It appears like we need to go back over the law of identity, and the difference between identical and equal. Remember, I don't accept set theory on the basis that it violates the law of identity, so why give me a proof based in a set? — Metaphysician Undercover

I don't accept set theory on the basis that it violates the law of identity — Metaphysician Undercover

The square root of two just won a Golden Globe award! — jgill

The construction procedure you described is never ending, just like the never ending digits. — Metaphysician Undercover

The problem is that you do not address the substance of the argument. You go off on some tangent using mathematical jargon, without addressing the issue. — Metaphysician Undercover

Fishfry! Get with the program, wake up and smell the coffee! — Metaphysician Undercover

it's pointless to speak sophisticated math at me. — Metaphysician Undercover

Computers can simulate physical systems. Human brains are physical systems. Human brains are conscious. So a simulation of a human brain will be conscious — Pfhorrest

By definition a simulation is an "imitation" — ZhouBoTong

This is an argument that we will experience identical lives over and over again — Devans99

The square root of two is rational? Am I misreading your sentence?/quote]

Oh that's a typo, sorry. Is that what you were asking earlier? Yes typo of course. I'll go back and fix it. — jgill

It doesn't matter if climate change is a complete lie! The obvious move is to cover your ass anyway! — Lif3r

OK, so we agree that if so-called "mathematical objects" are things which can be measured, Euclidian geometry creates distances which cannot be measured by that system. That agreement is a good starting point. — Metaphysician Undercover

OK, so we agree that if so-called "mathematical objects" are things which can be measured, — Metaphysician Undercover

Euclidian geometry creates distances which cannot be measured by that system. — Metaphysician Undercover

As a philosopher, doesn't the question, or wonderment, occur to you, of why we would create a geometrical system which does such a thing? — Metaphysician Undercover

That geometrical system is causing us problems, inability to measure things, by creating distances which it cannot measure. — Metaphysician Undercover

Maybe we can take this as another point of agreement. A "mathematical object" is nothing other than what you called a "funny gadget". Let's simplify this and call it a "mental tool". Do you agree that tools are not judged for truth or falsity, they are judged as "good" in relation to many different things like usefulness and efficiency, and they are judged as "bad" in relation to many different things, including the problems which they create. — Metaphysician Undercover

So a "good" tool might be very useful and efficient, but it might still be "bad" according to other concerns, accidental issues, or side effects. — Metaphysician Undercover

Bad is not necessarily the opposite of good, because these two may be determined according to different criteria. — Metaphysician Undercover

Let's look at the Euclidian geometry now. In relation to the fact that this system produces distances which cannot be measured within the system — Metaphysician Undercover

, can we say that it is bad, despite the fact that it is good in many ways? — Metaphysician Undercover

How should we proceed to rid ourselves of this badness? — Metaphysician Undercover

Should we produce another system, designed to measure these distances, which would necessarily be incompatible with the first system? — Metaphysician Undercover

Having two incompatible systems is another form of badness. Why not just redesign the first system to get rid of that initial badness, instead of creating another form of badness, and layering it on top of the initial badness, in an attempt to compensate for that badness? Two bads do not produce a good. — Metaphysician Undercover

Come on, get real fishfry. Check Wikipedia on set theory, the first sentence states that it deals with collections of "objects". — Metaphysician Undercover

Then it goes on and on discussing how set theory deals with objects. Clearly set theory assumes the existence of objects, if it deals with collections of objects. — Metaphysician Undercover

This is why it is so frustrating having a conversation with you. You are inclined to deny the obvious, common knowledge, because that is what is required to support your position. — Metaphysician Undercover

In the other thread, you consistently denied the difference between "equality" and "identity", day after day, week after week, despite me repeatedly explaining the difference to you. — Metaphysician Undercover

You have not explained how acceptance of a mathematical tool, through convention, converts it from a funny gadget, to an object. — Metaphysician Undercover

If you cannot demonstrate this conversion, then either the tool is always an object, or never an object. — Metaphysician Undercover

Then an extremely bad tool is just as much an object as an extremely good tool, and acceptance through convention is irrelevant to the question of whether the mental tool is an object. — Metaphysician Undercover

Until you recognize that an "element", or "member" of a set is an "object", you are simply in denial of the truth, denying fundamental brute facts because they are contrary to the position you are trying to justify. — Metaphysician Undercover

