Also, more precisely, the empirical / computational concept of Entropy ... :death: — 180 Proof

I don't think Entropy provides us with a principle to distinguish between future and past. It may distinguish between before and after, but this is insufficient to distinguish future from past.

A very simple technique would be memory. We don't have memories of the future but we can remember what has happened. The part of reality that is now in the past imprints itself onto our memory and we can recall certain events with varying degrees of clarity. The future, being unexperienced, hasn't had a chance to imprint itself on our memory and so can't be remembered. This would be a simple method of distinguishing the past from the future. — TheMadFool

We touched on this briefly already. It's true that we remember past things, yet we might imagine future things. How do you think we distinguish, within our minds, remembered past things from imagined future things?

The past as memory is grounded in coherency between all memories. This is applicable both intra-self and between selves. When memories result in logical contradictions, something is amiss and we infer that something about our specified set of memories is wrong. Its only when all recalled memories flow effortlessly into themselves that we hold confidence in them. This applies just as well when we interact with each other. Our history is, experientially, composed of intersubjective memory. To the same extent that our memories, both personal and interpersonal, are found to be fluidly coherent and, thus, devoid of logical contradictions, our past is then determinate for us – unchangable. — javra

OK, this is good, consistency, lack of contradiction, corroboration, personally and publicly is an indication that what is in the mind is a memory, and not imaginary.

Intentions are all goal driven. In Aristotelian terms, telos guided. Add the premise of limited freedom of will to a) choose between different alternatives toward that goal(s) aimed for and b) to choose between different goals and the intention facet of the future becomes to the same extent (semi-)indeterminate. Add the fact that the future is partly created by the intentions of multiple selves, and this same indeterminate aspect of the future becomes even more so. — javra

This is the future part, goals and expectations, and I think it is much more difficult than the past, because of the doubt and uncertainty which you mention. But maybe this uncertainty is key to recognition of the difference between past and future.

Let's say that with respect to the past, it is easy to establish consistency and certainty in relation to what has happened, but in relation to the future it is more difficult due to uncertainty. This produces the distinction between determinate and semi-determinate which you referred to. But why do you think that the future is semi-determinate, not completely indeterminate? Doesn't this confuse the distinction, making it unclear? What produces the idea that the future is in some way determinate?

Returning to the consistency and lack of contradiction which we find in past memories, we find this also in our predictions for the future. However, predictions are very different from memories, and to be true they rely on the fulfilment of certain conditions. These are conditions of continuity. It is this continuity which gives determinateness to the future. If things continue to be in the future, the way they have been in the past, the predictions will be true. So the determinateness of the future is distinct from the determinateness of the past, because it relies on the condition of continuity, whereas the determinateness of the past is based in a corroboration of memories.

1.1 We have the law of identity that says that for each natural number, it is equal to itself. — fishfry

This is our point of disagreement. The law of identity does not say this, you are claiming this. If there is a law in mathematics which states that each natural number is equal to itself, it is not the law of identity. it is a law of equality. So what I am asking is, on what grounds do you say that this law of equality is a law of identity, and supplant the real law of identity with this one?

This puts the matter to rest. The expressions 2+2 2+22 + 2 and 4 44 refer to the same number. — fishfry

It shows me that they are equal, it doesn't show me that they are the same. That's the disputed point, that being equal means being the same.

These are strings of symbols manipulated by formal rules. — fishfry

Your mistake is in your citation of the 'rules'. The law of identity does not say that a number is equal to itself. I suggest you revisit the difference between identity and equality. "Identical" means the same whereas "equal" means having the same value. Do you see a difference between these two? When two things have the same value they are not necessarily the same thing. Being the same thing is what is necessary to fulfill the conditions of the law of identity.

On the math there is no question. 2+2=4 2+2=42 + 2 = 4 is an identity derived directly from the law of identity, the Peano axioms, and the definitions of the numbers and of + ++. As I say it's practically a definition. — fishfry

You keep saying this, that it is "derived directly from the law of identity", and you refer me to websites which discuss equality. Nowhere have I found the law of identity mentioned in this discussion of equality. So I really think that it is just you (and perhaps many others) who mistakenly believe that equality is derived from identity, and I am trying to point this out to you. Perhaps I am the one who is wrong, and equality is really derived from identity, but if so, where is the evidence of this?

So just go to PA to fill in the missing part, you'll see that for yourself. — Zuhair

Well fishfry seems to have done this already, but it doesn''t show identity, it shows equality. That is the point being discussed, you and fishfry seem to think that in PA equal things are the same thing.

the + is a two place function symbol, it is an assignment that sends pairs of objects to single objects per each pair — Zuhair

Right, this is what I said,. By showing parts, '2+2' indicates a particular division of the object, unlike '4' which indicates no such difference. So '2+2' denotes an object divided in a particular way, in half, whereas '4' denotes no such division. Therefore '2+2' denotes a different object from '4'.

When we way 2+2 = 1+3 we (in mathematics) mean that the single object that 2+2 denotes is "identical" to the single object that 1+3 denotes, that's what is meant. It means identity of denotation, that's all. — Zuhair

This is not true, '=' means equal, it does not mean identical. You are arbitrarily replacing what '=' really denotes, with "identical" and this produces a false statement. When you arbitrarily change the meaning of symbols in your interpretation, you create false statements.

I can exactly mirror you argument to say that "The Sun" and "The nearest star to Earth and Jupiter" do not denote the same object? since the first is just involving one object, while the later is involving a process of two things being near to a third object, and it involves the meaning of star, earth, and Jupiter, so it is speaking of TWO entities with a relation from them (near) towards a third entity that at the end points to that third object, so the denotation of those two expressions is distinct, which is WRONG. — Zuhair

This is totally irrelevant. What is WRONG, is to arbitrarily claim that two equal (having the same value) things are identical (the same).

And by rules of arithmetic (say PA) it PROVES that the single object denoted by 2+2 is exactly identical to (i.e. the same as) the single object denoted by 4. — Zuhair

This is what fishfry claimed to show above. But the demonstration does not show that the two are exactly identical, it shows that they are equal. Then fishfry states a misrepresentation of the law of identity, claiming that the law of identity states "that for each natural number, it is equal to itself". Where is your understanding of the law of identity?

