he teacher insisted no, the numeral is not the number. So it took me very long to figure out that the numeral was not the "number" which the teacher was talking about, and that the number was just some fictitious thing existing in the teacher's mind — Metaphysician Undercover
Meanwhile, you're not even familiar with the distinction between semantics and syntax and the notion of model theoretic truth. — TonesInDeepFreeze
In any event, can you please respond to my point about chess? Surely if you learned to play chess, or any other artificial game -- monopoly, bridge, checkers, baseball -- you were willing to simply accept the rules as given, without objecting that they don't have proper referents in the real world or that they make unwarranted philosophical assumptions. If you could see math that way, even temporarily, for sake of discussion, you might learn a little about it. And then your criticisms would have more punch, because they'd be based on knowledge. I wonder if you can respond to this point. Why can't you just treat math like chess? Take it on its own terms and shelve your philosophical objections in favor of the pleasure of the game. — fishfry
It makes no sense to anyone else either. This is well known. Especially in terms of quantum fields being "probability waves." That makes no sense to me. Physics has perhaps lost its way. Many argue so. You and I might well be in agreement on this. — fishfry
Ok. I get that. And I've asked you this many times. You don't want to play the game of math. So then why the energetic objection to it? After all if someone invites me to play Parcheesi and I prefer not to, I don't then go on an anti-Parcheesi crusade to convince the enthusiasts of the game that they are mis-allocating their time on a philosophically wrong pursuit. So there must be more to it than that. With respect to a perfectly harmless pastime like Parcheesi or modern math, one can be for, against, or indifferent. You have explained why you are indifferent; but NOT why you are so vehemently against. — fishfry
Makes no sense. It's perfectly clear that you can order a random assemblage of disordered points any way you like, and that no one order is to be preferred over any other. — fishfry
Well yes, the random number generator I used was actually determined at the moment of the big bang, if one believes in determinism. But you're making a point about randomness, not about the order of the points. You are not persuading me with your claim that a completely random collection of points has an inherent order. — fishfry
You don't want to read the Wiki piece on order theory. — fishfry
Actually it doesn't make initial sense. Moving from one letter to the next is always a whole step, except from B to C and from E to F. And then double flats move you down a letter except from C to Cbb and from F to Fbb, and double sharps move you up a step except from B to B## and from E to E##. — TonesInDeepFreeze
You could see the quantity of objects but not the number of objects? — Luke
You must have already understood that the number is not the numeral in order to do simple arithmetic. Otherwise, the addition of any two numbers (i.e. numerals) would always equal 2 (numerals). — Luke
I didn't need a teacher to make me aware that numerals are not numbers. '2' and 'two' refer to the same thing. But '2' is not 'two'. So whatever they refer to is something else, which is a number, which is an abstraction. Rather than be a benighted bloviating ignoramus (such as you), I could see that thought uses concepts and abstraction and our explanations, reasoning and knowledge are not limited to always merely pointing at physical objects. — TonesInDeepFreeze
Right, I don't look at two chairs and see the number 2 there. — Metaphysician Undercover
No, the numeral represents a quantity, and a quantity must consist of particulars, or individual things. So "2"" represents a quantity, or number of individuals, two, and "1" represents a quantity of one individual. What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number. — Metaphysician Undercover
Have two individuals, add two more individuals, and you have four individuals. See, the operation is a manipulation of individuals, not a manipulation of some imaginary "numbers". — Metaphysician Undercover
What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number. — Metaphysician Undercover
I simply don't accept it as a realistic notion of "truth", and don't want to waste my time discussing it. — Metaphysician Undercover
Physicists, engineers, and others, applying mathematics in the world have a huge impact on the world in which I live [...] bad mathematics will have a bad effect. — Metaphysician Undercover
That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith — Metaphysician Undercover
The order which they have is their actual order, whereas all those others are possible orders. — Metaphysician Undercover
the term "random" — Metaphysician Undercover
I looked at the Wikipedia entry — Metaphysician Undercover
The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics. — Metaphysician Undercover
When I was seven years old I had no idea what an abstraction is, or what a concept is. I didn't understand this until much later when I studied philosophy. — Metaphysician Undercover
This is why mathematics really is like religion. We are required just to accept the rules, on faith, follow and obey, without any real understanding. — Metaphysician Undercover
What else could demonstrate falsity other than a reference to some form of inconsistency?.