The case I made is very clear, so let me restate it concisely. You appear to agree with me that mathematical tools are not objects, they are "mind" gadgets, yet you defend set theory which treats them as objects. — Metaphysician Undercover

This is nonsense. I can very easily say "the highest number". Just because I say it doesn't mean that what I've said "completely characterizes" it. We can say all sorts of things, including contradiction. Saying something doesn't completely characterize it. — Metaphysician Undercover

if you switch to a different number system, one which is incompatible with the first from which the irrational number is derived, like switching from rational numbers to real numbers, this does not qualify as a resolution, if the two systems remain incompatible. — Metaphysician Undercover

For instance, if there is infinite rational numbers between any two rational numbers, and we take another number system which uses infinitesimals or some such thing to limit that infinity, we cannot claim to have resolved the problem. The problem remains as the inconsistency between "infinite" in the rational system, and "infinitesimal" in the proposed system. — Metaphysician Undercover

This has no relevant significance. To say "the square root of two", or "the ratio of the circumference of a circle to its diameter" is to give a 'finite description". We've already had the "finite description" for thousands of years. And, this finite description determines that the decimal digits will follow a specific order, just like your example of 1/3 determines .333.... The issue is that there is no number which corresponds to the finite description, as is implied by the infinite procedure required to determine that number. — Metaphysician Undercover

So my analogy of "the highest number" is very relevant indeed. Highest number is a "finite description". And, the specific order by which the digits will be "computed" is predetermined. However, there is no number which matches that description, "highest number", just like there is no number which matches the description of "the square root of two", or "the ratio of the circumference of a circle to its diameter", or even "one third". — Metaphysician Undercover

This demonstrates that there is a problem we have with dividing magnitudes, which has not yet been resolved. — Metaphysician Undercover

Let me return your attention to this remark. If you agree with me, that the representations are "imperfect" from the start, then why not agree that we ought to revisit those representations. Constructing layer after layer of complex systems, with the goal of covering over those imperfections, doing something bad to cover up an existing bad, is not a solution. — Metaphysician Undercover

My objection was only this one: BT doesn't make integration inconsistent. — Mephist

You can reason about infinitesimal parts and be confident of the fact that integration works, if you decompose the object in open sets. — Mephist

Yes of course they have to be isometries. I meant: there is no way of decomposing an object in an infinite set of open sets and then recomposing them in a different way so that each peace has the same measure but the sum of the measures of all the pieces is different. If this were possible, the theory of integration would be inconsistent. — Mephist

I know your objection: if there is an infinite number of pieces the measure of each peace cannot be finite. OK, but you can build the limit of a sequence of decompositions, like you do with regular integration. — Mephist

I am not arguing that BT theorem is false, I am arguing that it works only because you perform the transformation on pieces that are not measurable. — Mephist

If the pieces were made using the decomposition in open sets, as with regular integration, it couldn't work. I know that you can even define a Lebesgue integral that is working on sets that are not open: this is not a necessary condition, but is a sufficient condition to preserve additivity. — Mephist

If topology has nothing to do with it why all the proofs of decomposition of objects that don't preserve volume are decomposing the objects in pieces that are not open sets? — Mephist

Can you find an example of decomposing an object and then recomposing it with different volume where the pieces are open sets? — Mephist

If topology has nothing to do with it why all the proofs of decomposition of objects that don't preserve volume are decomposing the objects in pieces that are not open sets? — Mephist

I linked it in the post just before this one. Here's the link:
https://thephilosophyforum.com/discussion/comment/302364 — Mephist

I linked it in the post just before this one. Here's the link:
https://thephilosophyforum.com/discussion/comment/302364 — Mephist

I submit that 5 is prime and the square root of 2 both exists and is rational. . . . But they are true.
— fishfry

What am I missing here? — jgill

I am satisfied with this principle if we can apply it consistently. We do not measure mathematical "objects", they are tools by which we measure objects. That's why I argued that they are not proper "objects". — Metaphysician Undercover

Now let's apply this to set theory. Cardinality, for example is a measure. — Metaphysician Undercover

If the applicable principle is that we do not measure mathematical "objects", then why allow this in set theory? It's inconsistency. — Metaphysician Undercover