We need first to agree on what constitutes a "denotation" of an expression, and then we can argue its identity. — Zuhair

What we need to agree on is definitions of "equal", and "same".

Equality axioms:
1. for all x (x=x)
2. if phi(x) is a formula in which x occur free, and never occur as bound, and y doesn't occur, and phi(y|x) is the formula obtained from phi(x) by merely replacing each occurrence of the symbol x in phi(x) by the symbol y, then all closures of — Zuhair

This is proof of your's and fishfry's mistake. You cite "equality axioms". Equality axioms are not identity axioms. You and fishfry both arbitrarily replace "equality with identity. Sophistry rules!

You are missing the power of potential. If a potential is not capable of causing anything, it's not potential, it's impotent. — Gnomon

I think you are twisting the distinction between actual and potential. Do you accept this division? If so, do you see that it is necessary for a cause to be actual? How can you say that a potential can cause something if you uphold the distinction between potential and actual and see that an act is required as a cause?

By definition, the cause of our world possessed the creative power to cause a world to exist. — Gnomon

Sure, but do you see that possessing the power to cause a world to exist is different from actually causing the world to exist? I possess the power to do all sorts of different things, but I don't necessarily do them. That's the point of contingent existence, 'potential' always refers to a multitude of possibilities, but the fact that one thing is actualized rather than some other possibility is only explained by causation. And, the cause must be something actual. So, we cannot account for the existence of our world, simply by saying that there was something which had that creative capacity, we need to also account for how that particular creative capacity was actualized.

Voltage is not a property, it's a prediction. — Gnomon

No, voltage is a description, not a prediction. According to Wikipedia it is the difference in electric potential between two points.

But that doesn't by itself entail that what they are denoting is not identical! — Zuhair

Right, and I've explained how what is denoted by '2+2' is different from what is denoted by '4'. Principally, '2+2' denotes two units of two whereas '4' denotes one unit of four. So, there are things which we can say that are true about 2+2 which are not true about 4, and vise versa.

The expression "The sun" and the expression "Nearest star to earth" are also not identical, the first contains two words, the last contains four words, but they do denote exactly the same object. — Zuhair

Sure, but '2+2' denotes two objects whereas '4' denotes one object. And, even if you construe '2+2' as one object, that object is divided in a vey specific way, in half. No such division is specified by '4'.

Now in PA the symbol 2 is meant to denote the object denoted by the expression S(S(0)), for simplicity let us use the notation || phi || where phi is a functional expression, to denote the OBJECT denoted by phi, so we have:

phi denotes || phi ||.

so according to that 2 is denoting the object || S(S(0)) ||.

Also 4 is denoting the object || S(S(S(S(0)))) ||

Now PA proves that the expression 2 + 2 is denoting the object || S(S(S(S(0)))) ||, which is the same object that expression 4 denotes! So by the meaning given to phi=pi in PA, PA proves that:

2+2=4

The proof of that is present in PA. — Zuhair

You seem to have left something out. You've taken the '+' for granted. You've shown me what '2' represents, and you've shown me what '4' represents. Then you claim that '2+2' magically represents the same thing as '4'. But all I see is a claim that S(S(0)) +S(S(0)) represents the same thing as S(S(S(S(0)))). Sorry to have to inform you of this, but you haven't provided the premise required to draw your conclusion. Consequently, you have no proof.

However to veer to YOUR side, one can in some sense use a terminology that separates identity from equality, you can stress that identity is full matching, i.e. even with expressions, those would be identical only if every property associated with one of them is also to be associated with the other whether at the language level or the meta-language level, and so you'll demand that everything must match between them even the way how those expressions are written. OK, by this we can say that equality is identity of denotation, and that identity is full matching. If we adopt such terminology then of course 2+2 won't be identical to 4, but 2+2 would be equal to 4, since there is identity of denotation of those expressions. This might be plausible, but it is not often used, well as far as I know of, but it might have its virtues. not sure though. — Zuhair

You really don't seem to understand the difference between equal and identical. Here's some principles which might help.
1. Two distinct things may be equal. For example, distinct human beings are said to be equal.
2. Two distinct things cannot be identical, "the same". "Same" refers to one and only one thing, (Leibniz principle for example, if x is the same as y then x is y, there is only one thing).
3. We do say sometimes, that a thing is equal to itself, as well as being the same as itself.

So, the First Cause of EnFormAction (creative power or energy) is BEING (the power to be; infinite potential). BEING (which I call G*D) is eternal, but non-physical. Physical beings are limited to space-time. Hence, back to digital information, 0 is non-physical potential, and 1 is physical actual. Likewise, BEING is potential (non-physical; meta-physical) and EnFormAction is the power to transform potential to actual : 0 into 1. — Gnomon

It appears like there is inconsistency here. You say that the first cause of EnFormAction is infinite potential. But don't you recognize that infinite potential could not contain any actuality, and therefore could not be a cause of anything? But then you say that EnFormAction is the power to transform potential to actual. Therefore it must be something actual, and also separate from infinite potential, which you call BEING.

In Aristotelian metaphysics, infinite potential is impossible, for the very reason that it would exclude any actuality, and therefore not be able to actualize anything. So "infinite potential" is really just incoherent nonsense, or a self-contradicting concept. This means that you need to change your description of BEING, because infinite potential could not be the cause of EnFormAction, and instead alter your inquiry to find a description for the cause of potential (BEING).

A simple analogy is a small battery in an electrical device. It is rated at 1.5 volts. But that potential voltage has no properties until it is actualized by completing a circuit from potential to actual and back; from nothing to something and back to no-thing (no property). The energy produced by the battery has no properties itself, except for sensible changes in the material through which it flows : heat, light, communication, etc. — Gnomon

You cannot really say that the potential of the battery has no properties because you have already defined it as 1.5 volts. This is the problem which arises if one tries to make sense of "infinite potential". Any 'real' potential is already limited, or restricted by the physical actualities which provide for its existence. The physical actuality of the battery provides for its potential, so that potential is restricted by those properties. Because any 'real' potential is limited in this way, it doesn't make any sense to speak of unlimited, or infinite potential. People often do speak of infinite potential though, as you just did, but Aristotle showed how this is purely imaginary, and cannot be substantiated by anything real. And it is important to note that it is not just the case that nothing real has been found to support the concept of infinite potential, and might be found in the future, it is the case that it is impossible for anything real to support the concept. Because it is impossible that there could be substance to the concept, the concept has no metaphysical application, it has absolutely no bearing on reality, and therefore must be rejected by metaphysicians.

