato and his dialogues. — alcontali

Before the so-called Enlightenment. there was a clear distinction between experientially known reality (what is known by reason) and what was accepted by faith. So, this is a solution to a problem that did not exist. You can confirm the by reading the beginning of the Summa Theologiae, or by reading about the doctrine of the two books (the book of revelation and the book of nature) in James Hannam, The Genesis of Science: How the Christian Middle Ages Launched the Scientific Revolution.

In point of historical fact, the Enlightenment was an intellectually retrograde movement, in which ancient origins were thought more important to judging truth than rational reflection on empirical evidence.

P does not need to be knowledge. For example, axioms are not knowledge, because they are not justified. — alcontali

If you do not assume that the axioms are true, then one cannot assume that anything derived from them is true. If we only need begin with unjustified axioms, we can start with any assumptions and prove anything. That may satisfy you, but it certainly does not satisfy the general desire of humans to know.

In my view, axioms can be justified by abstraction, and most mathematical axioms are. A few, like the parallel postulate, are hypothetical, and are justified (confirmed) empirically because the sum of the measured interior angles of triangles is invariably two right angles to within the error of the measurements. If such measurements did not confirm this prediction, we would reject the parallel postulate -- as we do for non-Euclidean metrics.

Since we know the axioms are true any valid deduction from the axioms must be true (logic is salve veritate.)

It will initially, and possibly even never, be possible to turn a philosophical idea into a rigorous system. — alcontali

Thank you for the unargued faith claim. You have made no case that we cannot come to a certain knowledge of fundamental principles (of being, mathematics, and even physics) by abstraction. Until[ you do, all you have is unjustified belief.

quote="alcontali;304563"]Yes, of course. However, with access to the ToE -- which will never happen -- the distinction between axiomatic and empirical would disappear.[/quote]

Your recurring appeal to what we both agree is an impossibility is an annoying and pointless distraction.

(2) that a putative reality must either be or not be — Dfpolis

Good Aristotelian that you are, you apparently don't know about JS Bell and Bell's theorem/Bell's inequality. Do I need to explicate?

The short of it is that if reality as you describe it is ascribed to entangled particles, then they'll break your heart.

Good Aristotelian that you are, you apparently don't know about JS Bell and Bell's theorem/Bell's inequality. Do I need to explicate?

The short of it is that if reality as you describe it is ascribed to entangled particles, then they'll break your heart. — tim wood

Good physicist that I am, I've been studying entanglement for years and have found the flaw in Bell's proof. It is quite possible to have a local, realist and deterministic account of quantum theory -- where realist is to be understood in the Aristotelian, not the Platonic sense. I have discussed this possibility for a long time and my explanation has become better defined over time.

The underlying error in most quantum mythology is Whitehead's fallacy of misplaced concreteness. It consists in treating abstractions as though they were actual, contextualized reality. The more formal and abstract, the more axiomatic, one's thinking, the more prone one is to this fallacy. — Dfpolis

Axiomatic thinking is meant to be used for abstract, Platonic worlds. It is not a tool for justifying statements about the real world, which are supposed to be backed by experimental testing.

There's no point in being bound to reality. — Dfpolis

In mathematics, indeed, no.

And the experience of being as quantifiable, from which to abstract the relevant concepts. — Dfpolis

Mathematics does not seek to be an abstraction of the real world. That is what physics seeks to be.

Clearly, we may not believe (accept) what we know, which would be impossible if knowledge were a species of belief. — Dfpolis

If you know it, it means that you can justify it. So, why would you not believe it?

If you do not assume that the axioms are true, then one cannot assume that anything derived from them is true. — Dfpolis

Mathematical theorems are not "true" in a correspondence theory (CT) sense. Theorems are merely provable from axioms, which themselves are never "true" in a correspondence theory (CT) sense.

Provable is never CT true --> because a provable theorem is part of an abstract, Platonic world
CT true is never provable --> because we do not have the axioms of the real world, i.e. the ToE.

Hence, CT true and provable exclude each other.

If we only need begin with unjustified axioms, we can start with any assumptions and prove anything. — Dfpolis

No. A system becomes trivialist because it contains a contradiction, for example.

In my view, axioms can be justified by abstraction, and most mathematical axioms are. — Dfpolis

Axioms do not need to resemble the real world in any way. That is simply not a requirement. Axioms can best be considered to be arbitrarily chosen.

If such measurements did not confirm this prediction, we would reject the parallel postulate -- as we do for non-Euclidean metrics. — Dfpolis

Justification by experimental testing, is not mathematics, but physics. Math does not justify axioms by experimental testing. In fact, Math does not justify axioms at all. If you justify axioms by experimental testing, then it is simply not math. In that case, you are doing something else.

