I continue to find your argumentation nonsensical, and have decided to stop wasting my time with it. Cheers.

If some judgements are true, and others false, then truth and falsity is a property of the judgement. Therefore it is impossible that truth and falsity are independent of the judgement. — Metaphysician Undercover

I never suggested otherwise. However, if a particular judgment is true, why is it true? And if a particular judgment is false, why is it false? In both cases, the answer is that there is a fact of the matter, and that fact is independent of whatever anyone thinks about it. A true judgment represents a fact, while a false judgment does not.

No I am saying that there is no such thing as the thing referred to by a word without the word. How is that absurd? — Metaphysician Undercover

Because it entails that the reality of an object somehow depends on the existence of a sign that represents it; but reality is precisely that which is as it is regardless of any representation thereof. In other words, a real thing (or quality or habit) is that thing (or quality or habit) regardless of whether there is any word that refers to it. The thing (or quality or habit) came before the name that some humans arbitrarily invented for it. There is no necessary connection between most words and most things (or qualities or habits), only a convention by which the words refer to the things (or qualities or habits) within a particular language or other system of signs.

What would dictate what roundness is without the word and a corresponding concept? — Metaphysician Undercover

This is exactly backwards. What would prompt the creation of the word "round" if there was nothing already observable for which such a name was needed?

I thought you said that the argument is "self-refuting". — Metaphysician Undercover

I said that recognizing some judgments as true and others as false entails that there is a fact of the matter, which is independent of whatever anyone thinks about it; and that any argument to the contrary is self-refuting. Why? Because disputing it requires presupposing it.

Is that how it is refuted, by you saying it's absurd? — Metaphysician Undercover

You seem to be asserting that something is not real unless and until a word for it exists, which is what I find patently absurd. The reality of (what we call) roundness and the world does not depend on the existence of those names. The world was real, and was really round(ish), before humans ever existed.

According to Charles Sanders Peirce:

• "Logic, regarded from one instructive, though partial and narrow, point of view, is the theory of deliberate thinking. To say that any thinking is deliberate is to imply that it is controlled with a view to making it conform to a purpose or ideal." (CP 1.573; 1906)
• "Logic may be defined as the science of the laws of the stable establishment of beliefs." (CP 3.429; 1896)

Combining and paraphrasing these definitions, logic is the normative science of how one ought to think if one intends to pursue truth; i.e., adopt belief-habits that would never by confounded by subsequent experience.

Thank you for so convincingly demonstrating the patent absurdity of nominalism.

I think the key point here is that saying a number is what it is regardless of what anyone thinks about it is not the same as saying that a number is what it is independently of all thought whatsoever. — Janus

Exactly right; according to Peirce, reality is independent of what any individual mind or finite collection of minds - including, notably, the collection of all actual minds - thinks about it; but reality is not independent of thought in general. As he once put it, "just as we say that a body is in motion and not that motion is in a body, we ought to say that we are in thought and not that thoughts are in us." In fact, another of his definitions is that reality is whatever would be included in the ultimate consensus of an infinite community after infinite inquiry. This is obviously a regulative ideal, not something that could ever actually be achieved.

I still don't get what it could mean to say that they have a reality independent of their instantiations. — Janus

Again, something exists iff it reacts with other things; something is real iff it is what it is regardless of how anyone thinks about it. Numbers clearly do not exist, because they do not react with anything; yet they are clearly real, because they are what they are regardless of how anyone thinks about them.

If you want to say that they are real over and above their instantiations, and then we imagine that there are no instantiations, then what could that reality consist in other than mere logical possibility? — Janus

I am saying that the reality of numbers does not depend on their particular instantiations (existence), and hence that at least some "mere logical possibilities" are real - i.e., independent of how anyone thinks about them.

Before there was the word "round", there was obviously nothing which the word "round" signifies, because there was no word "round" to signify anything . Therefore it is absolutely impossible that there was "the real character of roundness" before there was the word "round". That there is something which the word "round" signifies is very clearly dependent on the existence of the word "round". — Metaphysician Undercover

This is very clearly false. It conflates the object of a sign with the sign itself. The reality of a character, and the existence of things that possess it, is very clearly independent of any particular system of signs that represent that character and those things. Otherwise, the same claim would apply to the world - i.e., it is absolutely impossible that there was a world before there was the word "world" - which is obviously absurd.

