Does “1” refer to an object called “a number”? — Luke

No, of course not. That is the mistaken description of how "1" is used which I am trying to expose. If "1" referred to an object called a number, then we could not use "2" to refer to two distinct objects.

That is relevant to this thread because if someone takes it as the basis for an argument about infinity and the infinite, that 1 refers to a mathematical object called a number, it's a false premise. To assume that it does, for the sake of saying something about infinity, is to base what you are saying about infinity in a falsity.


We may disagree on what "the objects studied by metaphysics" refers to. Metaphysics must study all objects in order to have the capacity to distinguish objects existing only within the mind (imaginary and fictional objects) from objects which exist independent of an observer.

The problem is that the existence of each of these types, as a proposed type of object, is difficult to validate, substantiate, or ground, in real principles, without reference to objects of the other type. So there's generally a type of circularity involved in substantiating "existence". That's one reason why dualism has been a prominent metaphysics in the past. My position is that we cannot take the existence of objects, of any type, for granted. Therefore the concept of "object" wherever it is used, must be justified.

So we can’t add 1+1 - is that your argument? — Luke

No, "1" is a symbol. So long as each 1 represents a different object there is no problem to add 1+1 and get 2. But if both 1s are supposed to represent the same object I don't see how you could get two out of that.

It seems to me your "therefore" does not logically follow. The "substantial difference" requires a temporal distancing. — jgill

I believe a temporal distancing is required, to separate future from past. I think Peirce posits a vague now. But this separation between future and past is the prime reason why I believe we need a two dimensional time. We have one representation of time which presents us with a continuous time, past through future. If we posit an instantaneous point as the separation between one part of time and another part of time, future from past, we cannot account for the substantial difference between future and past. This substantial change, from future to past, requires a period of time to occur in, it is a form of becoming, and becoming cannot occur instantaneously. So we need to develop another dimension of time to account for this substantial change which occurs at the present, and relate it to the other dimension of time which is supposed to be a continuity through past and future. Some metaphysicians will talk about the present having width, I call it breadth.

I would say that since metaphysics is the discipline which addresses the issue of what is an "object", and metaphysics therefore determines the meaning of "object", there is no difference between "object" and "metaphysical object". Where I see a problem is that "mathematical object" as people on this thread have proposed, does not seem to be consistent with acceptable metaphysical principles. In other words, it appears to me like mathematicians have posited a type of "object" which is metaphysically unacceptable.

But hidden variables have been experimentally ruled out. If it is epistemic, you are left with a truly pathological metaphysics like MWI as your only refuge. — apokrisis

What I described is not hidden variables, it's faulty principles. That is epistemic, and it does not lead to MWI, far from it.

Physicists in fact tried their hardest to avoid ontic vagueness. — apokrisis

I don't see any physicists addressing the deficiency in their conception of time, which I described in this thread, to adopt a conception which is consistent with our experience of time. Our experience of time indicates that there is a substantial difference between future and past, and therefore no necessary continuity of substance at the present. If physicists had respect for this, they would seek the cause of continuity instead of taking it for granted, as conservation laws. The problem, as we discussed, is that physics is pragmatic, purpose driven toward the goal of prediction. Understanding the real nature of the universe is not the goal of modern physics, so the principles employed by physicists are not designed for this purpose. They are designed for prediction, not for understanding what makes prediction possible.

How can "two distinct instances of the same object" amount to only one object? — Luke

Isn't this obvious to you? If I count the object as "1" at time x, then I count the very same object as 2 at time y, this is a faulty count, counting the same object twice. Two instances of seeing the very same object, therefore a faulty count if I say there's two objects.

I should be asking you the opposite question, how do you think that two distinct instances of the very same object qualifies as two objects?

This is like arguing over the rules of chess with someone who doesn't know the rules. I'm done. — Luke

That's a sad analogy. Any time someone is going to argue with you over the rules of chess, you're going to insist that they do not know the rules, or else they wouldn't be arguing with you about them. Now I argue the rules of counting with you, and of course, you think that I do not know the rules of counting. Obviously it's you who doesn't know the rules of counting, because you think that the same object can be counted twice, for a count of two. Rule number one, you must count distinct objects, you cannot count the same object twice. No matter how many times the same object appears in front of you, you still only have one object.

In general, a mathematical value may be any definite mathematical object.

This is what I object to. In no way can a value be an object. Otherwise any count would be invalidated, as I explained. That there's a cult of mathematicians who believe that values are objects, when in actual usage value is really something predicated, indicates that these people believe falsity.

1+1=1? — Luke

If "1'" refers to an object called a number, then "1+1" indicates two distinct instances of the same object, which is still just the same object. So "1+1" would signify only 1 object if this were the case. However, in common usage it is correct to say "1+1=2". Therefore, to remain consistent with common usage and adhere to true principles of numerology, we must accept the conclusion that "1" does not refer to a mathematical object called a number because this would allow the representation of two distinct instances of the same object "1" to be the same as "2". But according to common usage in counting, "2" cannot refer to a second instance of the same thing.

Right, sort of like remembering the alphabet. Are you claiming it's not possible? Just because we can count (and do simple arithmetic) independently of "things" does not imply that we cannot count things or that we never count things. — Luke

What is not possible, is the notion that counting is a completely arbitrary ordering of symbols. If it were then mathematics would not be as useful as it is. So we can conclude that there is some meaning to these symbols, and learning to count is not a simple matter of learning an arbitrary ordering of symbols. It is a matter of learning the meaning of the symbols. Likewise, learning the alphabet is not a simple case of learning an arbitrary ordering of symbols, it is a matter of learning the sounds represented by the symbols.

The point I am making, is that if in learning how to count (learning the meaning of the symbols), we learned that one represents an object called a number, and two represents an object called a number, then we could not proceed from this understanding toward learning simple addition for the reasons described. However, this is not what we learn when we learn to count, we learn that "2" represents two distinct objects, not an object with equal value to two instances of the object represented by "1". Therefore, if someone comes along at a later time, after we've learned how to count, and tries to convince us that "1" represents a mathematical object, and "2" represents a mathematical object with the value of two distinct instance of the number named "1", we ought to reject this as a false representation of how we've learned to use numbers, and therefore a false premise. .

So is the vagueness of a quantum potential ontological or epistemic? — apokrisis

I think it's very clearly epistemic, as the uncertainty of the Fourier transform, to me is clearly an epistemic vagueness.

Do you believe nature is counterfactual all the way down despite the evidence? — apokrisis

I think I've sufficiently explained this already. What you claim as "evidence" of ontological vagueness is simply a failure in human description, i.e. inadequate description. If my eyes are not good, and I cannot distinguish whether an object is, or is not red, due to apparent vagueness, I might be inclined to say that it is both, or neither, if I am unwilling to accept the fact that my eyes are deficient, and admit this. Likewise, if the mathematical, and physical principles by which a physicist understands quantum potential, makes this thing called "quantum potential" appear to be vague, the physicist might not be willing to accept the fact that the apparent vagueness is due to deficiency in the principles.

So the physicists can't properly describe this aspect of reality because it appears vague to them. And you, instead of turning to other principles like theological principles, which I've argued provide a better description of the temporal aspect of reality than those principles adopted by physicists, refuse to even look this way. Instead you adhere to your biased scientistic metaphysics, assuming that if the physicists cannot describe it, it cannot be described, therefore the vagueness must be real, ontological.

How is, e.g. the set of natural numbers, relative to your own personal decision? — Luke

It's relative to human convention, or agreement. Whether it was your idea, or mine, or someone else's is not relevant

Also, how can it be relative if your decision "does not change the nature of what a value is, itself"? You're talking out of both sides of your mouth. — Luke

I don't see how you construe this. Value is relative to human decision, whether it's your decision, my decision, agreement between us, or an enforced law, doesn't change the fact that it is relative to human decision. Therefore these issues of who's decision it actually is, are irrelevant to the fact that "value" is relative to human decision. There's no "both sides of the mouth" here, it's human decision plain and simple. You just seem to think that whose decision it was is somehow relevant.