Since we know the axioms are true any valid deduction from the axioms must be true (logic is salve veritate.) — Dfpolis

Axioms are not correspondence-theory true, and any theorem proven from such axioms is not correspondence-theory true either.

Mathematics does not seek to model the real, physical world. Physics tries to do that. Mathematics and physics are different disciplines that are in many ways diametrically opposed.

I personally do not believe that a good physicist could ever be a good mathematician, nor the other way around. That what is mandatory in the one, is strictly forbidden in the other. The one's virtues are the other one's heresies.

Changing hats is really hard, because if you wear the same hat, day in day out, it becomes a second nature. The more advanced you become in the one, the less suitable you become for the other.

There's no point in being bound to reality. — Dfpolis

The real, physical world is something that will always be systematically eliminated from mathematics:

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

In mathematics, the real, physical world is treated as an unwanted impurity that needs to be cleaned away, until it is finally gone. Good riddance!

In my understanding, logic is consequent on the nature of being, and all being is traceable to God. So, logic is posterior, not prior, to God. — Dfpolis

Right, so then God could presumably make anything He desired logically possible. — Terrapin Station

Give this a little thought. As I said, logic, as correct thought about existents, is based on the nature of existence. You are suggesting that existence is limiting, but it can't be. Existence is not a predicate like other predicates. If something is red, for example, it is limited, because the opposite of red is not-red and not-red things can exist. But, if, as you think, something were limited by being, what is excluded is not other kinds of things, but non-being. So, "everythng that is logically or ontologically possible" only excludes non-being, which is nothing. Clearly excluding nothing is not a limitation.

Give this a little thought. As I said, logic, as correct thought about existents, is based on the nature of existence. You are suggesting that existence is limiting, but it can't be. Existence is not a predicate like other predicates. If something is red, for example, it is limited, because the opposite of red is not-red and not-red things can exist. But, if, as you think, something were limited by being, what is excluded is not other kinds of things, but non-being. So, "everythng that is logically or ontologically possible" only excludes non-being, which is nothing. Clearly excluding nothing is not a limitation. — Dfpolis

The idea is much simpler in a way:

If God exists (something like the typical ideas of God re the Judeo-Christian God), then either:

(a) God created logic, or it's at least part of His nature, and God could make logic however He'd want to make it--He has control over His own nature,

or

(b) Logic is more fundamental than God, and God can't buck it any more than we can. God must conform to it. It supersedes Him in its regard.

A finite being can act limited ways, and an Infinite Being can do any possible act. — Dfpolis

I apologize if you addressed this already, but could you clarify what you mean by any possible act? Could an infinite being eat a ham sandwich for lunch at my dining room table today?

(a) God created logic, or it's at least part of His nature, and God could make logic however He'd want to make it--He has control over His own nature,

or

(b) Logic is more fundamental than God, and God can't buck it any more than we can. God must conform to it. It supersedes Him in its regard. — Terrapin Station

Interesting point, a few notes:

- The act of the creation (of logic or anything else) requires logic. So God cannot of created logic.
- Logic constrains God just as it does us. God cannot make a square circle - he is limited to non-contradictions only.
- A world without logic (like X and ~X = true) is a world without information so no being could exist without information.
- So logic would appear to preexist God and be an unchangeable part of his nature.

1) What does contradiction inhere in? — tim wood

I am not claiming that the contradictions can inhere in things as accidents, i.e.,as what Aristotle calls secondary beings. I am claiming that they cannot exist, and so do not exist. As they do not exist, they do not inhere, and as they do not inhere, they have no need of something to inhere in.

If you're asking how we can form/justify this judgement given that what we are talking about does not exist, I respond that the judgement is not based on any experience of non-existence (which is impossible), but on our experience of being. Everything we encounter exists, and this allows us to abstract a notion of existence. (I say "notion" because it is not a concept like other concepts.)

When we do so, we see that existing utterly excludes not existing, and so we grasp the ontological principle of non-contradiction (A putative thing cannot both be and not be at one and the same time in one and the same sense.) It is this principle that is applied here.

Time for you to define existence and being, or to save you some trouble, to correct mine. Allow me to make a division into two classes: mental reality and extra-mental reality. Seven, for example, is a mental reality and not an extra-mental reality, as are all numbers, truth, justice, love, and the American way. — tim wood

I answered your definition question in the OP, saying that "Dynamic ontology is built on the notion of [that] being can be explicated as the capacity to act." I see now that I made a typo, which I just corrected. As de-finition limits, and being is intrinsically unlimited, it cannot be de-fined, but it can be explicated and this is what I have done. Existence and the ability to act are convertible.