That the world is round is a judgement. Whether any such judgement is true or false is irrelevant to the fact that such predications are judgements. — Metaphysician Undercover

That the world is round(ish) is a fact, whether anyone ever judged it to be so or not; i.e., the world is really round(ish), regardless of what anyone thinks about it.

If something counts as an object in the sense that Alethiest stipulates, then it certainly exists. If qualities exist, or subsist, only in their instantiations, then they are existent. My argument is only that there is no coherent sense in which we can say that they have an existence, or being or that they are real, whatever locution you prefer, beyond their instantiations and representations. — Janus

No, this completely ignores the accompanying definitions by which existence and reality are distinct. While qualities and habits only exist in their instantiations - as characters embodied in reacting things and laws governing such events - their reality does not depend on those instantiations; again, they are what they are regardless of what anyone thinks about them. Their mode of being is that of a conditional proposition; under certain circumstances, they would be instantiated.

Reality is that which is as it is regardless of what anyone thinks about it. The fact that someone had a particular dream is real, but the events within that dream itself are not real - they depend entirely on that one person's thoughts. The existence of Hamlet (the play) is real, but the existence of Hamlet (the person) is not real - it depends entirely on Shakespeare's thoughts as written down in the play.

Within mathematics in general, there are numerous contradictions such as Euclidean vs. non-Euclidean geometry, imaginary numbers vs. traditional use of negative integers. — Metaphysician Undercover

Again, mathematics is the science of reasoning necessarily about hypothetical states of affairs. Euclidean and non-Euclidean geometry employ exactly the same (deductive) logic, but draw different conclusions because they begin with different premises; specifically, non-Euclidean geometry adopts one fewer postulate. Imaginary numbers are the perfectly logical result of defining "i" as the square root of -1, regardless of whether this corresponds to something actual.

Mathematics is a subject, so we cannot attribute to mathematics, opposing hypotheses, without contradiction. — Metaphysician Undercover

Mathematics in itself does not require the adoption of a particular set of hypotheses; it simply derives necessary conclusions from any set of hypotheses whatsoever - including, in some cases, the conclusion that those hypotheses are contradictory. Euclidean and non-Euclidean geometry are different subjects with different hypotheses. Algebra with imaginary numbers and algebra without imaginary numbers are different subjects with different hypotheses.

I conclude that you believe the word "round" existed before anyone existed, because this is what is required for the earth to have been determined as round, before anyone existed. Do you not recognize that whether or not an object has a specific property is a judgement, and nothing else? — Metaphysician Undercover

Nonsense. That which the word "round" signifies - the real character of roundness - existed in everything that possessed it before any human being existed, and would continue to exist in everything that possessed it after every human being ceased to exist. Do you not recognize that some judgments are true and others are false? This entails that there is a fact of the matter, which is independent of whatever anyone thinks about it. Any argument to the contrary is self-refuting.

The objections to this understanding are usually based on the inability to make this distinction; hence the common objection to Platonic realism, 'where do numbers exist'? This is because we are by habit instinctively realist; we are oriented in respect of the domain of time and space, the objective realm, which for most of us defines the scope of what is real; everything that exists is 'out there somewhere' in the objective realm. — Wayfarer

On the contrary, the problem with such a question is that most moderns are nominalists, rather than realists; they treat reality as coextensive with existence. The "objective realm" of reality is not limited to that which exists in time and space.

The problem I see with this is that if a mathematical "object", say the number five, has no existence apart from its concrete representations, then it cannot qualify as an object at all, except in the most abstract conceptual sense ... — Janus

In this context, an object is whatever is capable of being represented. Hence qualities are objects just as much as the things that embody them, and habits (including laws of nature) are objects just as much as the events that they govern. Some of these possibilities and (conditional) necessities are real - i.e., their characters are not dependent on what anyone thinks about them - even though they do not exist apart from their instantiations.

The question is explicitly about the independence of math from our intellectual activity. Rovelli - rightly, imo - does not say anything about what is or is not 'real', partly, I suspect, because the question of 'the 'real' causes more muddles than it solves. — StreetlightX

But "independent of our intellectual activity" is precisely what "real" means, assuming that "our" refers to any individual person or finite collection of people. The muddle comes from conflating reality with actuality/existence.