The ambiguity exists in the language because the word "value" has more than one meaning. If you think that mathematical value, or the set of natural numbers, has anything to do with "the desirability of a thing", then you are plainly incorrect. — Luke

No, that's clearly wrong, mathematics has to do with the desire to count and measure things. Counting and measuring are desirable things. Therefore contrary to your ignorant assertion, assigning a quantitative value to things is the result of the desirability of something, counting and measuring, because these are desirable things to do, there's a purpose to them.

You're aware that we can count independently of counting things, right? — Luke

Oh yeah!, Finally you've gotten to the point. What exactly is a count, independent of counting things? It's just an arbitrary ordering of symbols. If we learned how to count, without actually counting things, we'd just be learning an arbitrary ordering of symbols. And as I explained in the last post, if "1" refers to an object called "a number", then "2" cannot refer to two distinct occurrences of that same number, or else we would not have two, but only one still. So in the act of counting, if it were independent of counting things, the symbols would refer to nothing, because they cannot refer to "a number", or else the count would be invalidated. Therefore that act of counting independent of counting something, is just an exercise in remembering an arbitrary ordering of symbols. If, on the other hand, you claim that three is one more than two, then there must be something which is being counted to validate this claim. It cannot be numbers which are being counted because each "one" being added which makes three one more than two, and four one more than three, must represent a distinct object, or else the count is invalid. So "one" cannot represent a number, nor can any of the other numerals represent a number because this would invalidate simple arithmetic. Therefore the act of counting, independent of counting things, is nothing other than an arbitrary ordering of symbols.

This appears quite different to your previous comments, where the value was not relative to a mathematical system, but instead relative to you: — Luke

The point is that it is relative to something. Whether it is relative to my own personal decision, or agreed upon decision (convention), does not change the nature of what a value is, itself.

It is clear that you have had this meaning of "value" in mind the entire time, and have misunderstood the meaning of "value" as used in mathematics, and by most of us here. — Luke

No, there you go again with your uncharitable interpretation for the sake of straw manning. You, yourself, introduced ambiguity onto the meaning of "value", trying to distance your use of "value" from my use of value, for the sake of your straw man, when no such separation is warranted.

In what sense is a mathematical value arbitrary? — Luke

Exactly as I explained. The value exists only relative to the system of evaluation. The system of evaluation may be entirely arbitrary if it is not grounded by something substantial. Look, it is completely arbitrary that the symbol "2" represents the quantitative value which we call "two". To remove the arbitrariness we might assume an object, a number, which "2" and "two" refer to. The reality of this object, the number two, must be substantiated in order that the arbitrariness be truthfully removed. This is the meaning of "2", which is to signify two distinct things that are not the same thing. Without this meaning of "2", what "2" refers to, the value associated with that symbol is completely arbitrary.

The important thing to notice, which is relevant to my argument, is that the two distinct things referred by "2" are necessarily distinct and different things, or else there would not be two distinct things, and the meaning of "2" would be lost. So when we say "1+1=2", or proceed in the act of counting, by adding another "1", to say 1,2,3,4,etc., each "1" must represent a distinct thing. Therefore each time "1" is used we must allow that this symbol may represent a distinct thing, and not necessarily the same thing (such as the number one). To claim that the symbol 1 represents the number one, or that the symbol 2 represents the number two is a false claim, because if it were true, then the fundamental use of these symbols in the act of counting would be invalid, "2' would not represent two distinct things, it would represent two instances of the same thing, the number one, which is only one thing, not two.

Therefore this attempt to remove the arbitrariness, which assumes that "1" refers to a number called "one", and "2" refers to a number called "two", is unacceptable, and the arbitrariness of the mathematical system of evaluation cannot been overcome in this way. Finally, the arbitrariness of the mathematical value system can only be overcome by grounding, or substantiating it, in principles which establish separation, individuation, difference between things, rather than an assumed sameness or equality of things. That two distinct things are equal, and therefore have the same value, is inherently arbitrary, but that they are distinct individuals, allowing us to number, or count them individually, is grounded in real difference.

The current approach in cosmology and particle physics would be to see any global regularity in terms of emergent constraints. That is why symmetry and symmetry breaking are at the heart of modern physics. They describe the form of nature in terms of the complementary emergent limits on free actions. A probabilistic view where change is change until change can no longer make a difference. At that point, the system is "stable" and its equilibrium balance can be encode as "a universal law". — apokrisis

This does not account for the problem that I mentioned, which is the issue of saying that the constraints apply themselves in this type of emergence. For the constraints to be applying themselves, the thing being constrained, indeterminacy, freedom, or whatever you want to call it, must be an inherent part of the constraints, thus allowing the constraints the freedom of application. Combining these two in this way provides you with no possibility of separating them in analysis for the purpose of understanding, and you are left with a vague union of constraints and the thing constrained rendering them both as fundamentally vague, unintelligible.

Yes. That is the distinction I have made all along. Potential would be simply a vagueness. The PNC fails to apply. — apokrisis

You are not applying Peirce's distinction between internal and external application of the LNC, as described by Lane in your referred article. There is a difference between saying 'x is red and x is not red', and saying 'it is true, and it is not true, that x is red'. The former is a proper violation of the LNC, the latter indicates an improper definition, or faulty representation of 'red'.

So if the terms of bivalent logic fail to apply in the proposed predication, then we have an improper proposal for predication, a faulty representation of the relationship between the subject and the property to be predicated, such that the LEM is actually what is violated as 'neither/nor'. But the LNC is not actually violated in this case, that it is violated, is an illusion created by an improper proposition. That's the point which Aristotle made with the concept of "potential", insisting that the LNC still applies, as he employed this principle against the sophists who based arguments in improper propositions for the sake of proving absurdities.

It is all made actual and concrete by the fact that every possibility is bivalent. A direction is asymmetric as it breaks - and hence reveals - an underlying symmetry. — apokrisis

This is the false representation, or description. Potential itself, as ontologically existing potential, indeterminacy in the universe, is not what is bivalent. It is the epistemic possibility of predication, represented as particular possibilities, or as you say above, "every possibility", which is bivalent. The ontologically existing potential remains outside the LEM, and cannot be predicated because the proper terms to describe it have not been developed. Nor can the ontological potential, which we describe in general terms, be expressed as particular possibilities. Therefore you have demonstrated a category mistake here.

The category mistake you are making is that you are taking the ontological potential, described as "underlying symmetry" which inherently violates the LEM due to our inability to describe it, and you are representing it as epistemic possibilities which are bivalent. Then you insist that it violates the LNC. But you have not created the necessary bridge across this gap between categories, so you claim the real thing, the ontological potential, violates the LNC, when in reality it violates the LEM. Therefore, you are really just expressing the desire to violate the LNC to allow the improperly described "potential" into your bivalent system without providing the necessary terms of description which are required to truthfully bring it into the bivalent system coherently.

Vagueness is where there just isn't any such general backdrop to local events or acts. If you are in a canoe in a thick fog on a still lake, do you move or are you still? The PNC can't apply unless there is some context to show that a change is happening, and even not happening. — apokrisis

If you analyze your own example here, you'll see that you cannot apply the PNC in this situation because of a deficient description of the situation, due to the fog. The deficient description creates the illusion that the PNC cannot be applied to the situation. However, that's just an illusion, and all we need to do is provide the adequate description (see through the fog) and then the PNC can be applied. So in reality, a claim such as "the PNC can't apply" is never warranted, because any time that it appears like this is the case, we need to make the effort to find the appropriate description so that we can apply it.

You dispute the distinction between vague potential and crisp possibility and then repeat the basic argument. — apokrisis

Huh? The "vague potential" we are talking about is ontological indeterminacy, real potential in the world. A "crisp possibility", is a described situation, an epistemic principle. In no way do I repeat your category mistake by repeating your argument.

The Peircean model says vagueness is only regulated. — apokrisis

We are not talking about "the Peircean model" here. We are talking about the apokrisist model, which utilizes an idiosyncratic interpretation of Peirce, along with a huge category mistake (perhaps initiated by Peirce).

A mathematical value is a type of "worth", it is the value which something has (what it is worth) within that mathematical system. Therefore that value is "relative" to that system. Evidence of this is the fact that if a person has not learned the system they will not be able to assign the proper value to the thing. The principles that the system is based in, the arbitrariness of the system, is a further matter.