— Metaphysician Undercover
Falsity is semantic; inconsistency is syntactical.
Given a model M of a theory T, a sentence may be false in M but not inconsistent with T. — TonesInDeepFreeze
An axiom is expressed as a bunch of symbols, so it must be interpreted.
— Metaphysician Undercover
Formulas don't have to be interpreted, though usually they are when they are substantively motivated. — TonesInDeepFreeze
If in interpretation, there is a contradiction with another principle then one or both must be false.
— Metaphysician Undercover
It might not be a matter of principles but of framework. Frameworks don't have to be evaluated as true or false, but may be regarded by their uselfulness in providing a conceptual context or their productivity in other ways. — TonesInDeepFreeze
Notice there is an exchange of "equal" and "same"
— Metaphysician Undercover
Even though there is nothing wrong with taking 'equal' to mean 'same', the axiom of extensionality doesn't require such mention.
Az(zex <-> zey) -> x=y.
"=' is mentioned, but not "same". — TonesInDeepFreeze
What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number.
— Metaphysician Undercover
That's just a plain contradiction from one sentence to the next. — Luke
The order which they have is their actual order — Metaphysician Undercover
without any order — Metaphysician Undercover
This is what Tones and I discussed earlier. How can we count a specific number of points without assigning some sort of order to them? To count them we need to distinguish one from the other by some means or else we do not know which ones have been counted and which have not been counted. — Metaphysician Undercover
There was a process which placed the dots where they are, therefore they were ordered by that process — Metaphysician Undercover
You said your teacher insisted that "the numeral is not the number" and that you couldn't understand it. But you also said that you had no problem with basic arithmetic. My point was that you must have understood that "the numeral is not the number" in order to do basic arithmetic. — Luke
But "1" or "2" are the number of individuals, not the individuals. — Luke
That is one of the best, most risible, evasions of a challenge I've ever read. What is "the order they actually have" as opposed to all the others? Saying that they have the order they "actually" have is not telling us what you contend to be the order nor how other orderings are not the "actual" ordering. You are so transparently evading and obfuscating here. — TonesInDeepFreeze
When confronted with the challenge of points in a plane, a reasonable response by you would be "Let me think about that." But instead you reflexively resort to the first specious and evasive reply that comes to you and post it twice with supposed serious intent. That indicates once again your lack of intellectual curiosity, honesty or credibility. — TonesInDeepFreeze
You were presented with points in a plane, without being given a stated particular ordering. — TonesInDeepFreeze
One could just as well say 'unstated'. — TonesInDeepFreeze
It is not the case that there are not orderings. The point though is that there is not a single ordering that is "THE actual ordering". There are many orderings and they are actual even though 'actual' is gratuitious. — TonesInDeepFreeze
First, of course, is that we may take a collection of dots as given, without stipulating that a particular person placed the dots herself. — TonesInDeepFreeze
Second, let's even suppose that "actual order" is a function of a person placing the dots. Say that Joe places the dots in temporal succession and Val places the dots in a different temporal succession. But that both collection of dots look exactly the same to us. So there's "Joes actual (temporal) order" and "Val's actual (temporal) order", but no one can say which is THE actual order of the collection of dots we are looking at without Joe and Val there to tell us (if they even remember) the different order of placement they used. — TonesInDeepFreeze
There is no need to assume that the number 2 is distinct from the symbol, to do basic arithmetic.. — Metaphysician Undercover
Why not just say that the symbols "'1" and "2" represent how many individuals there are, directly? — Metaphysician Undercover
Fishfry posted the order, it's right here:
↪fishfry — Metaphysician Undercover
What more do you want? — Metaphysician Undercover
How can you not see that 'points in a plane without a particular ordering' is a blatant contradiction? — Metaphysician Undercover
What else could demonstrate falsity other than a reference to some form of inconsistency?.