Time is a genuine continuum; it does not consist of discrete "instants," any more than space consists of discrete "points." We can arbitrarily designate an instant (or a point) for some purpose, thereby creating a discontinuity; but we cannot experience any such thing, because each infinitesimal moment blends indistinguishably into its immediate predecessor and successor.

Charles Sanders Peirce described himself as an extreme scholastic realist, rather than a Platonist, and the distinction that he carefully made between existence and reality seems pertinent here. Something exists iff it reacts with other like things in the environment; something is real iff it possesses certain characters regardless of what anyone thinks about it. As such, mathematical objects do not exist apart from their concrete representations, but they are nevertheless real. In fact, Peirce defined pure mathematics as the science of reasoning necessarily about strictly hypothetical states of affairs; it deals only with the logically possible, not the actual.

But rationality has questioned God's existence and where does that lead to? — TheMadFool

Rationality has also contemplated the reality of God by interpreting how He has revealed Himself in nature, Scripture, etc. Again, the problem is not rationality itself, but the (non-rational) assumptions that serve as our first premises.

The possibility of mistake indicates that the belief may be wrong, and if the belief may be wrong, we are justified in doubting it. — Metaphysician Undercover

The possibility of mistake pertains to all of our beliefs; does this mean that we are justified in doubting all of our beliefs? In any case, what you state here is a belief, and it may be wrong; therefore, by its own criterion, I am justified in doubting it.

objective criteria, i.e. physical criteria — sime

What exactly do you mean by "physical criteria"? What is your warrant for equating objective criteria with physical criteria?

What you say doesn't make sense. You are claiming that the possibility of mistake is not grounds for questioning a belief. — Metaphysician Undercover

What you say doesn't make sense. You are claiming that the mere possibility of mistake is grounds for questioning a belief--and therefore that we have grounds for questioning all of our beliefs, which is absurd.

If we wait until a belief actually confounds our experience then it is an actual mistake, and the belief has already been proven wrong at this point. — Metaphysician Undercover

Why should we seriously doubt any of our present beliefs that have never previously been confounded by our experience? Perhaps you are unfamiliar with the expression, "learn from your mistakes."

Doubt is justified prior to the confounding experience, in order to avoid that mistake. Your position could only be correct if you didn't think it was reasonable to attempt to avoid mistake. But that's nonsense. — Metaphysician Undercover

None of us is infallible; i.e., it is impossible for any of us to avoid mistake. Therefore, it is indeed unreasonable to doubt any particular belief, simply because it might be mistaken. After all, doubting that belief could turn out to be the mistake, rather than maintaining it.

If the possibility of mistake cannot be ruled out with respect to any particular belief, then this is a positive reason to question that particular belief, i.e. doubt is warranted. — Metaphysician Undercover

My point was that the possibility of mistake cannot be ruled out with respect to any of our beliefs, but this is not a positive reason to question all of our beliefs; such universal doubt is never warranted. We only have a positive reason to doubt a particular belief when it is actually confounded by experience, not simply because it might possibly be confounded by experience.

It seems rather impractical--perhaps even impossible--to operate reasonably under the assumption that the future will work differently from the past. What would (or could) warrant any particular expectation or corresponding course of action?

In any case, induction is justified because its method is such that experience would, sooner or later, correct any erroneous beliefs adopted by following it.

This means that anytime when certitude cannot be justified, then doubt is justified ... Accordingly, doubt is justified anytime the possibility of mistake cannot be logically excluded. Agree? — Metaphysician Undercover

No, simply recognizing our fallibility--i.e., the fact that certitude can never truly be justified, since the mere possibility of mistake cannot be logically excluded for any of our current beliefs--does not warrant genuine doubt. It is only justified when one has a positive reason to question a currently held belief, regardless of whether one has certitude toward it; e.g., because of a surprising experience or disappointed expectation.

We can be good without being rational but we can't be bad without being rational. — TheMadFool

This is obviously false. People rationally do good things and irrationally do bad things all the time.

The problem is not so much with rationality itself as with the set of presuppositions--i.e., the worldview--that serves as the starting point for any individual process of reasoning undertaken by a person or group of people. Deductive logic, just like a computer, conforms to the law of "garbage in, garbage out." A perfectly valid deductive argument that has even one false premise produces a false conclusion. I often say that the most valuable service the discipline of philosophy can provide is helping us recognize and critically evaluate our own presuppositions/worldview, which is no easy task.