You are the one referring to the "application". And the obvious answer from my point of view is that the constraints are self-applied. — apokrisis

That use of :application was a quote from your post. Nevertheless, I've explained how }self-applied constraints" is illogical involving contradiction. If the constraints are fixed constraints (what the laws of physics are generally believed to describe) then there can be no potential to behave in any other way, and the constraints are not applied, they are just there. If the constraints are capable of applying themselves, then there must be freedom of application inherent within the constraints themselves. This would mean that there is an element of freedom inherent within the constraint, and this is contradictory.

Nonsense? Or science?

Cosmolology shows how everything is self-organising back to the Planck scale. I provided you with the hyperbolic curve as a model of how there need be "nothing" before this self-organising was already going. — apokrisis

Such self-organization is not science, it's you attempting to produce a metaphysics which will account for what science gives us in a naturalistic way. And you refuse to accept the contradictions inherent within your naturalistic metaphysics as indication that you ought to move along toward a more acceptable metaphysics. Instead you'd rather appeal to an ontology of vagueness which allows you to leave the contradiction where they lie.

That is why we are talking about habits developing. At first, everything would try to happen willy-nilly. Then later, things would self organise into an efficient flow. — apokrisis

I see you reject the principle of sufficient reason as well as the principle of non-contradiction. Do you see why I am fully justified in referring to your metaphysics as nonsense?

Possibilities come in matched pairs. — apokrisis

This is a key point you seem to be missing about possibility, or potential. Potential is completely incompatible with with the bivalent system, and therefore needs to be represented in a completely different way. Peirce clearly pointed this out. Possibility is something general. If it is reduced to a particular possibility such that we can represent its binary opposite, we are not representing the possibility properly, because possibility always relates to numerous things, not one thing. If actualizing possibility X means not actualizing possibility Y, this does not mean that X is the opposite of Y. But this is also why the idea of infinite potential, or possibility, is nonsensical. It leaves nothing actual to make the choice as to which possibility will be actualized. A possibility does not have the capacity to actualize itself.

Right, I've said this numerous times already in this thread, there is no question of whether or not 2+2=4. It does, without a doubt. What is at issue is whether "2+2" refers to the same thing, or even has the same meaning, as "4".

Some here seem to believe that "having the same value" implies "being the same mathematical object", such that "2+2" represents the same mathematical object as "4" does. I have argued that since "2+2" represents a more specific configuration of the four things indicated, it does not refer to the same intelligible object as the more general "4".

I just can't see how the fact that a specific variable can be assigned different values, is at all relevant. That's simply the nature of a value, because value is relative there is a degree of arbitrariness. One dollar appears to be a constant value, but when considered within the context of the international market, it is variable. This arbitrariness of "a value" is just further evidence that having the same value does not imply being the same intelligible object. Otherwise I could arbitrarily say that a chair and a table have the same value to me, therefore they are the same intelligible object.

here is no "logical premise" involved; that's simply how we use mathematical equations: the equals sign means that the value on the left is equal to the value on the right. "2+2=4" is a mathematical equation. — Luke

Do you not understand that a logical principle is required to say that ten dimes is equal to a dollar? Suppose that you had not learned any arithmetic and some one showed you ten dimes and taught you how to count the dimes, such that you knew there was ten dimes. How would you know that the ten dimes is a dollar unless you learned this further principle? Likewise, if someone just taught you how to count, and then said now take one two and add it to another two, you would not know that this is four. You need to know the further principle of addition to know that two plus two is equal to four.

Therefore, you cannot say that it is the equals sign between "2+2" and "4" which makes these two equal, nor can you even say that the equals sign means that they are equal. It is by means of that logical principle that they are equal. Otherwise, I could write "3+2=4", and the equals sign would mean that the value on the left is equal to the value on the right. But this is not true, because the logical principle of addition is not followed and adhered to, in this representation.

To make the case that each side of the equation is different in a way which is unrelated to their values, i.e. in their symbols, or in what those symbols refer to, is just being a troll. Obviously, they are different in that sense; just look at the bloody symbols. That difference does not need to be pointed out. You are trolling for a response, and I won't oblige you any further. — Luke

Call it "being a troll" if you like. I look at it as a trivial matter. The problem is that the difference needed to be pointed out, because fishfry kept insisting that the very same thing is represented on the left side as the right side of the equation. And when fishfry ceased arguing this, you took up that position. Therefore, I was obliged to point this out to you as well. If you now realize how obvious this is, I am amazed that it took you so long, because I stated very explicitly what I was pointing out, over and over again.

It really seems more like you were trolling me, arguing against me just for the sake of arguing against me, until you realized that what I am arguing is an extremely obvious truth. Now you accuse me of trolling, for making you look like a fool for arguing against something so obvious. But you engaged me, so you really trolled yourself.

But If I visited another planet and found only mountains and rivers, plate tectonics and dissipative flows, then I would conclude something else. An absence of intelligent creators. Only the presence of self organising entropy-driven physical structure. — apokrisis

Who would be applying constraints on this planet then? It would not be appropriate to refer the "application of constraints" unless there is something which is applying constraints. You have a habit of talking in this way, as if there is something, some being, applying constraints, or acting in some other intentional way, but when questioned about that you tend to just assume that constraints are applying themselves. Then you proceed into nonsense about self-organizing systems, as if inanimate matter could organize itself to produce its own existence from nothing.

He emphasised the role of habit instead. Constraints on action that explain both human psychology, hence “freewill”, and cosmology if the lawful regularity of nature is best understood as a habit that develops. — apokrisis

A habit is the propensity of potential to be actualized in a particular way. What is fundamental to "potential" is that no particular actualization is necessary from any specific state of potential. If a specific state of potential tends to actualize in a particular way (habit), there must be a reason for this. The reason cannot be "constraints on action", because the nature of potential is such that no particular actualization is necessary, and constraints would necessitate a particular action negating the nature of "potential", as having no particular actualization necessary. Therefore we must dismiss "constraints on action" as an explanation for habit, and allow that each instance of actualizing a potential must be freely decided, like a freewill action, to maintain the essence of "contingent" as not-necessary.

This is the difference between a habitual act of a living being, and the necessary act of an inanimate object. The habitual act must be "decided" upon, at each instance of occurrence, or else we cannot truthfully say that there is the potential to do otherwise. So "potential" is excluded from the habitual act if the habitual act is caused by constraints, because the constraints would necessitate the action, and there would be no possibility of anything other than that action. If there is something, such as a being, which applies the constraints, to direct the activity, allowing that the potential might be actualized in some other way if the constraints were not applied, then the not-necessary nature of potential is maintained by the choices of that intentional being applying the constraints. But this implies that some intentional being, acting with final cause is applying the constraints to suit its purpose.

And note that the argument I’m making seeks to resolve the continuous-discrete debate via the logic of vagueness. — apokrisis

I've explained a number of times now in this thread, the logic of vagueness does not solve any problems, it simply represents them as unsolvable, so we might leave them and not concern ourselves with them, thinking that is impossible to resolve them, instead of inquiring toward the truth of the matter.

You repeat the confusion. "Different expressions of the same value" are different wrt their expressions (or "representations"), but the same wrt their value. — Luke

You're missing something, what the expression represents, it's meaning. So there are three layers, the expression "four quarters", what it represents four twenty five cent pieces, and a third thing, the value we give that collection of coins, one dollar. Likewise, the expression "2+2", what it represents, the number two added to the number two, and the third thing, the value, four.

In each of these expressions, "ten dimes" and "four quarters", what the expression represents is different, not the same, regardless of whatever value you assign. The "value" is something else assigned to it through some principle of equality, or equivalence. Notice that this principle is not stated in either of the expressions. So the expression "four quarters" does not say "one dollar". You only conclude that value by applying that principle.

es, but "ten dimes" and "four quarters" have the same value; they both "refer" to a value of one dollar. — Luke

No, they do not "refer" to a value of one dollar. That's a false assumption. That four quarters has the value of a dollar is a conclusion produced by a logical process. Neither "four quarters" nor "ten dimes" refers to a dollar, but you can take what is referred to, and infer one dollar, when the logical process is applied. Do you see the difference between what an expression refers to, and what can be inferred from what is referred to by the expression, through a logical process? The implied conclusion requires further premises (often taken for granted) which are not stated in the expression, nor referred to by the expression. So, that four quarters is equal to a dollar, is a logical conclusion which requires a further premise not stated within the expression "four quarters".