So either we can measure mathematical objects, like squares, and the sides of squares, just like we can measure the cardinality of sets, or we cannot measure these so-called mathematical objects. — Metaphysician Undercover

But if we allow that we can measure these so-called objects, then we can measure a square, and find that the diagonal cannot be measured. — Metaphysician Undercover

It's what we call an "irrational number", implying an immeasurable length. Are you familiar with basic geometry? — Metaphysician Undercover

This is not at all what I've been saying, so I think we might not really be making any progress. — Metaphysician Undercover

Neither you nor I is talking about physical objects here. What we are talking about is the "made-up gadgets" which you describe here. — Metaphysician Undercover

You seem to imply that there is a difference between these funny gadgets, and "first-rate mathematical objects" — Metaphysician Undercover

I deny such a difference, claiming all mathematics consists of made-up gadgets, and there is no such thing as mathematical objects. — Metaphysician Undercover

But this is contrary to set theory which is based in the assumption of mathematical objects. — Metaphysician Undercover

If you really think that a "funny gadget" becomes a "mathematical object" through use, you'd have to demonstrate this process to me, to convince me that this is true. — Metaphysician Undercover

How can you not see that this is a problem for set theory? — Metaphysician Undercover

Set theory assumes that it is dealing with real, actual mathematical "objects". — Metaphysician Undercover

That is a fundamental premise. — Metaphysician Undercover

Now you agree with me, that mathematics can never give us this, real or actual things being represented by the symbols. — Metaphysician Undercover

So why don't you see that set theory is completely misguided? — Metaphysician Undercover

So your argument is that the "funny gadget" gets made into a "first-rate mathematical object" through convention, just like driving laws. — Metaphysician Undercover

But those are ";laws", not "objects". Let's suppose that the mathematical symbols referred to conventional laws instead of "objects", as this is what is implied by your statement. How would this affect set theory? Remember what I argued earlier in the thread, sometimes when a symbol like "2" or "3" is used, a different law is referred to, depending on the context. — Metaphysician Undercover

I don't see how "the square root of 2 exists" could possibly be true, It is an irrational ratio which has never been resolved, just like pi. — Metaphysician Undercover

How can you assert that the solution to a problem which has not yet been resolved, "exists"? — Metaphysician Undercover

Isn't this just like saying that the highest number exists? — Metaphysician Undercover

But we know that there is not a highest number, we define "number" that way. — Metaphysician Undercover

Likewise, we know that pi, and the square root of two, will never be resolved, — Metaphysician Undercover

#!/usr/bin/python3

low  = 1
high = 2

loops = 1000

for i in range(loops) :
    lowsq  = low * low
    highsq = high * high

    trial   = (low + high) / 2
    trialsq = trial * trial

    if trialsq < 2 :  # too small
        low = trial

    else :   # too big. 
        high = trial
    
print(trial)    

Climate denier — Xtrix

I would like to get a sense of what most people on here believe is the most important problem facing humanity today. — Xtrix

Please substantially tell us and the science community how climate change is “hysteria.” — Xtrix

What a stupid, stupid position. — Xtrix

Thank you fishfry. I'm vey impressed that you actually took the time to read and try to understand what I was saying. — Metaphysician Undercover

Most just dismiss me as incomprehensible or unreasonable ... — Metaphysician Undercover

It seems to me your entire post is deeply confused, rampant with ambiguity, amphiboly, conflation, undefined terms - or if they'e defined then the definitions are not held to - and faulty argument, all in a toxic mix and mess, that like most messes, is easy to make but labor intensive to clean up . — tim wood

I'm afraid you have your own free will and I can't make you go away. — Metaphysician Undercover

I would say that it works even if you consider infinitesimals as really existing entities — Mephist

As I wrote in my explanation about Banach-Tarski mounts ago, the theorem works because it uses isometric transformations, but applied to set of points that are isolated from each other (not on open sets). If you impose the restriction that your isometric transformations should be even continuous (going from open sets to open sets), you can't do it any more. — Mephist

Again, I am not promoting any philosophical view, just trying to make very general but meaningful statements that I think everyone can agree on, so we can talk about the same thing rather than talking past each other. — Zelebg

What if I told you that feelings are a special kind of information or signal that carries its meaning within? Like a magical language no one has to learn, but is innately and universally “understood” by all the living. — Zelebg