Lawrence Krauss became famous for a book called The Physics of Star Trek in the mid-nineties, which analysed how much physical data you would have to convert to 'beam Scotty up'. My vague memory of it was that to fully convert all of the specifications for a single individual into binary code would take a stack of hard drives larger than the known universe. (Or was it solar system?? Of course, technology has advanced since then, but still....) — Wayfarer

That was before PS3 and the 'Cell' processor, therefore old information. The size of these things has really shrunk.

I understand 'naturalism' as epistemologically - methodologically - assuming that 'the natural world' can be intelligibly explained without recourse to, or excluding, any non/supernatural entities, forces, agencies, etc independent of any specific ontology, or explicitly metaphysical considerations. — 180 Proof

Is there actually people who believe that the natural world could be explained without metaphysical considerations? I haven't seen anyone even attempt at such an explanation, though I respect the fact that some people might claim that it could be done, without actually trying. But do they really believe this? Even Stephen Hawking turns to metaphysics. Do you know anyone who's actually tried to explain the natural world without recourse to metaphysics?

in a more informal manner, x is equal (identical) to y if every expression true of x is also true of y and vise verse, what we mean by true of is the truth of the denotation of that expression about objects and not the truth of its grammatical structure. — Zuhair

OK, I've said true things about '2+2' which are not true about '4'. Therefore the two are not identical. It's what I've been doing for last number of posts, explaining how '2+2' signifies something different from '4".

Actually equality is nothing but identity. In first order logic it boils down to substitutivity, as mentioned above. — Zuhair

Clearly equality is not identity, because different things are true concerning what is expressed on the right side of an equation than are true concerning what is expressed on the left side. This is by your own definition of "identical", above. How can you deny this?

But you need always to discriminate between what an expression is denoting and what an expression is. I already gave a simple example "The Sun" and "The nearest Star to Earth", in physics those two expressions are referring to exactly the same object but they are indeed two distinct expression! — Zuhair

I don't dispute that distinct symbols can refer to the same object. What I dispute is that '2+2' refers to the same object as '4'. So your example proves nothing.

In the game of arithmetic the expression "2+2" is identical to "4", in the sense that they both denote the same object.. — Zuhair

If this is true, then show me the object which both '2+2' and '4' refer to. If that object is a concept, then explain to me this concept which they both refer to. I've already explained how they each refer to a different concept, but you refuse to listen. So now it's your turn to describe to me this one concept which you believe both '2+2' and '4' refer to.

This appears to be the extent of your argument, a simple assertion that '2+2', and '4' both refer to the same object. Now see if you can justify this assertion by showing me the object which they both refer to. It will be difficult for you, because I already see that '2+2' refers to something completely different from '4', as I've explained. So you need to dispel this false belief that I have, demonstrate how the differences I described are not real, and show me how they really refer to the same object. Assertion does not justify.

I have repeatedly explained to you that the axiom of extensionality is directly derived from the logical law of identity. — fishfry

You provided no such explanation, only an assertion. The web pages you've referred me to do not support your claim. They speak of "equality", not identity. This is from the Wikipedia page on the axiom of extensionality which you referred.

Given any set A and any set B, if for every set X, X is a member of A if and only if X is a member of B, then A is equal to B. — Wikipedia

Where's the reference to the "logical law of identity" which you are asserting?

A mathematical equality states that the sets on either side of the equation are the same set. — fishfry

That is not true, you are inverting what is stated in the axiom of extensionality. It is stated that if two sets have the same members, the sets are equal. It does not state that the sets are the same, it states that if the members are the same, then the sets are equal. Therefore the sets remain distinct, as two equal sets, not one and the same set.

But if you are making a mathematical claim, you're just factually wrong. Mathematical equality is identity of sets. A mathematical equality states that the sets on either side of the equation are the same set. — fishfry

This is exactly the point of contention. Let's say that two things are said to be mathematically equal. By what law of identity do two equal things become the same thing?

They are the same according to the game of identity called as "equality theory". — Zuhair

We've been through this already. "Equal" does not mean "the same", or "identical". Identity is defined by the law of identity, equality is defined by mathematical principles. If you think that there is a principle of identity which makes equality into identity, then please produce this new law of identity, what you call "equality theory". I've asked fishfry for this principle of identity, to no avail.

There is a confusion here between expressions and what they denote, "The Sun" , "The nearest star to Earth" are two DIFFERENT (i.e. not identical) expressions, yes, but they denote the same object! so when we say for example "The Sun = The nearest star to Earth", what we mean is that the object denoted by the expression "The Sun" is Identical to the object denoted by the expression "The nearest star to Earth", — Zuhair

You are using '=' here in a way other than how it is used in mathematics. Argument by equivocation is useless to me. Sure you can use '=' to mean identical if you want, but we are talking about the way it is used in mathematics, 2+2=4 for example, and it is not used here to mean identical.

Along this understanding the expression "2+2" is meant to denote some object x, and the expression "4" is also meant to denote some object x, however both expression (though different) denote the SAME object exactly. — Zuhair

This is obviously not true. There are three symbols on the left side '2', '+', and '2'. There is only one symbol on the right side '4'. That is the first indication that the right side does not denote the same object as the left side. there is a plurality of symbols on the left, so there is likely a plurality of objects symbolized on the left. Furthermore, if the three symbols on the left side are meant to signify one entity, it is not the same entity as is signified on the right side, or else it would be signified in the same way as the right side. The symbols on the left are not meant to signify the same thing as on the right, or else the same symbol would be used. If they happen to symbolize the same thing this would be by mistake, but there is no mistake here. If two distinct symbols are meant to symbolize the very same thing, this would only be intended to create the illusion of different things being represented, and there would be no reason for this except to deceive. Therefore we must conclude that they are meant to symbolize something different. If the two sides were meant to symbolize the very same thing, the equation would read '4=4', and this would be a useless equation. And if the very same thing was meant to be symbolized by different symbols this would be an act of deception. Since '2+2=4' is not a useless equation, nor an expression of deception, we must conclude that what is signified on the left side is not the same object as what is signified on the right side.