I only went as far as claiming that they could be brute facts, not that they are. — Sapientia

Would you likewise go as far as acknowledging that they could be the intentional product of a creative intelligence?

That's more warranted than either position unless and until there's sufficient evidence to decide one way or the other. — Sapientia

How should we determine what counts as evidence and how much is sufficient?

In such circumstances it's more reasonable to leave such presuppositions behind. — Sapientia

It is impossible to leave all of our presuppositions behind.

You can't just presuppose teleology because that would beg the question. — Sapientia

As I said before, how we answer the question depends entirely on our presuppositions. Treating the laws of nature as brute facts is no more "scientifically" warranted than treating them as the intentional product of a creative intelligence.

Science has a definition of 'ordered', and the universe tends towards disorder. A tendency in the other direction would imply the orderer. — noAxioms

The question is how the initial state of order came about, from which the universe has been tending toward disorder ever since, at least according to our current scientific understanding. The answer depends heavily on one's presuppositions.

Apologies if I seem evasive, but I am not in the right frame of mind to delve into this any deeper at the moment. Perhaps another time.

It depends on how you define "ideas." I will stick with my answer as written for now.

Presumably reasonable inferences from perceptual judgments prompted by past sensations and corroborated by subsequent experiences.

Something other than visual content is included in the basis of belief in the tree. What is that other thing? — Mongrel

I am still not sure where you are going with this. Something other than visual content is the sole basis of a blind person's belief in anything.

There seem to be some missing premisses here. How do we know that 2 is true? How does C1 follow from 1 and 2? How does 3 follow from C1? What exactly do you mean by "apriori" in this context? What does it have to do with one's "visual field"? Where does realism come into play?

I recommend not wasting your time. MU clearly has no clue about how mathematical modeling works as diagrammatic abstraction, primarily embodying relations rather than objects. And remember, he believes that every difference makes a difference. :-}

No, we utilize non-dimensional points (and other mathematical constructions) as strictly hypothetical objects, and recognize that they do not have real existence. — aletheist

Which means, according to you, the Standard Model is wrong. — tom

No, it means that it is irrelevant within mathematics whether its strictly hypothetical models represent anything that really exists. In other words, a non-dimensional point does not necessarily have to represent something that is actually non-dimensional. If it helps, we can amend my initial comment by changing "do not have" to "need not have."

If you would have paid attention to what I said, you would have noticed that what I was saying is that we do not have any way of representing real, non-dimensional existence. — Metaphysician Undercover

If you had actually said this in the first place, I would not have commented at all. What you actually said was:

The representation is as a non-dimensional point, but what does this actually represent? It can't be a particle, because a real particle cannot be at a non-dimensional point. — Metaphysician Undercover

I took you to be claiming that a non-dimensional point cannot represent a real particle, which is false.

I said nothing at all about quarks, leptons, bosons, or the Standard Model. My claim is strictly about mathematics.

The fact that you think I am just blabbering makes my point for me.

If we are utilizing mathematics, we are dealing with strictly hypothetical objects, which may be (and often are) diagrammatic models of actual phenomena.

The representation is as a non-dimensional point, but what does this actually represent? It can't be a particle, because a real particle cannot be at a non-dimensional point. — Metaphysician Undercover

You have no idea how mathematical modeling works, do you? Or representation in general, since obviously a representation does not have all the same properties as whatever it represents, because then it would actually be that object.

You are conflating the actual particles with the hypothetical (i.e., mathematical) representations.

Mathematicians and physicists utilize non-dimensional points, as if they have real existence. — Metaphysician Undercover

No, we utilize non-dimensional points (and other mathematical constructions) as strictly hypothetical objects, and recognize that they do not have real existence.

The big bang is the model of what happened if the laws of physics are more or less consistent throughout time. — VagabondSpectre

I agree, and your acknowledgment of this presupposition is what I was seeking all along. Of course, you are also presupposing that our current understanding of the laws of physics is correct.

The longer our instruments continue to measure no change in the psychical constants we have identified, the weaker the presupposition that they suddenly changed becomes weaker and weaker. — VagabondSpectre

I am guessing that you meant physical, not psychical. In any case, to repeat myself yet again: I am not talking about sudden changes, but gradual ones that would be imperceptible over many human lifetimes - perhaps even the entire history of the human race.