It doesn't work because in integral calculus you have to take "open sets" as infinitesimal pieces ( but I would prefer to not go into details about this issue, because surely fishfry will read this and will not agree :wink: ) — Mephist

OK, then there is this little "glitch" in the fabric of the universe named Banach Tarski theorem... :smile: — Mephist

I'm not sure why NOR is important to you
— fishfry

Because it's a sole sufficient operator. — Pfhorrest

Furthermore, I seriously suspect that Trump was informed about the operation only after the facts. This is quite a victory for "incorruptible" Benjamin, of course. He must have had a big late-night party with his friends in Tel Aviv after this. — alcontali

↪fishfry I think you meant to quote the part where I wrote "And the complement of the empty set, all that is not nothing, is everything. The end." That part was a joke, and I immediately backtracked to get back to the actual point of that first post. — Pfhorrest

I could use a little clarification though, because as I understand it the logical operations are all equivalent to set operations, and as I understand it complement is the set-theoretic equivalent of negation, but negation isn't quite the same as joint negation though it can trivially be made to function as such (just feed an operand into both arguments of NOR instead of the single argument of NOT), so I'm not entirely sure if complement can be treated as the set-theoretic equivalent of joint negation too, or just plain unary negation, and in the latter case, what actually is the set-theoretic equivalent of joint negation? — Pfhorrest

↪fishfry what sites do people discuss 2nd amendment without behaving like they could kill someone any day? I have done some work on the topic and I cant find any serious, or more notably, kind, people to look at it. — ernestm

I will remind you, that Pythagoras demonstrated the irrational nature of the square. The relation between two perpendicular sides of a square produces the infinite, which as I argued above is bad. This makes the square a truly impossible, or irrational figure. And, all "powers" are fundamentally derived from the square. Therefore any exponentiation is fundamentally unsound in relation to a spatial representation.. — Metaphysician Undercover

I will remind you, that Pythagoras demonstrated the irrational nature of the square. — Metaphysician Undercover

The relation between two perpendicular sides of a square produces the infinite ... — Metaphysician Undercover

which as I argued above is bad. — Metaphysician Undercover

This makes the square a truly impossible ... — Metaphysician Undercover

, or irrational figure. — Metaphysician Undercover

And, all "powers" are fundamentally derived from the square. — Metaphysician Undercover

Therefore any exponentiation is fundamentally unsound in relation to a spatial representation.. — Metaphysician Undercover

From my perspective, ZFC has unsound axioms concerning the nature of objects, as we discussed earlier. Therefore any proof using ZFC is unsound. — Metaphysician Undercover

“Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.” — Uncle Bertie

In Facebook groups on the 2nd Amendment and gun control, guys now say things like they want to masturbate when someone gets their face blown off, and get liked for it. — ernestm

Human beings may have gotten over this, but they did not resolve the problem. — Metaphysician Undercover

Consider the problem this way. Take a supposed "point". Now measure a specific distance in one direction, and the same distance in a direction ninety degrees to the first. Despite the fact that you use the exact same scale of measurement, in both of these measurements, the two measurements are incommensurable. Why is that the case? — Metaphysician Undercover

Doesn't this tell you something about the thing being measured (space)? — Metaphysician Undercover

What it tells me, is that this thing being measured (space), cannot actually be measured in this way. The irrational nature of pi tells us the very same thing. Two dimensional objects have a fundamental problem which demonstrates that space cannot actually be represented in this way. — Metaphysician Undercover

We see a very similar problem in the relation between zero dimensional figures (points), and one dimensional figures (lines), as discussed in the other thread. So if we get done to the basics, remove dimensionality and focus solely on numbers, we can learn to understand first the properties of numbers, quantity, and order, without applying any relations to spatial features. Then we can see that it is only when we apply numbers to our dimensional concepts of space, that these problems occur. The problems result in establishing a variety of different number systems mentioned in this thread. None of these numbers systems has resolved the problem because the problem lies within the way that we model space, not within any number system. We do not have a representation of space which is compatible with numbers. — Metaphysician Undercover

Two dimensional objects have a fundamental problem which demonstrates that space cannot actually be represented in this way. — Metaphysician Undercover

And the joint negation or complement operation is the sole sufficient operation, which returns the set of everything that is not any of the arguments fed into i — Pfhorrest