Here's another example. If you have a red car, and I say, "the roof of my house is red", you could infer that the colour of my roof is the same as the colour of your car. But in no way am I talking about the colour of your roof. Likewise, if I say "I have four quarters", you could infer that I have a dollar, but in no way am I talking about having a dollar. And, if I say "2+2", you could infer that I am taking about the quantity represented by "4", but in no way am I talking about the quantity represented by "4". You simply apply some logical premise and make that conclusion. But applying a further premise, not stated by the expression, and making a logical conclusion from this premise, to insist that this is what the expression is saying, is faulty interpretation. It is not what the expression is saying, it is a logic conclusion that you've derived from what the expression is saying, through the application of a further premise.

Edit: There is no philosophical significance in pointing out that a dime is different to a quarter, or that "2" is different to "4". It goes without saying. You clearly exploit those cases where the values are the same (but the expressions are different) merely to provoke a response. — Luke

What are you talking about? That a dime is different from a quarter is obvious. What I am stating ought to be just as obvious, that ten dimes is different from four quarters, regardless of whatever value you assign to these things. Do you accept this fact, or are you in denial of the obvious, like fishfry? Do you believe that four quarters is the very same thing as ten dimes, just because you can apply some logical principle which makes them equal?

If having the same value meant being the same as, we could assign any random thing the same value as any other random thing, and conclude therefore that they are the same thing. That's nonsense.

Everyone else understanding should tell you something. — jorndoe

Well jorndoe, it seems very obvious from this thread that many people misunderstand. Jgill seems to be about the only one who does understand. Maybe you need to change that statement, and your perspective.

That is only a problem from your theistic presumptions. It is the basic inconsistency in theism or idealism that my version of physicalism resolves. — apokrisis

No, it's an observation. I did not grow up with any theistic assumptions, I didn't go to church, and was not indoctrinated. I studied philosophy in university, and found that the theological metaphysics is consistent with my observed experience, unlike your naturalist metaphysics.

I don't know what "inconsistency" you are talking about. You have described the constraints of past time, and the "application of these constraints" toward the indeterminacy of the future. Do you not apprehend the necessity of a "being" which applies these constraints? Simply assuming constraints from the past, and indeterminacy in the future, does not provide the premises necessary to create an ordered, or organized existence, an object, which "applying these constraints" implies..

Finality is not about "free will". — apokrisis

This demonstrates very clearly that you do not understand final cause, nor do you understand freewill. "Final cause" refers to the cause of an act carried out for a purpose, an intentional act. "Freewill" is derived from an understanding of final cause, in conjunction with the notion that the intentional act is not determined (caused) by past material existence.

You don't understand Peirce's metaphysics yet. But this is the guts of it. — apokrisis

If Peirce's metaphysics states that final cause is not related to free will, then it's a misrepresentation. However, I think that Peirce had very little to say about either of these, and you are just projecting your misunderstanding of final cause and free will onto Peirce's metaphysics. The reality here is that Peirce's metaphysics, being pragmatic, does not account for freewill or final cause, it takes these for granted. So you present a twisted misunderstood representation of final cause, which you think would be consistent with Peirce's metaphysics, and propose it with the intent of making Peirce's metaphysics appear naturalistic..

The issue is that final cause, being what is responsible for artificial things, is fundamentally inconsistent with naturalism. This is because of the classical dichotomy between natural and artificial. Naturalism pretends that it can explain artificial things by classing human beings as natural things, and claiming that artificial things "emerge", just like human beings "emerge", and insisting that to believe other wise is to "believe in the supernatural" which has bad connotations. But the fact of the matter is that the existence of artificial things is much more accurately described by the philosophy of final cause and freewill, and naturalism can only attempt to make itself consistent with final cause by misrepresenting final cause. So there is a deep chasm of separation between final cause as understood by classical philosophy and theology, and final cause as represented by naturalist metaphysicians like you. Of course, the real representation, the one which is consistent with observation, and true, is the classical representation.

So at the beginning everything is the same "size" and so indistinct or vague. — apokrisis

Yes this is my point. You assume that things are unintelligible at the beginning, therefore we ought not even try to understand the beginning. The theological way assumes that the beginning is fundamentally, and supremely intelligible. The idea of physical or material existence being derived from the intelligible forms of the creator, explicitly indicates that whatever it is which is prior to the beginning of physical or material existence is fundamentally intelligible. You ought to be able to see why the theological way is much more appealing to anyone with a desire to know the truth about the beginning. If intelligibility is lost in vagueness at the beginning, as you suggest, then there is no point in attempting to understand the beginning, it is simply impossible. But, if the beginning of orderly existence (as we understand the universe to be), necessarily proceeds from an act of final cause, then we might be inspired to proceed toward understanding that act.

In the Heat Depth, the visible universe has reached its maximum extent due to the inherent limits of its holographic event horizons - technical jargon for the distance any light ray can reach before the ground under it is moving so fast that effectively it winds up standing still ... as is the case when you fall into a Black Hole.

And it has also reached its minimum average energy density as every location within that spread of spacetime now has a temperature of 0 degrees K and so the only material action is a faint quantum rustle of virtual particles. — apokrisis

As I explained, this is completely perspective dependent, and cannot be considered to be anything even remotely related to the truth.

So this is a very different conception of "time" than your Newtonian one. It is not a collection of instants - truncated or endless. — apokrisis

My conception of time cannot be said to be Newtonian. I've read much of Newton's material and he doesn't even present a conception of time, just taking for granted what has come from before him. Furthermore, I never described any "collection of instants", nor did Newton rely on any such conception. Newton's three laws of motion clearly rely on time existing as a continuity. Continuous time, i.e. without the separation of instants, is what supports the concepts of mass, inertia, and velocity in Newton's laws.

And the only representation of time which I offered is a separation between future and past. so you're just misrepresenting what I've proposed, in order to say that you are offering something different. You are offering something different though, without appealing to the misrepresentation. You offer a naturalistic metaphysics based in a conception of time which does not respect the substantial difference between past and future. That is the issue which modern physics faces, it does not respect the substantial difference between past and future. That there is a substantial difference between past and future is the most fundamental ontological principle, as it is the principle with the best empirical support.

It is the only test of bad metaphysical theories. — apokrisis

Sure, pragmaticism might be the only test for metaphysical theories, but it has no business putting forth metaphysical theories itself. Look at the results you've described. Existing metaphysical theories lead to the conclusion that the beginning of the cosmos is not understood. Therefore the beginning of the cosmos cannot be understood. That's what you've described. The problem is that your pragmatism has not taken into account, and tried to understand the existence of itself pragmaticism, and such a venture leads us to final cause. So until you properly understand final cause, you cannot understand the failings of pragmaticism.

This is no different to what I mean when I say that they are different expressions of the same value. — Luke

OK, good, you are clarifying what you mean by expressions of value. MY point is that "different expressions of the same value" refer to different things. "Ten dimes" refers to something different than "four quarters".

You seem to think that the law of identity has some bearing on mathematics, or that A=A is somehow relevant to mathematical equations. I fail to understand what the relevance is. There would be little point using mathematical equations to state, e.g., 4=4. It seems that you just enjoy the confusion you create by treating the law of identity like a mathematical equation, or vice versa. — Luke

Fishfry has been insisting for months now, that what you call "different expressions of the same value" refer to the very same thing. It is claimed that each side of the equation, "2+2", and "4", both refer to the same mathematical object. I believe this idea is derived from the axiom of extensionality.

Feel free to explain the difference between "representing the value one dollar" and "representing something equal to a dollar" to anyone who cares to listen. — Luke

I just did. This is how I represent "one dollar", like that or like this, $1. Something equal to a dollar is "ten dimes", or "four quarters". I really do not believe that you can't see the difference, I think you're in denial.

I explained the difference, in reference to "2+2+4" and I will explain it again. "One dollar", just like "4", says something very general. It allows for "four quarters", "ten dimes", or whatever, just like "4" allows for "2+2", "3+1", 6-2", whatever. However, "ten dimes" refers to something specific. It cannot be represented as "four quarters", or anything else, because the particular form, "ten dimes" is specified, and ten dimes is not four quarters, though they both equal a dollar. Likewise, "2+2" represents something specific, and though it is equal to "6-2", we cannot represent "2+2" as "6-2". They have distinct meaning, just like four quarters has a meaning distinct from ten dimes.