I think I understand your point but I have some counterpoints. I believe you are saying that when we say 2 + 2 = 4 we are saying two things: One, that they represent the same natural number; and two, that 2 + 2 is a legal decomposition of 4, which is not necessarily known beforehand. So 2 + 2 = 4 asserts something more than merely saying 2 + 2 or 4 by themselves. And you're right about that. — fishfry

I wouldn't even say that. '2+2' represents two distinct quantities of two, being added together. So there are two distinct units, a unit of two, and another unit of two represent here with '2' and '2'. On the other hand '4' represents one unit of four, so there is only one unit represented, a unit of four. Notice there are two symbols of 2, so two distinct things represented on the left side, and only one symbol.'4', therefore one thing represented on the right side.

However it's not an ontological fact, it's an epistemological fact. — fishfry

What I am talking about is ontological, because it is the objects which are represented by the symbols. We need to first clarify what is represented by the symbols before we can proceed to epistemological principles.

That is, the partition of 4 into 2 + 2 is literally a matter of definition. — fishfry

It's not a partition which is represented, that would be division, four divided by two. What we have in 2+2 is two distinct units of two being unified with the symbol '+'. Conversely, we could take a unit of four, and divide it into two distinct units of two. That would be a partitioning.

So I think you have things reversed. Ontologically, 2+2 is clearly distinct from 4, but epistemologically we might say that they have the same value. They are equivalent by an epistemic principle, but distinct by ontological principles.

It was always an identity, even before we learned it. — fishfry

It's not an identity though, it's an epistemic principle. '2' Identifies one thing, '4' identifies another thing. That two '2's has the same value as one '4' is not an identity it is a conclusion drawn from an epistemic principle, what alcontali called number theory.

So I would say that 2 + 2 = 4 is an expression of the law of identity; but we did not always KNOW that until someone discovered it and taught it to others. — fishfry

That's not an expression of the law of identity at all. That's an expression of an equation. As alcontali explained, it's a conclusion drawn from the principles of number theory. Do you know the law of identity? A thing is the same as itself.

But there aren't. There are infinitely many different representations of the concept of 4, just as schnee and snow are two representations of the white stuff that falls from the sky in the winter. And you are right that it may sometimes take hundreds or thousands of years for us to discover that two representations represent the same thing. But they were always the same even before we knew that. — fishfry

What I've been trying to explain to you, is that '2+2' does not represent the concept of four, '4' does. As I explained already, if both sides of an equation represented the exact same concept the equation would be useless. But equations are not useless, they are very useful for many different purposes, and that is because they express an equality between two distinct concepts. It's nonsense to say that the right side and left side of an equation each represent the exact same concept. What could an equation do for us if all it expressed was '4=4', or '2=2', or '50=50'? If both sides represented the same concept, that's all we'd have. It's only because the one side represents something different from the other, that the equation is useful.

Do you agree that schnee and snow are identical, even though one has to pick up a little German (or English as the case may be) in order to discover that? — fishfry

This is not relevant. It's a simple fact that '2+2' does not say the same thing as '4'. There is no language in which '2+2' would be translated as '4'. Each of these says something different, and they maintain their difference in all languages, so '2+2' is never translated into another language as '4'. That would be a mistaken translation. So it's very clearly a mistake on your part, to say that '2=2', and '4' "are "two representations of the exact same identical thing". It seems so basic that I can't believe you actually believe that.

If I understand you correctly, you are saying that if a thing has physical existence, there is a cause of its existence, what you call "the cause of physical properties". After all, having physical properties is the same as having physical existence. This cause is what you call EnFormAction.

I prefer the extra space, it gives me more room to breathe.

Perhaps I should have said that Energy is what Mass is composed of. Mass is also a property of Matter. So again, what substance is Matter or Mass made of? — Gnomon

You can't really say 'what substance is', or 'what matter is', because if you could describe it you would be talking about its properties, not substance itself. Substance is what has properties, so you can't really describe it by referring to what properties it has.

Matter is now known to be composed of Energy, but what is energy made of? Nobody knows, so the essence of energy is undefined. — Gnomon

Energy is defined as the capacity to do work. Energy is not what matter is composed of, it is a property of moving objects.

So Philosophy is becoming relevant again for understanding the real world. — Gnomon

Yes, philosophy is relevant, as necessary to avoid misunderstanding, like above.

And in visual psychology, it should not be regarded as an error if a test subject reports that he saw 5+7 as 13. It simply means that visual phenomena are not a good model of ordinary arithmetic and vice versa. — sime

I think my eye doctor would prescribe glasses if I saw 5+7 as 13.

There was also a 90-100% chance it would hit Florida. No hurricane there either. — NOS4A2

The map shows the probability of tropical storm force winds, which Florida did receive. I believe Florida also receive some hurricane force winds as well as a large storm surge.

I took philosophy in university in the eighties, started as a general arts student. My first year philosophy professor called me to his office, and was very critical of the questions I was asking in class, but said that he was quite impressed that I had actually read the required readings, while the vast majority of his first year students never do. He recommended that I continue in philosophy.

Yes, actually, because you can see the data yourself with your own two eyes. — NOS4A2

Hmm, a 5 -20% probability of tropical storm force winds in the extreme south east corner of Alabama, no hurricane there. No wonder it wasn't included in the forecast.

It is a thing. It’s a non-scandal perpetrated by the press in the US. It’s quite shameful. — NOS4A2

The problem is that when the president issues a warning, you'd expect people to take heed. But if the president is always crying wolf, just to watch people get excited, then there's a problem.

Computers, unlike typewriters, auto format, with some fonts having letters of differing sizes, and some fully justify the words on both margins. This causes the computer to reformat the spacing. It's not correcting grammar or punctuation. It's just formatting. — Hanover

That's bullshit. The computer doesn't automatically remove all double spaces because this reformatting is required to make the words fit within the margins. Come on Hanover, get real.