I am happy to accept your distinction between mental reality and extra-mental reality, but I don't think you've thought it through properly. Mental existents may be thought of in two ways: as they are in themselves, and as possible objects of thought. As they are in themselves, they are intentional beings, which is to say that their very nature is to be about something. The concept of red is about possible red objects, and the hope for happiness is about attaining a happy state. So, they are not monadic, but relational -- always beyond themselves to something that may or may not be real.

As possible objects of thought, mental realities are in the same class as any other possible object of thought. So, I don't see mental reality as disjoint from extramental reality, because I do not see knowing thought as any different than knowing beach balls. In order to be known, each must do something intelligible that existentially penetrates us -- that is presented to our awareness. To know is to be aware of present intelligibility -- and reality makes itself present by acting on us, by existentially penetrating us.

Why do I say "penetrating"? Because things are where they act. My seeing a ball is identically the ball being seen by me. This identity is only possible if we both act at the same time and place.

Now, let's discuss some of the abstactions you've mentioned. We are not born with the concept seven. We learn it in learning to count extramental objects. A collection of seven objects has a cardinality of seven -- i.e. it has a note of intelligiblity with a determinate relation to the concept seven. So, again, the concept is not monadic, but bears relational. It is applicable to any collection with a cardinality of seven, because any such collection is properly able to evoke it.

Truth also has a foundation in reality. We come to the concept when we realize that some thoughts and locutions are adequate to reality and some are not. So, again, we could not have the concept of truth independently of experiencing reality.

Because all of our concepts have a similar story, no concept is monadic. The ontogenesis of each is based on our experience of reality. So, while they may appear monadic when considered abstractly, their genesis is inexorably grounded in our experience of reality. The same applies to God. Sound proofs are based on experiences that implicate an infinite being.

Contradiction, then, being of thought, is not reified by being thought. But that only tells us about our own thought and our own limitations on our own thoughts. — tim wood

No, it does not. Contrary to Boole, logic is not about the laws of thought. It is about rules we must follow if we want our thought to reflect reality -- to be salve veritate, truth preserving. I have no trouble thinking "square circle," "five-sided triangle," or "infinite wealth." Nothing in my mental constitution, no "law of thought," precludes such thoughts. It is only when I wish my thought to reflect the nature of reality, of being, that I realize that such concepts should be excluded. Why? Because my understanding of being entails that no contradiction can be instantianted.

Our suppositions about contradictions, then, remain exactly - merely - and only that. — tim wood

No, as I just argued, they reflect the nature of being. Our experiential grasp of being is such that we know that it is utterly incompatible with non-being.

That is, references to extra-mental realities. It's easy to think in terms of cause, here, but "cause" is a very tricky word. — tim wood

That is why I have avoided it.

It seems to me that the extra-mental reality referenced by the explanation must be coterminous with the thing explained in both space and time. — tim wood

Yes, I would say "concurrent."

This says that if one thing exists (extra-mentally), then other things must exist (extra-mentally) as explanation. But this "argument" is a mental construct - not necessarily conclusive with respect to extra-mental reality. — tim wood

That is why I have outlined the relation between thought and reality. First, wrt traditional logic, that it reflects the nature of existence, and second wrt to concepts that ideogenesis is the result of our awarenss of present intellibility -- of the object existentially penetrating (acting within) us. For example, the neural modification that represents a sensed apple is identially the modification of my neural system by the apple acting on me. This identity is real, but partial. The modification of my neural system is not all of me, but it is still part of me. The modification of my neural system is not all the apple can do, but it is still the apple doing it. So, part of me is identically an act of the apple. That means the apple is really present (via its act) in me. We are not separate, but one and, as you say, coterminus.

Thus reason seems limited by itself and its own limitations. — tim wood

This is a very Kantian view, and, to my mind, wholly unjustified. I hope the little I've said will help you rethink it, but really, it deservfes a thread of its own.

I do not see more than one brute fact as a problem; all that is required is a brute fact to act as the first cause for causality/time. — Devans99

But, there is no objective reason for such a limitation. It is all very subjective. Whenever you do not like where a line of explanation is leading, you can stop it by pulling the "brute fact" cord.

I think we have a very different conception of what God is. — Devans99

I agree.

Thank you for your reflections.

I apologize if you addressed this already, but could you clarify what you mean by any possible act? Could an infinite being eat a ham sandwich for lunch at my dining room table today? — Theorem

No, because that would entail the contraction of Its being limited, but It could create a finite being capable of doing so. Am I invited?