Do you understand that "four quarters" represents something different from "ten dimes"?

Last time I explained this to you, just above, you completely ignored it and made no indication whether you understood what I said or not, arguing that in terms of value, they say the same thing. Sure, that's why they are equal, but 'the whole point is that say they are equal in terms of value does not mean that they represent the same thing.

Do you understand the difference between saying "4 objects", and specifying a specific configuration of four objects? A specified configuration is not the same thing as the more general "4 objects". This is the type of difference I am talking about here. In both cases, "2 apples + 2 apples", and "4 apples", we are saying something about four apples, but "2 apples + 2 apples" says something more specific than the more general "4 apples". So we cannot say that the two phrases represent the same thing. — Metaphysician Undercover

So please, before you proceed, give me some indication that you've understood what I have said here.

You can't be serious.

"Based on those samples we calculated an average value of so-and-so."

My young nephew and niece understand what's meant in the English language. If you can't, then you're missing something. — jorndoe

Sure, I'm missing something, I do not know what a national carbon footprint is. There's more than samples involved here, there's principles and a scale. Of which I have absolutely no understanding. Do you know how they take some samples and produce "the value of a national carbon footprint" from them? You might explain it to me, but I don't see how it's relevant.

Or rather that the past is the determining context. The future is created by what then becomes determinate due to the application of these constraints. — apokrisis

The problem here is that you do not account for the acting free will, final cause. It does not act according to these constraints, the determining context. It acts according to what is desired for the future. Yes it is constrained, but the primary objective is to bring about what is desired, regardless of constraints.

The present is the "now" where global historical constraints are acting on residual indeterminacy to fix it as some new actualised event. So the present is defined by the actualisation of a local potential via the limitations of global historical context. — apokrisis

So this scenario is missing something, final cause. You have "global historic constraints", and you have "indeterminacy", but you neglect the free willing being who utilizes the indeterminacy amidst the constraints, to bring about the desired "new actualised events". That is the key point, that the new actualized event is not any random event, produced from the indeterminacy amidst the constraints, it is a final cause event, intended for some purpose.

Potential becomes increasingly restricted or constrained over time as it realised in particular happenings. — apokrisis

This is a perspective dependent claim. "Potential" is a human conception which is perspective dependent. An apple hanging in the tree has potential energy due to the force of gravity. If it starts to fall it gains kinetic energy, but this is still potential, in the sense that it is the capacity to do work. And every time the energy is converted to a different form, it is still the same potential, according to conservation laws. The problem is that some forms of energy (potential) are harder for the human being to harness, and some might even appear to us, as impossible to harness. So we might say that potential (energy) becomes increasingly restricted, but this is a judgement based in the human perspective. Theories about entropy and heat death, only describe potential from the human perspective, the human capacity to harness energy.

Events remove possibilities from the world. And so shape more clearly the possibilities that remain. — apokrisis

So this is not really correct. Events change the possibilities in the world. Any event can open up as many, or more new possibilities as it removes. In reality an event just changes the possibilities in the world. And since the possibilities in the world are countless at any given moment, it doesn't make sense to even think about numbering them, or if there is more possibilities at one moment than at another. The law of conservation of energy states that energy, the potential to do work, remains constant. Some energy might slip away from the human capacity to harness it, as entropy, but this is a perspective dependent description.

Time thus arises as the macroscale description of this directional flow. Potential becomes increasingly restricted or constrained over time as it realised in particular happenings. The business of change takes on an increasingly determinate character - even if there thus also has to be a residual indeterminancy to give this temporal trajectory something further to be determined by contextual acts of determination. — apokrisis

Therefore, this is a faulty claim, created through the notion that the human perspective gives us the absolute. This is why the theological perspective is superior on this issue. It recognizes that claims such as the idea that potential is becoming increasing restricted, are simply a product of the human perspective. We have no idea of the potential available to a superior being like God, so such claims are not ontologically meaningful. For example, a culture living and thriving, in the designed conditions of a petri dish, (if it could think), would think that the available potential was running out, as it consumed the nutrients provided for it. But many other cultures could use the waste of that culture as potential for their activities. Such claims about potential becoming restricted are completely perspective dependent.

The present as an act of local actualisation has to emerge from the interaction of what is past (the development of some global contextual condition) and what is future (the indeterminancy still to be shaped - but not eliminated - by that process of actualisation). — apokrisis

But at the first moment in time there is necessarily no past. Can you apprehend this? All your talk about the past which the present emerges from is nonsense, because there can be no past whatsoever until time starts passing, and at that moment the past begins to emerge. So the past is really what emerges. As soon as there is time, there is an emergent past, and the past continues to emerge so long as time keeps passing.

Prior to this first moment of time, there can still be future, as the future is not determined by the passing of time, being prior to it. Thus if the past emerges it emerges from the future, because the future is prior to it. This is why the idea of infinite determinacy, or infinite potential, prior to the beginning of time, seems to make sense. It appears like prior to the first moment of time there is infinite potential because there is no past (constraints), and only future, therefore potential without constraint The reason why this doesn't really make sense is explained by the cosmological argument. If time hasn't started passing, and the potential is infinite, there would be nothing to make time start passing. So we would need to posit an act which would start time passing, and this actuality cannot come out of the infinite potential, because it's an actuality. The act which appears to be derived from potential, but is really an act (which appears to come out of the future), is the intentional act, final cause. So we assume that this is the type of act which orders time itself.

But vagueness would describe the state of things at the beginning of time because the indeterminism in the system is macro. There is no history of actualisation as yet, and so no determining context in play.

However by the time you get halfway through the life of the Comos - as we are in the present era - then it has grown so large and cold that it is most of the way to having only a microscale indeterminacy. The potential has been so squeezed that you can only really see it at the quantum level of physical events.

At the macroscale, the Cosmos is now getting close to the other end of its time - its classically fixed state of maximum possible global determinacy. It has arrived at what Peirce calls generality. (Or continuity, or synechism, etc).

Don't worry. It all makes sense. — apokrisis

Well, it makes sense, but it's completely a perspective dependent assessment of the situation which you offer so despite it making sense, it's not a good ontology. The human concept of potential is based in the human capacity to bring about change in the world. The human being, as a small, insignificant being in comparison to the universe as a whole, has a relatively small capacity to bring about change in the universe. So the human being assesses indeterminacy as being only in the microscale, the assessment of indeterminacy being directly related to the human capacity to produce change through intentional acts, final cause. A far more significant being, with a much greater capacity to bring about change through intentional, free will acts, would apprehend indeterminacy within what we call the macroscale. Your ontology is rather skewed, taking the human perspective as some sort of absolute.

But who wants to go with the MWI? — apokrisis

That's the point, if denying the LNC gives us something like MWI, who wants that?

Alternatively, this is pragmatism. Accepting that we can only model reality. And so what matters is that the model works. It can solve our practical problems. — apokrisis

As I've explained already, describing things on the basis of it works for some pragmatic purpose, is quite different from the quest for truth. Pragmaticism does not produce good metaphysics.

So can you lift the carpet and provide the detail of who is God and how He does these things? What first act did He perform with the Big Bang? What intent we can read into its unfolding symmetry breaking? How much choice did He have over the maths of the situation? — apokrisis

The point is to apprehend that the first act is of the same sort of act as the intentional, freewill act, or final cause, such that we can move in the proper direction towards an understanding of it. To deny that it was this sort of act, and pretend that it was some type of random fluctuation or something like that, is to mislead ourselves, guide us in the wrong direction.

No, I'm not arguing against the notion that 2+2=4. And, the fact that I've explicitly stated this numerous times, and explained that what I am arguing is the difference between being the same and being equal is a clear indication of this. It appears like you have not a good capacity to read English, because you intentionally interpret ambiguous words in a way which is inconsistent with what I've explicitly stated I am arguing, such that they mean something inconsistent with what I am arguing, when it is possible to interpret them in a consistent way.. This is why I did not want to follow you down this road of ambiguity, into discussing the meaning of "expressing a value", because I am familiar with this mode of argumentation of yours. You intentional misinterpret another person's writing, just for the sake of saying "see you've contradicted yourself". But the apparent contradiction is just intentional misinterpretation for the straw man purpose, which is a symptom of bad interpretation. .