True, probable because the people that designed the editing software figured that an educated person would only leave double spaces by accident and that everything else they wrote was because that was what they wanted to say. — Sir2u

Those software designers were wrong then. Do you think that no one has corrected them on this yet, or do they persist in this practise just to exercise control over us peons, and continually display this mastery with incessant annoyance? Spell-check is bad enough, when you have to re-correct stuff after it acts, then the spell-check sneaks back in again to overrule you when you hit 'send'. But at least it's there for a good reason. This double space editing is only there to let you know that the programmers have control over how your composition (creative work) will appear in it's finished form.

On the other hand, Quine's naturalistic epistemology involves a conception of objects as posits that we introduce in our theories about the world. — Janus

When you have to posit the existence of something, whose existence is not justified by anything other than that it is needed to make a particular theory work, you can be sure that the theory is faulty. This is the case with the cosmological constant (post above). But the existence of objects is much more complicated than this because it is supported at a fundamental level, empirically. Individuating, and identifying objects is a fundamental object (goal) of sensation. So empirical experience itself, as sensation, is fundamentally guided by this 'posit', that there are objects.

This places that 'posit' (the existence of objects) as prior to sensation itself because sensation is guided toward recognizing objects.. But when we reflect on this we see that this original, or primitive posit, is not really a posit of the existence of objects, but of what is required for us to conceive of objects. This is evident in Kant, as what is required for the "possibility" of experience, and it is manifest in Aristotle as the concept of "matter". There is not a primitive positing of the existence of objects, but a preconditioning which establishes the attitude (belief?) which allows us to apprehend the world as consisting of objects.

So the process of understanding the existence of objects might be something like this. Objects are present to the conscious mind, so we are inclined to simply assume or 'posit' their existence. But when we reflect on this, we see that this assumption is not really justified, it is only supported as a precondition for sensation. And, we are warned by philosophers to be skeptical of sensation. With a healthy dose of skepticism, and analysis, we see that this precondition doesn't really exist as an assumption of the existence of objects, or a positing of objects, what it is is extremely complicated and difficult to understand, and that's why metaphysics is not simple.

I will depart from this thread, feeling on my side that I can't talk to someone who is claiming that 2 + 2 is something other than 4. And also feeling deep down that I must be missing something really profound, but I don't think it's something I'd want to get even if I could. — fishfry

I suppose the feeling is mutual. I really cannot believe that there is a rational human being who truly believes that 2+2 is the same thing as 4. Isn't this what we learn in basic math, first grade? You take two things, add to them another two things, and you have four things. Very good. But we can get four by adding three to one, or by subtracting two from six, and an infinite number of 'different' ways. So it is impossible that 2+2 is the same as 4, because there would be infinitely many different things which are the same as four. Does it make any sense to you, to believe that there is an infinite number of different things which are all the same? Or can you see that 2+2 is not the same as 8-4?

Einstein didn’t predict the expansion of the universe, or rather this theory made no such prediction. I think it was Hubble and Le Maître that discovered the expanding universe some years after Einstein published his general theory. — Wayfarer

That's right, Einstein wanted a static universe, and introduced the 'cosmological constant'. It was meant to counter the effects of gravity which Einstein thought should be making the universe contract. Friedman argued otherwise. The point is that this principle could not be held because observations of the universe, interpreted through the lens of general relativity, revealed an expanding universe, which is not what Einstein thought general relativity should predict.

Now it is understood that expansion is accelerating, so dark energy is posited to account for this. In reality, general relativity cannot predict anything concerning the expansion of the universe, it has no mechanism for dealing with this phenomenon. And that's why the issue is so confused, the phenomenon known as "the expansion of the universe" is completely inconsistent with general relativity. The appearance of "the expansion of the universe" (which is a completely confused concept) is produced because the universe is observed from the artificial perspective of general relativity, and this perspective is faulty, so confusion results. Here's a quote from the Wikipedia page on "cosmological constant":

According to quantum field theory (QFT) which underlies modern particle physics, empty space is defined by the vacuum state which is a collection of quantum fields. All these quantum fields exhibit fluctuations in their ground state (lowest energy density) arising from the zero-point energy present everywhere in space. These zero-point fluctuations should act as a contribution to the cosmological constant Λ, but when calculations are performed these fluctuations give rise to an enormous vacuum energy.[7] The discrepancy between theorized vacuum energy from QFT and observed vacuum energy from cosmology is a source of major contention, with the values predicted exceeding observation by some 120 orders of magnitude, a discrepancy that has been called "the worst theoretical prediction in the history of physics!".[8] This issue is called the cosmological constant problem and it is one of the greatest unsolved mysteries in science with many physicists believing that "the vacuum holds the key to a full understanding of nature".[9] — Wikipedia

the lounge is hidden from view because it makes the philosophers of the site look bad if it comes up on the front page.

You show your age it seems. — Hanover

It's not a question of which age group has a better method, it's a question of why does the computer take it upon itself to correct this non-mistake. My spell-check never corrects this. And, my spell-check shows me many errors which, if I post them will pass right through onto the posting. So there's all kinds of grammatical errors which are not corrected when I post, yet for some odd reason a double space after a period is corrected. Why? Is the double space such an evil thing that it is singled out as the one thing which needs to be corrected? And it can't even be said to be 'wrong' anyway, just something practised by a different age group.

It is in a forum, spaces count the same as any other character. That means that for every sentence there is an extra character. over several thousand sentences that adds up to a lot of extra space on the server drive and extra download time for the people viewing the thread. There are some people that have limited data mobile services so every byte counts. — Sir2u

OOKK, BBuutt II bbeett II ccoouulldd ddoouubbllee uupp aannyy cchhaarraacctteerr,, aanndd oonnllyy tthhee ssppaacceess wwoouulldd bbee eeddiitteedd..

Same for distance, which, as Einstein pointed out, is actually the same thing (i.e. spacetime.) — Wayfarer

But this is a mistaken perspective. The concept of "the expansion of the universe", which is a consequence of the Einsteinian perspective, gives us a sort of movement which is incompatible with "movement" within the theoretical framework, distances which are not distances. So the theoretical framework given by Einsteinian relativity must adapted, exceptions described, in order to account for this movement which is not movement according to the framework. This indicates that the proposed relationship between space and time, which is described by Einsteinian relativity, is deficient, it's incorrect.