— Metaphysician Undercover
Falsity is semantic; inconsistency is syntactical.
Given a model M of a theory T, a sentence may be false in M but not inconsistent with T.
— TonesInDeepFreeze — TonesInDeepFreeze
An axiom is expressed as a bunch of symbols, so it must be interpreted.
— Metaphysician Undercover
Formulas don't have to be interpreted, though usually they are when they are substantively motivated.
— TonesInDeepFreeze — TonesInDeepFreeze
If in interpretation, there is a contradiction with another principle then one or both must be false.
— Metaphysician Undercover
It might not be a matter of principles but of framework. Frameworks don't have to be evaluated as true or false, but may be regarded by their uselfulness in providing a conceptual context or their productivity in other ways.
— TonesInDeepFreeze — TonesInDeepFreeze
Notice there is an exchange of "equal" and "same"
— Metaphysician Undercover
Even though there is nothing wrong with taking 'equal' to mean 'same', the axiom of extensionality doesn't require such mention.
Az(zex <-> zey) -> x=y.
"=' is mentioned, but not "same".
— TonesInDeepFreeze — TonesInDeepFreeze
What is added or multiplied is the quantity or number of individuals. The number is of the individual, a predication, and what is added or subtracted is the individuals, not the number.
— Metaphysician Undercover
That's just a plain contradiction from one sentence to the next. — Luke
That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith
— Metaphysician Undercover
But in the philosophy of mathematics, which includes many mathematicians themselves, people do investigate, question, and debate the axioms - giving reasoned arguments for and against axioms. It's just that you are ignorant of that. — TonesInDeepFreeze
The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics.
— Metaphysician Undercover
I want to understand: Are you saying that music theory is wrong just as you say mathematics is wrong? And, by the way, do you know any music theory? — TonesInDeepFreeze
This is why mathematics really is like religion. We are required just to accept the rules, on faith, follow and obey, without any real understanding.
— Metaphysician Undercover
That is false. It's the opposite. That describes the grade school memorization and regurgitation of tables and rules for basic addition, subtraction, multiplication, and division that you find so suitable. Mathematics though provides understanding of the bases for those rules. — TonesInDeepFreeze
without any order
— Metaphysician Undercover
You are obfuscating by sliding between adressing "order" and "actual order" (or "inherent order"). That's typical of your intellectual sloppiness.
It is not the case that there are not orderings. The point though is that there is not a single ordering that is "THE actual ordering". There are many orderings and they are actual even though 'actual' is gratuitious. — TonesInDeepFreeze
The numeral 2 represents how many objects there are. We could also call that symbol the number 2, which represents how many objects there are. — Metaphysician Undercover
Why not just say that the symbols "'1" and "2" represent how many individuals there are, directly? — Metaphysician Undercover
So, I was told that "1" and "2" are symbols, which represent the numbers 1 and 2, and the number represent how many individuals there are. — Metaphysician Undercover
First thing I really want to know what are the bad things that you think mathematicians and scientists are going to cause to happen? — TonesInDeepFreeze
Suppose the number 2 is not distinct from the numeral '2'. Suppose also that the number 2 is not distinct from the Hebrew numeral for 2. Then both the numeral '2' and the Hebrew numeral for 2 are the same. But they are not. — TonesInDeepFreeze
That's a picture of dots in a disk. It's not an ordering. — TonesInDeepFreeze
. That means for you to state which dots come before other dots, for each dot. — TonesInDeepFreeze
The symbols do represent how many individuals there are. What do you mean by “directly”? — Luke
Do you recognize that the word 'tree' is not a tree? — TonesInDeepFreeze
But you fail to recognize that the word 'two' or the symbol '2' are not the number 2. — TonesInDeepFreeze
The number does not represent how many individuals there are.
The number is how many individuals there are. — Luke
And, modern physics looks at time as the fourth dimension of space — Metaphysician Undercover
We don't say that the word "tree" represents a conceptual object, tree, and this concept represents the individual tree. — Metaphysician Undercover
The number is how many individuals there are.