If you cannot see the difference between representing the value "one dollar", (which is represented as $!), and representing something equal to a dollar ("four quarters", or "ten dimes"), then I think you've got a problem. Or, as fishfry seems to do, you do recognize the difference but deny that it's a difference, as if it's a difference which does not make a difference, or something like that..

2+2=4. You said that you don't deny this equation. How can "2+2" and "4" be equal if "2+2" does not express a value (i.e. a quantity, number, amount)? — Luke

I don't see how this can be so difficult for you.
Let's assume "4" represents an amount, number, or quantity. And we can also say that "2" represents an amount, number, or quantity. Doesn't "2+2" represent two distinct amounts, numbers, or quantities, related to each other with "+"? If "2" represents an amount, number, or quantity, how can you not see that there are two such amounts, numbers or quantities represented by "2+2"?

So, "2+2" does not represent a value, it represents two distinct values related with "+", and we say that this is equal to the value of "4". Here's an example, go to the store, and pick out three items. Now you have item number one, item number two, item number three, each has a distinct value. Place a plus sign between them and you have the cost of item number one plus cost of item number two plus the cost of item number three. Clearly what is represented here is three distinct values being added together. And we say that this is "equal" to one value, which is the sum of the three.

Therefore, a phrase such as "2+2", which does not express a value, but expresses a multitude of values in a specific relation, can and does, equal "a value".

Really? And yet you understood it fine? And well enough that you could, say, go look up annual carbon footprints and such...? (I could start listing examples ... maybe another day) — jorndoe

I really can't say I understood it at all. I have absolutely no idea what "the value of a national carbon footprint" is. Examples would not help. As I said, you need a scale of some sort.

The conclusion I draw is that yes, we can't presume complete determinism. But nor do we then need to lapse into complete indeterminism.

Pragmatisim is the middle path of constructing a theory of logic in which indeterminism is what gets constrained.

As an ontology, that says reality is foundationally indeterminate, and yet emergently determinate. And the determinate aspect is not merely something passively existent (as often is taken to be the case with emergence - ie: supervenient or epiphenomenal). It is an active regulatory power. The power of emergent habit. The power of formal and final cause to really shape indeterminate potential into an actualised reality.

So it is a logical system large enough to speak of the world we find ourselves in - complete with its indeterminant potentials and determining contraints. — apokrisis

If we look at reality, as we know it, to find out what distinguishes or separates the determinate from the indeterminate, we see that the past is determinate, and the future indeterminate, with the present separating these two. So Aristotle assigned indeterminacy to future events, what may or may not be, and these future occurrences are not ruled by the LEM. His famous example, the sea battle tomorrow.

If I understand Peirce correctly, he wants to take one step further, and say that the present, which separates the determinate past from the indeterminate future (LEM not applicable), is itself a "vague" division. So at this time, the present, the LNC does not apply. So we have a determinate past, an indeterminate future which can only be predicted through generalizations (LEM not applicable), and a present which violates the LNC.

The present is the most difficult to apprehend. If the future is really indeterminate, as free will, and final cause indicate, and the past is really determinate, as the fact that we cannot change what has occurred indicates, then the present must exist as a time of transition between these two. This transition we can call "becoming". Becoming, as Aristotle demonstrated, is incompatible with the logical categories of being and not being. This is one reason why he was led to violate the LEM. But "incompatible with", means neither being nor not being, and he insisted that the LNC be maintained.

Let's say that the present cannot be a crisp division between future and past, because this would deny the activity, becoming, which we observe to occur at the present. So the indeterminate world of the future cannot pass into the determined world of the past, at a crisp moment. Therefore we might need to assign vagueness to the present. But this vagueness is not a vagueness described by a violation of the LNC, it is described as an incompatibility with the LNC. This means that we cannot describe becoming, which occurs at the present, in the same bivalent logic of truth and falsity that we use to describe the static past, what has occurred, so it is more like a violation of the LEM. But if we look toward the future now, is it possible to say that the LNC is violated? Of the sea battle tomorrow for example, can we say that it is both true and false that it will occur. Suppose we take a many worlds interpretation of quantum physics, does this say that the sea battle both will and will not occur?

A fluctuation has to be a fluctuation in something - or so it would seem.

This is precisely the obvious hole in the vogue for accounts of the Big Bang as simply a rather large quantum fluctuation. Even if a quantum field is treated as the most abstract thing possible, the field seems to have to pre-date its fluctuation. Verbally at least, we remain trapped in the "prime mover" and "first efficient cause" maze you so enjoy. — apokrisis

This is the problem with wave theory. A wave needs a medium, and electromagnetism is understood by wave theory. Denying that there is a medium, and insisting that the activity is "wavelike" doesn't solve the problem.

A step further is "potential" properly understood as a true vagueness. A fluctuation is a spontaneity that is not caused by "the past". It is called for by the finality of its own future - the world it starts to reveal. This is one of the things that smashes the conventional notion of time you prefer to employ. — apokrisis

This idea of firstness really doesn't make sense. Suppose there is a first moment in time. Prior to the first moment there would be infinite potential, because there is only future with not any past. There would be absolute indeterminateness, with no past whatsoever, to determine anything. That means absolute freedom. However, whatever it is that acts with such absolute freedom, and causes the passing of time to start, must act for some reason, and this is why we assign final cause to this first act. So the indeterminateness of the first potential is not absolute at all, it's just that we do not understand the final causes (intention) involved.

However when we get to ontological questions about the machinery of creation, then this background to the laws of thought become relevant. The details of how things really work can no longer be brushed under the carpet, or shoved in a black box labelled "God". — apokrisis

Appealing to God is not to brush things under the carpet, but to realize the true nature of time, and how the first act must necessarily be an intentional act, final cause. Because when we look back to the point when all was future, and there was no past, (the first moment in time), we see that the acting thing must be capable of being completely in the future, and this is the nature of final cause. So as time passes, material existence can be determined according to the will of that being.

"We calculated the value of the national carbon footprint for last year to so-and-so."

"I greatly value a cold beer on a hot summer night." — jorndoe

The use of "value" in the first statement is extremely ambiguous because it is not related (grounded) to anything. The supposed "value of the carbon footprint" needs to be substantiated by a scale of some sort in order to have meaning. Without that scale the supposed "value" is meaningless. In the second case, "I" substantiates the value, with personal beliefs and a personal hierarchy. So the meaning of "value" is revealed by your use of "I".

Yes, because our discussion was in the context of mathematics. Or do you think that mathematics is all about monetary value (i.e. desirability/worth)? Don’t be daft. — Luke

So, back to my point then. If it is true that "4" expresses a value, then "2+2" does not express a value. The latter expresses a mathematical operation which is a different type of expression than an expression of value. Do you see the difference? Do you see that if "4" is an example of an expression of value, then in "2+2" there are two distinct values expressed, "2" and "2" whereas only one value "4" is expressed with "4"?

Do we agree that "value", being inherently subjective, is not a thing?

That's because we qualified value with "quantitative" value. But your assertion "different expressions of the same value" does not show that qualification. Hence the ambiguity. And I know the way you argue through ambiguity, I've been exposed to it too many times. So I would not accept an ambiguous proposition from you.

Thanks for the reference, it's a good read. You might understand, from what I wrote, that I do not disagree that it is possible to treat the LNC and LEM in the way that Peirce does. However, as I explained, he does this by divorcing these laws from the primary law, the law of identity. Determinateness is a function of identity. So it is by removing the need for an identified particular allows for Peirce's categories of the general, and the vague, in the first place. It is only in this context that these categories make any sense. Without an identified particular object, what Aristotle called "primary substance", the LNC and LEM are bound only by inductive principles, which are based in probability. Probability is not consistent with the three laws, when maintained as three, because identity of an object gives us determinateness. It is only by removing this determinate object, that we are forced to resort to general principles instead. But the general principles are produced from induction, which gives us probability instead of determinateness.