When a theory is supposed to describe the relationship between two things, and it comes up short, we can conclude that the theory is incorrect. But modern physics is trapped within the confines of this incorrect theory, and this is really what is behind the "observer problem". Physicists have assigned to the observer a perspective which is false. The physicist observes through the lens of 'spacetime', and doesn't understand how the deficiencies of the theory affect the observations. From this false perspective the observations are incomprehensible.

Edit: The software automatically edits out the extra space, so you'll have to use your imagination, or I can come over to your house and show you with a pen and paper. — Hanover

Why? I learned in school to leave a double space after a period. So I diligently do that. Now the computer always edits it out. Why? It's not like it's a huge waste of valuable space or anything.

The view I am coming around to is that 'nothing exists without a perspective'. — Wayfarer

I find that this is easy to understand when one considers the temporal perspective. If you imagine what the world, or the universe, would be like with no human beings, then there is nothing to establish the temporal perspective. So you can ask yourself, at what time, in the existence of the universe, are you thinking about. Now, you cannot tell yourself that you are thinking about now, the time when human beings would have been here, and the universe would be exactly the same at this time, as it is now, because the exercise is to remove the presence of human beings.

This leaves you with the entirety of the temporal extension of the universe from its beginning to end, with no means of choosing one particular time, at which time you could say that the universe would be like this or like that. And, since things are moving, there is no way to say this would be here, or that would be there, because we are considering all of time now, so everything would sort of be everywhere. Furthermore, If you wanted to imagine how things would be like at a particular point in time, you would need some way of determining what a particular point in time is. We experience time as passing, so how long of a period of time would a point in time be, a Planck length? a nanosecond? a second? a minute? an hour? a year?, a few billion years? It doesn't even make sense to talk about a particular point in time without the human perspective, because the point in time is a product of the human perspective

I walked through this in detail a few posts ago. In the Peano axioms they are both the number SSSS0. In ZF they are both the set {0, 1, 2, 3}. = { ∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}} }. — fishfry

This does not show me the principle of identity. Saying that two things are the same does not make them the same. It's a hollow assertion without a principle. And I don't see any reference to sameness in your reference.

We must be talking past each other in some way. I cannot conceive of anyone claiming 2 + 2 and 4 are not the same thing. — fishfry

I can't believe there is a person who does not see a difference between 2+2 and 4. The two are equivalent. And, as I explained equivalence would be meaningless, and equations useless, if there was not a difference between the left side of an equation and the right. The Wikipedia page on "equation provides an analogy. "An equation is analogous to a scale into which weights are placed." Do you see that the things on the two separate sides of a balance are not "the same"? They are said to have the same weight, but this does not make them the same thing.

So, in the case of ZFC, by what property are the two sets said to be "the same"? It's not the same weight, as in the scale analogy, nor is it the same numerical value, as is the case in the equation (what alcontali refers to as "number theory" above). What is the principle of sameness?

Perhaps you have a reference to support your point of view. — fishfry

If you have no idea of what equivalent means, or of how equations are used, then I don't think I can help you. If you are simply asserting 2+2 is the same as 4 without thinking about what you are saying, because it supports your metaphysics, then why don't you smarten up?

But you claim that 2 + 2 and 4 are not the same object in ZFC. And THAT is an area where I am not ignorant. You're just wrong. 2 + 2 and 4 represent the same set in ZFC. — fishfry

I fully acknowledge, that in ZFC 2+2 is "the same" as 4. I am not denying this. I am saying that it is wrong, because it violates the law of identity, without any justification. If one wants to establish a principle in violation of a fundamental law of logic like the law of identity, then that person ought to provide justification for the proposed principle. Without justification, use of that principle is mere sophistry.

Well, first there is the understanding that the "=" symbol pretty much never means "identical". — alcontali

Tell that to fishfry, who is arguing the opposite, that the left and right of the equation actually are the same.

You tell me how 2 + 2 is not 4. If it's not, what is it? — fishfry

Refer to alcontali's post above. Thanks al.

Of course 2 + 2 is the same thing as 4. I cannot imagine the contrary nor what you might mean by that claim. — fishfry

Explain to me then, how this set '2+2', is the same thing as this set, '4'. They look very different to me, and also have a completely different meaning. By what principle do you say that they are the same?

But more importantly, they are the same set in ZFC. So it's not an example of your claim that ZFC allows two distinct things to be regarded as the same. — fishfry

Yes, that's exactly the point. ZFC says that they are "the same" set, when they are clearly not the same by any intelligent reading of the law of identity. Therefore ZFC must employ some other principle of identity in order to say that they are the same. Can you state ZFC's law of identity?

But you hold that 2 + 2 and 4 are not the same? How so? Without quotes around them they are not strings of symbols, they are the abstract concept they represent. And they represent the same abstract concept, namely the number 4. You deny this? I do confess to bafflement. — fishfry

This is absolutely false. The symbol 2 has a meaning, the symbol 4 has a meaning, and the symbol + has a meaning. Clearly 2+2 is not the same concept as 4. Otherwise there would be no point in writing the exact same concept in two different ways, and the symbol =, which is commonly used to express the relationship between these two different concepts, would be meaningless. Do you see that 4=4 would be a meaningless equation in mathematics? Therefore it is very evident that 2+2 is not the same concept as 4, and the = sign expresses a meaningful relationship between these two distinct concepts, a relationship which is quite different from the useless expression of 4=4. The usefulness of an equation is due to the fact that something different from what is expressed on the right side, is expressed on the left side

Here's the sort short irony:

"The number three is used in the Torah to mediate between two opposing or contradictory values. The third value mediates, reconciles, and connects the two. Three is the number of truth." — 3017amen

Having to deal with the number three is what messes up the Pythagorean scale, causing the occurrence of the comma. For example, If we start with "one" unit of frequency, a designated length of string or whatever, as the base unit, then we double to two units, this gives us the harmony of the octave. If we double again, we have four, as the next octave. Now three is excluded, but we want to fit it in, as the half way point of the octave, halfway between two and three, thinking that the halfway point ought to be harmonic. The halfway point of the first octave is one and a half (3:2), and of second octave it is 3.