— Luke
Well no, this is not true. The number is how many individuals it is said that there are. The number is supposed to be what the numeral stands for. It is conceptual, and a representation of a particular quantity of individuals. Being universal, we cannot say that it is actually a feature of the individuals involved, but a feature of our description, therefore a representation. — Metaphysician Undercover
What I am asking is why can't the symbol "2" be used to represent a quantity of two individuals, just like the word "tree" is used to represent a tree? Why must the symbol "2" represent a mathematical object, the number two, and the number two represents a quantity of two individuals? — Metaphysician Undercover
If the number is not a representation of how many individuals there are, but actually "how many individuals there are", there would be no possibility of error, or falsity. If I said "there are 2 chairs", and the supposed mathematical object, the number 2 which is said to be signified by the numeral "2" was "how many individuals there are", rather than how many there are said to be, how could I possibly lie? — Metaphysician Undercover
I didn't answer, because it's not relevant. Philosophy is not a game in which you either accept the rules of play or you don't,, neither is theoretical physics such a game, nor is what you call "pure mathematics" (or as close to "pure" as is possible). In these fields we determine, and create rules which are deemed applicable. So your analogy is not relevant, because the issue here is not a matter of "will you follow the rules or not", it's a matter of making up the rules. And there's no point to arguing that people must follow rules in the act of making up rules because this is circular, and does not account for how rules come into existence in the first place. — Metaphysician Undercover
Ok, we've found a point of agreement, physics has lost it's way. Do you ever think that there must be a reason for this? — Metaphysician Undercover
And, since physics is firmly based in mathematics, don't you see the implication, that perhaps the root of the problem is actually that mathematics has lost its way. — Metaphysician Undercover
Physicists, engineers, and others, applying mathematics in the world have a huge impact on the world in which I live, unlike Parcheesi players. — Metaphysician Undercover
Despite arguments that mathematical objects exist in some realm of eternal truth where they are ineffectual, non-causal, I think it is undeniable, that the mathematical principles which are applied, have an impact on our world. I believe it is inevitable that bad mathematics will have a bad effect. — Metaphysician Undercover
That people vehemently support and defend fundamental axioms which may or may not be true, refusing to analyze and understand the meaning of these axioms, simply accepting them on faith, and applying them in the conventional way, in new situations, with little or no understanding of the situation, or the axioms, to me is a clear indication that bad results are inevitable. — Metaphysician Undercover
You do not seem to be making any effort to understand this fundamental principle, which is the key to understanding what I am arguing. A group of particles, or dots (we cannot really use "points" here because they are imaginary) existing in a spatial layout, have an order by that very fact that they are existing in a spatial arrangement. — Metaphysician Undercover
Yes, they can be "ordered any way you like", but not without changing the order that they already have. The order which they have is their actual order, whereas all those others are possible orders. — Metaphysician Undercover
Do you understand and accept this? — Metaphysician Undercover
Or do you dispute it, and know some way to demonstrate how a spatial arrangement of dots or particles could exist without any order? — Metaphysician Undercover
It's one thing to move to imaginary points, and claim to have a specific number of imaginary points, in your mind, which have no spatial arrangement, but once you give them a spatial arrangement you give them order. — Metaphysician Undercover
Even if we just claim "a specific number of points", we need to validate that imaginary number of points without ordering them. — Metaphysician Undercover
This is what Tones and I discussed earlier. — Metaphysician Undercover
How can we count a specific number of points without assigning some sort of order to them? — Metaphysician Undercover
To count them we need to distinguish one from the other by some means or else we do not know which ones have been counted and which have not been counted. So even to have "a specific number of points", imaginary, in your mind, requires that they have an order, or else that specific number cannot be validated. — Metaphysician Undercover
Yes, I'm making a point about "randomness" because you are using the term "random" to justify your claim that a bunch of dots in a spatial arrangement could have no order. — "Metaphysician