Further, the author of your referred article, Robert Lane, explains how Peirce allows that the term of predication might be defined in a multitude of ways. This is why I argued that reference must be prior to definition. If Bob Dole is the identified object, and we say "Bob Dole's hair is red", then the colour of Bob Dole's hair tells us what "red" is. This is the importance of having an identified object, substance, which provides an example of what the term of predication means, rather than having to rely on a definition, and the sophistry involved in different interpretations of the same word.

Notice how Robert Lane provides no indication, throughout that article, as to how Peirce shows any respect whatsoever to the law of identity in his discussion of the LNC and LEM.

Your point is simply that "2+2" and "4" are written differently or use different symbols. Or, as I said earlier, they are different expressions of the same value, or different ways of expressing the same value. Very profound :roll: — Luke

If you were looking for something profound, you've come to the wrong person. I was just pointing out the mistake of those who say that "2+2" and "4" refer to the same thing. It's really quite trivial, but some people seem to act like I'm attacking their God. Perhaps it was the behaviour of others which made you think I might be saying something profound.

By the way, in case I didn't make this clear last time, I consider "different expressions of the same value" to be ambiguous nonsense, and "different ways of expressing the same value" does very little to clarify what you could possibly mean. Do you even know what "value" means? It refers to the desirability of a thing, or what a thing is worth. How do you apprehend "2+2", or "4", as an expression of what a thing is worth?

You are reading it backwards. — apokrisis

Oh here we go, I see everything you do as backward, and see what I do as backward.

A logical definition of vagueness (and generality) is what helps ground your desired "truth-telling" apparatus. It tells you the conditions under which the laws of thought will fail - ensuring you do what is needed to fix those holes. — apokrisis

This is not true. We cannot ground truth in a definition. Your definition could be random fantasy. So you would end up with a coherent logical system without any correspondence with reality. That's why Aristotle introduced "substance", to ground logic in reality.

So you have to establish that you are dealing with a concrete case where a binary judgement can apply. The thing in question has to be that thing and no other thing. You can't simply presume it. You have to check it. — apokrisis

This is why we cannot begin with a definition. A definition consists of words. The words used must refer to something. So we must establish what the words refer to (identity) first, prior to proceeding to a definition. This is demonstrated by Platonic dialectic. You, and Peirce, have it backward. "Vagueness" represents the unidentified, what we have no words to describe. So you think that instead of analyzing "the vague", apprehending and identifying its various aspects, such that we can bring it out of its current appearance as vagueness, into a crisp clear understanding through the process of identifying its parts, we ought to just define "vague" as identifying something unintelligible.

Notice that you and Peirce, by claiming that vagueness is a real aspect of the universe, have actually proceeded in the way that I have described. You have identified something, and named it "vagueness". The problem though, is that you want to assign to this identified thing, the property of being inconsistent with the laws of logic. That is how we know it is an untruthful way to proceed. What it indicates is that you have not properly identified and described the thing which you call "vagueness".

And what does that effort look like? — apokrisis

I've been describing this effort. It is to provide real coherent and truthful descriptions, rather than the lazy way of saying "it's vague" and cannot be described in an intelligible way. The difference between your way and the theistic way, is that theism maintains that God is supremely intelligible, despite the fact that the human intellect cannot very well grasp Him. This is the opposite to your approach which says that vagueness inheres within the thing, making the thing impossible for any intellect to apprehend. Do you see why your approach is backward?

So you agree that the group resulting from this operation of addition is “4 apples”? That is, you agree that “2 apples + 2 apples” = “4 apples”? — Luke

Yes, I think I've stated about four times now, on this thread alone, that I agree that two plus two equals four.

It is obviously signified by the equation “2 apples + 2 apples = 4 apples”. Both sides of the equation are equal in value or quantity. They “represent the same thing” in terms of value or quantity, which is the point of the mathematical equation. I’m not sure what point you are trying to make instead. — Luke

I've been very clear in the point I'm making, so I don't understand why you're not clear about it. The point is that "2+2", and "4", do not represent the same thing, as "same" is defined by the law of identity, contrary to what has been claimed on this and other threads.

To say that "they represent the same thing in terms of value or quantity", is to qualify "same thing". It is to say that they have some quality which is the same, this quality being named as "quantity". Therefore it is does not say that they represent "the same thing" as determined by the law of identity. I can say "red roof" and "red car", and claim that these two expressions represent the same thing in terms of colour, just like you say "2+2", and "4" represent the same thing in terms of quantity. This does not mean that they represent the same thing in any strict definition of "same thing".

Jorndoe claimed that I confuse quantity with predication, but obviously quantity is a form of predication, and it is jorndoe who is confused, not I.

Thus, although it is true that "Any proposition you please, 'once you have determined its identity', is either true or false"; yet 'so long as it remains indeterminate and so without identity', it need neither be true that any proposition you please is true, nor that any proposition you please is false.

This is exactly what I was talking about. If you take the laws of non-contradiction and excluded middle out of context, remove them from their relationship with the law of identity, you no longer have anything to ground truth or falsity in, no substance. Without identity truth and falsity is not relevant.

Therefore, in the quest for truth, the law of identity is of the utmost importance. We seek to apply the law of identity, and this brings the other laws to bear fruit in relation to truth and falsity.

That is rather the point. Peirce was highlighting the presumption you have “truthfully” identified an object. Some concrete particular under the first law. And he was drawing out the logical implications of the corollary - the case when the principle of identity doesn’t apply. — apokrisis

When we are seeking truth, there is no such thing as "the case when the principle of identity doesn’t apply". If it appears to you, like the principle of identity cannot be applied, I would reply that you are not trying hard enough. Truth does not come easy, it requires effort.

We can never simply assume that the law of identity has been truthfully applied, Peirce was correct in this, and it's the starting point for skepticism. So when the logic leads to vagueness or other absurdities, we need to revisit how the law of identity has, or has not, been applied in these cases. It makes no sense to conclude that the law of identity cannot be applied, because that just demonstrates a lack of effort.

And why does "2 apples + 2 apples" "not represent the same thing" as "4 apples"? — Luke

Quite obviously,"2 apples + 2 apples" signifies two distinct groups of two apples, and the "+" represents an operation of putting the two groups of two apples together into one group. There is no such two distinct groups of two, nor the operation of addition signified by "4 apples". Therefore it is very clear that the phrase "2 apples + 2 apples" represents something very different from "4 apples".

Do you understand the difference between saying "4 objects", and specifying a specific configuration of four objects? A specified configuration is not the same thing as the more general "4 objects". This is the type of difference I am talking about here. In both cases, "2 apples + 2 apples", and "4 apples", we are saying something about four apples, but "2 apples + 2 apples" says something more specific than the more general "4 apples". So we cannot say that the two phrases represent the same thing.

Start over? — jorndoe

Go ahead. You're the one quizzing me. It appears we have great difficulty understanding each other.

(A4) If something is epistemically random, the uncertainty associated with that randomness can be arbitrarily reduced by sufficient sampling. — fdrake

I don't think I agree with this (A4). If the appearance of randomness is caused by inadequate principles by which the samples are modeled, then no degree of sampling will reduce the appearance of randomness.

The PNC is not about "truth". It is about "validity". Or indeed, merely about "computability". — apokrisis

That's incorrect. The three so-called fundamental laws of logic, the law of identity, the law of non-contradiction, and the law of excluded middle, are guidelines for making judgements of truth and falsity. That's why they describe a binary system. The first, the law of identity establishes correspondence between the language being used and an identified object which is the substance. Notice that the thing identified is an object, consistent with Aristotle's "primary substance", not a logic subject, which would be "secondary substance". The identifier, the name, let's say "Socrates", is presumed to directly correspond with an object, and only that unique object, by the law of identity . Any faults in this correspondence relation will allow falsity. Further, the laws of non-contradiction and excluded middle, provide guidelines as to what we can truthfully say about any identified object. We can say that these two laws make propositions of "validity", but what they tell us is that when we cannot decide which of the two contradictory propositions ought to be accepted, we need to return to the object, as the primary substance, to make that judgement based in correspondence, or truth.

If we replace the named object with a subject, secondary substance, suppose that "Socrates" refers to a subject rather than a named object, then our guidance is only validity. We are not dealing with correspondence, or truth, but validity alone, because we have removed the applicability of the law of identity which identifies an object We can make whatever predications we want of that subject, so long as they are valid, but we have nothing to substantiate these judgements, no object of correspondence, no means for truth, with only an imaginary subject.