The problem is that the first set of octaves produced, 1, 2, 4, 8, etc., is fundamentally incompatible with the second set which is produced at the halfway point, 11/2, 3, 6, etc. However, if we take the base unit, 1, and cut that in half to get 1/2, this is compatible. So we can always take a designated frequency, cut it in half and produce a perfect harmony of an octave. But we cannot take a designated octave and cut it in half, to find the midpoint, without producing dissonance.

You made the statement that ZFC allows two different things to be equal. I said I know of no such example and you have not backed up your claim or put it in any context that I can understand. You must be thinking of something, I'm just curious to know what. — fishfry

I was in discussion with alcontali, referring to what was said by alcontali:

S1 and S2 describe the same set. Therefore, S1 = S2. — alcontali

2 + 2 and 4 represent the exact same mathematical set. '2+ 2" and '4' are distinct strings of symbols. I don't know any mathematicians confused about this. And, as you agree, the discovery that these two strings of symbols represent the same set, is a nontrivial accomplishment of humanity and is meaningful. — fishfry

The point I made is that 2+2 is not the same as 4. So if set theory treats them as the same, it is in violation of the law of identity.

I really don't understand your remark that ZFC allows distinct things to be regarded as the same. Unless you mean colloquially, as in the integer 1 and the real number 1 being identified via a natural injection. — fishfry

'2+2' is clearly different from '4'. Each of those two expressions are composed of different symbols, having different meaning. Despite the fact that they are said to be equal, in no way are they the same. If ZFC allows that they are the same, as you say above, then ZFC allows two distinct things to be regarded as the same.

Since they are not the same according to the law of identity, by what principle of identity does ZFC claim that '2+2' is the same as '4'?

Furthermore, their assumed input could still truly be random, because there is no method available to distinguish between the output of unknown mental faculties and sheer randomness. — alcontali

I think we've been through this all before, you and I. I don't think that just because there is no method available, the input is out of reach. Methods come into existence, and evolve, so things which are reached by existing methods were at one time out of reach. Therefore it's reasonable to believe that a method could be developed to reach the things which presently cannot be reached. So if someone reaches a conclusion through a mental process which you consider to be by your standards, not rational, this does not mean that it is impossible to reach that conclusion through a rational process. It is possible that the required rational process could be developed.

Still, the uncanny sensation of recognition suggests that this link is not necessarily, completely out of scope for other, unknown mental faculties. — alcontali

Yes, my point is that it requires effort to distinguish the good from the bad, but these "unknown mental faculties" may be brought into the realm of the known.

Very good description. I see why you say that my description is confused. I see the importance of the problem in a slightly different way.

We produce perfect harmony with the octave, doubling the frequency. But every time the frequency is doubled, there are many frequencies, notes, in between. These in between notes must be determined, in order to scale the octave. This requires division of frequency. The Pythagorean method proceeds by using only divisions of half. Half way between one and two is one and a half. Half way between two and four is three, half way between four and eight is six. Notice, that the only division employed is the half, though the half is always taken three times, each time it produces another in between note to scale the octave. The half is always in harmony with the unit that it is half of (as an octave) and that is why the Pythagorean method of scaling the octave is considered to be more truly harmonic. That the Pythagorean method produces the Pythagorean comma is a problem which has not been resolved. Going to a less harmonic system of division, equal temperament, is not a real solution. It's a simple fix which lowers the quality.

It is the same situation as with a sequence generated by a Mersenne Twister. From the outside, it looks random. From the inside, we can see that you will always get the same sequence depending on the seed that you use. Is the sequence random? For outsiders, yes. For insiders, no. — alcontali

It's not arbitrary then, it just looks arbitrary, in appearance, but it really is not. That it is arbitrary is an illusion. Would you see mathematical axioms in the same way? They look arbitrary, but they really are not. What is required to get beyond the illusion of arbitrariness is to get inside of the head of the artist. This does not mean to literally get inside, but to learn how to think in the same way as the artist. Then you will no longer be an outsider who sees mathematical axioms as arbitrary.

That would almost amount to saying that an artist's design choices are exclusively rational, and could therefore even be expressed in formal language. My own take is that I do not believe that. I believe that artists make use of other mental faculties, that are not rationality, when making their design choices. I also do not believe that it is possible to express, even in natural language, the output of these other mental faculties. — alcontali

Well, that would depend on how you define "arbitrary". Use of mental faculties in one's decisions negates randomness. If such decisions are arbitrary, then how do you understand "arbitrary"?

Actually, I don't know if I quite got it right. I learned a lot (from jamalrob I think) on the old forum, and followed up study of some of the principles on my own, being a musician and composer who was always lost in the theory. I believe the basic issue is that division starts from an assumed unit, which is divided, while multiplication starts from an assumed multiplicity. So, despite the fact that we look at division as a simple inversion of multiplication, it is not, there is a fundamental inconsistency between the two. One presupposes a unit, while the other presupposes a multiplicity. Since a conclusion always follows the principles of the premises, an act of division will always produce a specified unit, while an act of multiplication will always produce a specified multiplicity.

I think that resolving the problem of the Pythagorean comma will produce the universal key (the key to the universe), because it requires a determination of the fundamental unit of time, and producing a scale based in something real rather than an arbitrary frequency. This is where the wave theory of modern physics is currently lost. I am obsessed

Arbitrary axioms are the hallmark of creativity! — alcontali

Well, I really don't agree, and I think you misunderstand creativity. Art is not a product of arbitrariness, there are reasons for what the artist does, purpose, so arbitrariness is not the hallmark of creativity.