That is why I have outlined the relation between thought and reality. — Dfpolis

What you may regard to be the relationship between thought and reality is simply your thoughts on that relationship. A clear example of why your simplistic bivalent logic fails:

... the opposite of red is not-red ... — Dfpolis

What is the opposite of red? Is blue the opposite of red? Is green or yellow? All of them are not-red but are all of them the opposite of red? You are not-red, so are you the opposite of red? A car is not red even if it is a red car. Cars and colors are not the same and are not opposites.

Am I invited? — Dfpolis

Sure, if you like ham sandwiches.

No, because that would entail the contraction of Its being limited, but It could create a finite being capable of doing so. — Dfpolis

Wait, so an infinite being cannot engage in any possible act? You seem to be saying that there are certain acts that only a finite being can accomplish. This seems problematic. You said that the difference between infinite being and finite being is that the latter can only engage in some possible acts whereas the former can engage in any possible act. If that's no longer true then your distinction between finite and infinite being collapses.

I should like something to be in order - clear to me - before diving in. I have here in hand (I actually do) a brick, red, standard-sized, first cousin to all those bricks found in structures the world 'round. This brick possesses, sez I, extra-mental reality. It is; it doesn't need me to be. By "it" I simply mean that that founds my own thought of it.

Now I have in mind (because I have troubled to think it) an idea of a brick which comprises a mental picture and various thoughts. This brick has mental reality but not extra-mental reality. In ordinary language it's just an idea of a brick, as opposed to the real brick now on a towel on my table top.

Both bricks be. And I am not aware of any confusion on my part as to which is which or what the special provinces are of one compared with the other.

And the same with all the other extra-mentally real furniture of the world. I can distinguish a chair from an idea of a chair, in simplest terms because they are different.

I deny, then, that mental realities are extra-mental realities or vice versa. Neither is species in the genus of the other.

Agreed?

You might think it genius but as you said in the OP, thinking something does not make it exist. — Fooloso4

That is why I provided a proof.

Aristotle saw that the cause of being cannot be a being. Aquinas, in line with the belief in a Creator, avoids the problem by simply declaring that there is an uncaused being that is the cause of other beings. A being that is (existence) because to be is what it is (essence). — Fooloso4

Do you have a citation for Aristotle?

No, Aquinas did not make a faith claim. He provided a proof. Also, my use of "explanation" is not the same as Aquinas's use of "cause" in "uncaused cause." Aquinas's "causes" must be extrinsic, while my "explanation" can be intrinsic or extrinsic.

The same tired old argument. — Fooloso4

I agree that my argument uses insights due to Aristotle, ibn Sina and Aquinas. Still, being old is not a fallacy. Do you have an objection other than the ancient roots of my thought?

Aquinas did not write in ancient Greece — Fooloso4

Aquinas wrote for a more philosophically literate audience -- one that knew the distinction between essential and accidental causality.

The point is you are using the term in two fundamentally different ways - (1) fact(s) that are not dependent (God/infinite being) and (2) all other facts which are dependent on (1). — Fooloso4

Has that caused you any difficulty?

Let's clarify the "dependence" of facts. There is epistemological dependence. We need not know God before we know empirical facts. And, there is ontological/dynamical dependence. Contingent facts cannot explain themselves.

How does your argument for a self-explaining God differ from Aquinas' first cause, an efficient cause, an uncaused cause? — Fooloso4

I think you can work that out for yourself. The question is irrelevant to the soundness of my argument.

Wait, so an infinite being cannot engage in any possible act? — Theorem

Yes, it can. An infinite being acting as only a finite being can is not a possible act.

You seem to be saying that there are certain acts that only a finite being can accomplish. This seems problematic. — Theorem

Why is it problematic? Truly eating requires a number of operations that imply finiteness: changing in the course of chewing means that the eater has unrealized potencies. Using and requiring nutrients to maintain one's being implies contingency. and so on. So, you must see the acts, not in abstraction (which would be Whitehead's fallacy of misplaced concreteness), but in the context of being done by an unlimited being.

Yes, it can. An infinite being acting as only a finite being can is not a possible act. — Dfpolis

Using this line of reasoning, we could say that a finite being acting as only an infinite being or as only any other finite being can is also not a possible act. Therefore, finite beings can engage in any possible act.

Why is it problematic? Truly eating requires a number of operations that imply finiteness: changing in the course of chewing means that the eater has unrealized potencies. Using and requiring nutrients to maintain one's being implies contingency. and so on. So, you must see the acts, not in abstraction (which would be Whitehead's fallacy of misplaced concreteness), but in the context of being done by an unlimited being. — Dfpolis

That's not the issue. The issue is that your distinction between infinite and finite beings is made in terms of an ambiguous definition of "possible acts". See above.