So the PNC may be used as a tool of validity, or it may be used as tool for truth, depending on the relationship you build between it and the law of identity. Of course it is well known that the three fundamental laws must be applied together, as a unit, so your removal of that law from its relationship to the others, to say that it is only about validity, is a false representation. Maintaining that the law of identity relates directly to an object in correspondence, as it is intended to, and maintaining the proper relation between the law of identity and the law of non-contradiction ensures that we apply the law of non-contradiction toward truth.

But it is quite reasonable to question the claim the world in fact is divided quite so crisply. — apokrisis

This is a valid concern. It may be the case that the world is not actually arranged in such a way that the PNC applies. However, we have seen that the PNC is extremely useful, and applicable in a vast majority of cases. And, whenever it appears like the PNC does not apply we can assume that the descriptions we've made from observations are somewhat faulty, so that we can go back and revisit those descriptions until we find the appropriate ones in which the PNC is observed.

If, whenever it appears like some aspect of the world is not arranged in such a way that the PNC applies, we simply assume that this is the way that aspect of the world is, and leave that aspect of the world as unintelligible, then we have no inspiration to revisit our observation based descriptions, to determine the instances when the descriptions were faulty. So it really provides no pragmatic service to us, to assume that the world might not be divided so crisply, unless we can find another way to make these aspects which appear as vague, intelligible. All we can do, is assume that the world really is arranged in such a crisp way, which makes it intelligible to us, despite the fact that our descriptions make it appear unintelligible. Then we can continue to seek the deficiencies in our observation based descriptions, which make it appear unintelligible. But to assume that it might really be unintelligible is nothing but counterproductive to these efforts.

Indeed, that is the very thing that quantum indeterminism has challenged in the most fundamental way. If two particles are entangled, there is no fact of the matter as to their individual identity. They happily embody contradictory identities - until the further thing of a wavefunction collapse. A thermal measurement. — apokrisis

This is a good example. It demonstrates that we need to revisit those methods of observation, and keep doing so, until we find a way of description which makes this aspect of the world intelligible. To simply assume that this aspect of the world is unintelligible, (there is no truth) and therefore give up the effort is counterproductive.

So right there is a canonical modern example of how reality is vague (a quantum potential in which identity is accepting of contradictions). — apokrisis

No, it is not an example of how reality is vague. It is an example of how you are willing to give up on the quest for truth. Instead of researching all the observational premises, and theoretical principles employed, to determine the mistakes within, and correct them, so that this aspect of the world might become intelligible to us, you are completely uninspired to make that effort, and ready to sit in the corner whining "it can't be done", the world is simply unintelligible.

So a logic of vagueness, in which the PNC becomes an emergent feature of classical reality, has direct empirical proof now. — apokrisis

Again, you are incorrect here. The fact that a certain aspect of the world appears to be unintelligible to us, does not prove that it is unintelligible absolutely. Unless you can prove that the methods employed are the only possible methods, or the best possible methods, you cannot claim "empirical proof" of such a thing. That's actually a ridiculous sort of claim. It's like a blind person claiming to another blind person, to have "direct empirical proof" that there is no such thing as colour. Deficiency in one's capacity to apprehend something does not prove that the thing cannot be apprehended.

.. or of anything/whatever, hence the utility of a calculator.
Say, a set of my left ear, that soccer match, the Moon, and the experience of vanilla taste I had the other day when eating icecream, comes to 4 in quantity; kind of trivial to count. — jorndoe

So you're agreeing with me, a quantity is necessarily a number of things, therefore a property of those things, hence a predication. You named that group of things as a thing itself, "a set", and you predicate "quantity" as a property of that named thing, the set..

You're now confusing quantity, predication, measurement, ...
Say, a set of you and I comes to a quantity of 2, |{you,I}|=2|{you,I}|=2; kind of trivial to count.
Say, where ϕϕ = is human (predicate), it so happens that ϕ(you)∧ϕ(I)ϕ(you)∧ϕ(I), I assume.
You're making a wicked mess of things. :confused: — jorndoe

I can't agree with your conclusion. To me, your use of strange symbols is what is making a "wicked mess". We can look at what is meant by "quantity", "predication", and "measurement" without leaving the English language. Quantity and measurement are both types of predication. You seem to agree with me, so why complain that I'm confused and making a mess of things? In your examples you predicate "quantity" as the property of a set. Do you not consider this to be predication?

If ““2+2”...does not represent the same thing as “4””, then in what sense are they equal? — Luke

In a mathematical sense, obviously. As I explained to fishfry, it's really the only sense of "equal" that there is. "Equal" is a mathematical term. To say that two things are equal is to render them in a form which allows us to proceed with mathematical operations such as counting them. We cannot count apples and oranges unless we say that an apple is equal to an orange. It is only by assigning equality to distinct things that we are able to count them One apple is equal to an orange, and then we count them, 1,2. So apprehending different things as having an equal value allows us to count them, 1,2,3,4....

Notice that it is necessary and fundamental to the operation of counting, that equal things are distinct things. If equal things were the same thing, we would count the same thing over and over again, and the count would clearly be invalid. Therefore, we can conclude that it is a fundamental and necessary axiom of arithmetic, that equal things are not the same thing. Otherwise all arithmetic would be invalid, like counting the same thing over and over again to claim a quantity of things, is an invalid count.

But the equal sign is not the topic of discussion. — fishfry

It was when I first produced that quote. We were interpreting "2+2=4", a phrase which the equals sign is a part of.

2 + 2 and 4 point to or refer to or represent the exact same object. It's not possible to do math without that understanding. — fishfry

That is bull shit. Clearly I do not have that understanding, which you claim is necessary, in fact I insist it's a misunderstanding. Yet I can get four from two plus two. Therefore I can do math without that misunderstanding, which you say is required to do math. I don't deny that two plus two equals four.

I only assert the obvious, that "2+2", which represents an operation of addition, does not represent the same thing as "4", which does not represent an operation of addition. If you, and your mathematician friends, want to keep living your deluded lives of believing that they do represent the same thing, then so be it.

The PNC is a case in point. — apokrisis

Right, that's because without the PNC, there is no such thing as truth. That's why I frame it as a contest between pragmatic naturalism and the quest for truth.

But that is why pragmatism – particular in the Peircean sense - is the royal route to "truth". — apokrisis

Perhaps you can explain to me how can know the truth about the nature of the universe, when you claim that its fundamentals violate the PNC.

Your reaction to Peirce's relaxation of the PNC is telling. He makes the PNC an emergent limit whereas you cling to it as a brute fact. — apokrisis

Yes, you told me this already, to avoid the problem that "time is emergent" is contradictory, you simply assume that existence according to the PNC emerged at a later time than time emerged, therefore the contradiction of "time is emergent" is allowed, because this happened at a time when the PNC was not applicable.

Sure, you can have an argument against that. But it has to be better than: "I don't like the challenge it creates for my necessary presumptions". — apokrisis

The only necessary presumption I've expressed is the PNC. I adhere to it because I believe that without it, knowing the truth is impossible. In a quest for truth, one must adhere to some criteria for judgement. If you can show me how knowing the truth is possible when the PNC is violated, then I might give up that necessary presumption.

So, the PNC isn't "the" necessary presumption. A presumption is necessary as the criteria for judgement, and the PNC is the one which seems most fitting. But I'm open to other proposals. Do you have what you believe is a better criteria for judgement?

Quantity is a predication. There is no such thing as quantity, without it being a quantity of something. I think that's half the problem here, some people seem to think that quantity is a thing in itself, rather than a predication, as all measurements are. That way, instead of looking at what "2+2" really represents, they just assume that it represents "a quantity".

One might want to discuss "What is a force?" — unenlightened

I've got a better idea. Let's not discuss "force". It would take me years to get over that one.

Yes, we can consider this a contest between pragmatic naturalism and dogmatic theism if you like. One holds consequences here in the real world. The other not so much. — apokrisis

I'd prefer to frame it as the contest between pragmatic naturalism and the quest for truth. Your approach is, who cares if this naturalist metaphysics leads us into contradiction, so long as we adhere to naturalism at all costs. My approach is, if it leads to contradiction there's a problem with it, let's look at other proposals.