I don't think that can really be true though. Math IS useful and meaningful because it takes human effort to determine whether two different representations of a thing are actually the same thing. Don't you agree? 2 + 2 = 4 is formally a tautology. But historically, it was a really big deal for humanity. Agree or no? — fishfry

Yes I agree, but the key is understanding the limitations of math. If some logician were to argue that '2+2' and '4' are both the very same thing, because they are equal, we'd have to correct that person, showing that these are symbols, and '2+2' clearly has a different meaning from '4'. But then we are at the position of needing to explain what it is that is signified by these symbols. If we take the Platonic route, we say that the numeral '2' represents the number 2, and we avoid the question of meaning altogether. There is now no problem of what '2' means, because '2' represents a mathematical object which is 2. But now we are totally lost, because we can have no idea what the number 2 is, it's just a mathematical object. We cannot turn to meaning, because then we might as well just go back to the symbol, the numeral '2', and ask what it means. At this point we cannot turn to Platonism and say it's a mathematical object, because we want to know what the symbol actually means, not just say that it stands for an object (the existence of which cannot be validated).

I seem to recall the old philosophical standby of the morning star and the evening star, which appear to be two different things but (upon astronomical research that took millennia) turn out to be the same thing, namely the planet Venus and not a star at all. — fishfry

OK, but this analogy assumes that there is a thing, an object which "morning star" refers to, and it turns out to be the same object that "evening star" refers to. We cannot do that here with mathematical objects, because as I described above, if the symbol refers to an object, then we deny that there is any real meaning. The symbol stands for a mathematical object, and this is the only meaning there is. The symbol stands for an object, and that's that. There is no meaning. This is pretty much the stance that alcontali takes, axiom s are arbitrary, so there is no such thing as the axiom's meaning, it's just an arbitrary thing.

If you reduce everything to the law of identity, you are saying those millennia of observation and theory and hard work by humans means nothing. I don't accept that. — fishfry

No, this is exactly the opposite to what I am arguing. When we adhere to the law of identity, then everything has an identity proper to itself, therefore its own meaning. This does not rob meaning from mathematics, it only establishes clear limits to the possibilities of mathematics, so that mathematicians will not believe themselves to have accomplished the impossible, like putting the infinite within a set.

Modern tuning of the twelve tone scale is usually "equal temperament", in which the octave is divided into twelve equal parts.The Pythagorean tuning of the 12 tone scale is called pure temperament, or just temperament, because the designated notes are derived from the 3:2 ratio which gives the perfect fifth, pure consonance. With the numerous octaves required to produce the twelve notes of the scale in the Pythagorean method, a slight gap opens up, called the Pythagorean comma. This creates a slight difference between the same note, played in a different key. So modern musicians have turned to equal temperament to avoid this problem, making modulations smooth.

Incidentally, the problem of the Pythagorean comma is a function of the relation between frequency and time. There is no starting point, no base unit or fundamental frequency. So divisions or multiplications may proceed infinitely. Therefore your harmonies are always determined by your starting point, which due to the nature of time cannot be well-defined. I believe it is this same inability to define perfect harmony, because there is no base unit, which produces the infamous uncertainty principle from the Fourier transform. You might say that the Pythagorean comma and the uncertainty principle are symptoms of the very same problem.

They probably worked it out by trial and error until they got something that sounded good to them. — Bitter Crank

Well, you cannot keep drilling holes in the same piece of wood, in the process of trial and error, because your instrument would be ruined. So measurement would be necessary, to ensure that the errors were not repeated, and the successes were maintained. I think therefore, that the holes in your 40,000 year old instrument were measured. Otherwise it wouldn't be an instrument at all, it would be a stick with random holes.

The axiom of extensionality depends on the law of identity, which is a principle of logic and not of set theory. A thing is equal to itself. Then we define two sets to be equal if they have "the same" elements, meaning that we can pair off their respective elements using the law of identity. — fishfry

By the law of identity, two distinct sets cannot be the same. If they actually are the same, then they are necessarily one, the same set. It's contradictory to say that two things are the same. If it is the same, it is only one. Being equal and being the same are very different because "equal" refers to a multitude while "same" according to the law of identity refers to one, and only one. If ZFC states that two equal things are the same, it clearly violates the law of identity, which necessitates that the appearance of two is an illusion, there is really just one (Leibniz principle). And we cannot talk about one being equal, because there is nothing for it to be equal with.

This is a fundamental problem with the so-called "objects" of mathematics. Distinct things are allowed to be the same object, contrary to the law of identity, through the means of a principle of equivalence. Mathematicians will defend the existence of these objects, as objects, through reference to a difference which doesn't make a difference. But strict adherence to the law of identity allows no such contradictory nonsense. If there is a difference between what "2+2" refers to, and what "4" refers to, then these cannot be the same object, despite the assertion that this is a difference which doesn't make a difference.



I am concerned with the principles of the system, not any installed base, or legacy, these are irrelevant to the acceptability of the principles. I know that you believe axioms are completely arbitrary, making such things very relevant, so join the mob, if you like the "mob rules" philosophy.

That's all fine and dandy, but the instrument in question proceeded Pythagoras by maybe 40,000 years. What the 40,000 BCE people had discovered was a) pleasant sound could be made by blowing into a hollow bone and that b) holes in the bone, covered and uncovered, would change the sound. c) one could play the same sounds over and over. Not enough of the bone remains to know how the sound was initiated; an unknown amount of the bone tube has been lost--we can't know how long it was. — Bitter Crank

If the positioning of the holes was not random, it was measured. And it couldn't have been random or the sound wouldn't be musical. Don't you agree? The fundamental ratios, which Pythagoras laid our were very basic division, 1/2, 1/3, and 1/4. The 3:2 ratio is one and a half. I would expect that the people of 40,000 years ago knew how to divide lengths into halves, and into quarters, that was how harmonies were produced.

I believe Pythagoras developed the twelve tone scale, based on the 3:2 ratio which gives the prefect fifth. Though the designated intervals could be recognized by the human ear, he taught that they ought to be determined my mathematical ratios to maintain the pure tones. The Pythagoreans extended the mathematical principles of harmony to the entire cosmos such that each of the orbits of the planets were described as emitting different tones according to their orbits. He called it the harmony of the spheres, which is a similar concept to cosmic vibration.

However, their brains were pretty much like ours by the time the flute was made, so maybe... but we just don't know what kind of quantitative thinking they did. — Bitter Crank

Musical instrument makers think in terms of ratios, so there is necessarily measurement involved, to get the right notes.