You simply say, the points are "randomly distributed" and you think that just because you say "randomly", this means that there actually could be existing dots in a spatial assemblage, without any order. But your use of the term does not support your claim. There was a process which placed the dots where they are, therefore they were ordered by that process, regardless of whether you call that process "random" or not. — Metaphysician Undercover
I looked at the Wikipedia entry, — Metaphysician Undercover
and it does not appear to cover the issue of whether existing things necessarily have an order or not. So it seems to provide nothing which bears on the point which I am trying to get you to understand. — Metaphysician Undercover
A contradiction is a statement and its negation. — TonesInDeepFreeze
This was in reference to my question, Why don't you treat math like chess, and accept it on its own terms? — fishfry
Then your complaint is with the physicists, engineers, and others; and not the mathematicians, who frankly are harmless. — fishfry
Again, your complaint is with those mis-applying math or applying math to bad ends. — fishfry
Particles? Dots? What are those? In math, the elements of sets are other sets. There are no particles or dots. Again, you confuse math with physics. — fishfry
I can't argue with the fantasies in your head. Set theory is what it is. — fishfry
There are no dots. I don't know what dots are. I tried to give you a visual example but perhaps that was yet another rhetorical error. I should just refer you to the axiom of extensionality and be done with it, because in truth that is all there is to the matter. — fishfry
Demonstrate to me how there could be a set with elements, and no order to these elements. — Metaphysician Undercover
You [fishfry], and Tones alike [...], are simply in denial of these logical fallacies existing in the fundamental principles of mathematics, and you say truth and falsity is irrelevant to the pure mathematicians. — Metaphysician Undercover
the complete denial of the faults, from people like you. — Metaphysician Undercover
I love to mention you, and see your response. — Metaphysician Undercover
The part that doesn't make sense is when you move deeper into the theory. This is just like mathematics.
— Metaphysician Undercover
I want to understand: Are you saying that music theory is wrong just as you say mathematics is wrong? And, by the way, do you know any music theory? — TonesInDeepFreeze
If one could predict the bad things that were going to happen, before they happened, then we could take the necessary measures to ensure that they don't happen. — Metaphysician Undercover
It's like asking me what accident are you going to have today. — Metaphysician Undercover
The biggest problem, I think, is the complete denial of the faults, from people like you. — Metaphysician Undercover
This creates a false sense of certainty. That's why it's like religion, you completely submit to the power of the mathematics, with your faith, believing that your omnibenevolent "God", the mathematics would never mislead you. — Metaphysician Undercover
we ought not say that the numeral 2 says the same thing as the Hebrew symbol. — Metaphysician Undercover
This would be very clear to you if you would consider all the different numbering systems discussed on this forum, natural, rational, real, cardinals, ordinals, etc.. — Metaphysician Undercover
The same symbol has a different meaning depending on the system. If we do not keep these distinguished, and adhere to the rules of the specific system, we have equivocation. — Metaphysician Undercover
.That means for you to state which dots come before other dots, for each dot.
— TonesInDeepFreeze
Order is not necessarily temporal — Metaphysician Undercover
So if you cannot see order in an arrangement on a two dimensional plane, I don't see any point in discussing "order" with you. — Metaphysician Undercover
What I am asking is why can't the symbol "2" be used to represent a quantity of two individuals, — Metaphysician Undercover
Why must the symbol "2" represent a mathematical object, the number two, and the number two represents a quantity of two individuals? We don't say that the word "tree" represents a conceptual object, tree, and this concept represents the individual tree. — Metaphysician Undercover
In reality we simply use the word "tree" to represent a tree, and we use the symbol "2" to represent a quantity of two individuals. — Metaphysician Undercover
The number does not represent how many individuals there are.
The number is how many individuals there are.
— Luke
Well no, this is not true. — Metaphysician Undercover
Contradiction may be implied. Here's Wikipedia's opening statement:
'In traditional logic, a contradiction consists of a logical incompatibility or incongruity between two or more propositions."
The problem is that you refuse to recognize that an arrangement of points on a plane, logically implies order, therefore "an arrangement of points on a plane without order" is contradictory. — Metaphysician Undercover
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