I see that you are confused about the most basic aspects of mathematics, language and reasoning. On certain points, your understanding is not even at the level of a six year old child. I'm offering you help here, though I doubt you'll take it in. — GrandMinnow

Quite a soap opera. Can't wait for the next episode. :lol:

I'm offering you help here, though I doubt you'll take it in. — GrandMinnow

If it makes sense, I'll take it. But so far all you've offered is inconsistency. Let me see if I can follow you.

'2+1' denotes the result of the operation — GrandMinnow

I see the number 2 denoted, and the operation + denoted, and the number 1 denoted. So there is clearly an operation denoted. What denotes that the operation has a result?

Would you agree that a finite operation is distinct from an infinite operation, the one having a result, the other not? If this is the case then there is a need to distinguish between an operation with a result, and one without a result.

You got it exactly backwards. Our method does not lead to '2+1' denoting infinitely many things. '2+1' denotes exactly one thing. On the other hand, 2+1 is denoted infinitely many ways:

2+1 is denoted by '2+1'

2+1 is denoted by '3'

2+1 is denoted 'sqrt(9)'

2+1 is denoted by '((100-40)/3)-17'

etc. — GrandMinnow

It appears to me, like 2+1 demotes exactly nothing then. You can say the same thing in an infinite number of different ways, but none of these ways refer to anything. Each expression simply say I am the same as the infinity of others. If one of them refers to anything real, then they all must refer to something real, and you have an infinity of equivocation, with an infinity of different things referred to by on signification. Even the numeral "3" must refer to the result of an operation, exactly as the others, so there is nothing to validate any object

So what makes 2+1 different from 3+1 then? Each can be said in an infinity of different ways, and there is nothing which is actually being referred to be either one. How can they differ?

If we want to know how much a company did in sales, the accountant starts by seeing that the company got 500 dollars from Acme Corp., and 894 dollars from Babco Corp, and 202 dollars from Champco Corp. Then the accountant reports:

500+894+202 = 1596 — GrandMinnow

This is incorrect. The accountant writes out 500+ 894+202=?, or x, or some other placeholder for the unknown, because the sum is unknown. But if it were like you say, that "500+ 894+202" already says 1596, then the accountant would not have to sum up the numbers, because the result of the operation would already be stated.

That's why your way of looking at things, if it were true, would render the equation completely unnecessary and redundant. By the time the left side was stated, (500+ 894+202) the right side would already be known, because you claim that the left side states the result of an operation. Clearly this is false, because equations contain unknowns, and this is how we solve problems, by carrying out the operations required to determine the unknowns. Obviously you are spinning a web of deceit.

One wouldn't honestly claim to know that the equation is true until one worked it out that it is true. Or to find a right side without '+' in it, then first one might have to perform the addition on the left side. This doesn't vitiate anything I've said. — GrandMinnow

How do you apprehend a need to work things out? If "2+1" says sqrt(9), how is there any need to work out any equivalencies?

[This is GrandMinnow with a different name.]

all you've offered is inconsistency — Metaphysician Undercover

Again, you argue by mere assertion while evading the replies given to you. This is a paraphrase:

You: You are inconsistent.

Me: To be inconsistent is to claim or imply a contradiction, which is a statement and its negation. You have not shown that I've implied both a statement and its negation.

You: You are inconsistent.

What denotes that the operation has a result? — Metaphysician Undercover

That is just so daft!

The term itself doesn't denote that it has a result.

'+' is an operation symbol. An operation is a function. The usage "result of an operation" is an informal way of referring to the value of the function for the arguments. Every function has a value for arguments in its domain. That is, every function has a result when applied to arguments in its domain.

Would you agree that a finite operation is distinct from an infinite operation — Metaphysician Undercover

For a while, in order not to split hairs, I went along with your term 'process', even though you have not defined it. That was okay for a while, but I was concerned that it would cause confusion, since there are actually two different notions: (1) a function. (2) a procedure for determining the value of a function applied to an argument. (I did touch on this earlier.)

So I'm not going to go along with your undefined terminology 'process'. Instead I'll use 'operation' (meaning a function) and 'procedure' (meaning an algorithm).

As I touched on before, there are:

(1) procedures that terminate, (2) procedures that do not terminate, and (3) supertasks that are not finite but terminate. (1) and (2) are mathematical, and (3) is philosophical (or I am not versed in whatever mathematics there might be about it).

2+1 demotes exactly nothing then — Metaphysician Undercover

Use-mention! Please, I've pointed out a dozen times: use-mention!

2+1 is a number. '2+1' is a term that denotes.

Do you even know what the use-mention distinction is? I doubt you care to know even the most basic considerations in the subject of mathematical language.

There are an infinite number of ways to refer to the number 3. That doesn't mean they don't refer! Your argument is so daft!

infinity of different things referred to by on signification — Metaphysician Undercover

I pointed out in my last post that you have this exactly backwards. And you just repeat yourself again.

what makes 2+1 different from 3+1 then? — Metaphysician Undercover

Are you serious? Are you trolling?

The accountant writes out 500+ 894+202=?, or x — Metaphysician Undercover

No he doesn't. If he does, he's wasting precious billable seconds. Instead, he just goes ahead to add the numbers.

it were like you say, that "500+ 894+202" already says 1596, then the accountant would not have to sum up the numbers — Metaphysician Undercover

No, the term '500+ 894+202' already denotes 1596. It's just that the accountant doesn't know that until he performs the addition. The term doesn't start denoting only upon the knowledge of the account. The term doesn't spring into denotation every time some human being or computer somewhere in the world does a calculation.

equations contain unknowns — Metaphysician Undercover

You have no idea how daft that is.

An equation might contain only constants such as:

2+1 = 3

or it might contain a combination of constants and variables such as:

2+1 = x

or it might contain only variables such as:

x+ y = z

If "2+1" says sqrt(9), how is there any need to work out any equivalencies? — Metaphysician Undercover

Because we might not know that 2+1 = sqrt(9). The fact that at some point we don't yet know that 2+1 = sqrt(9) doesn't mean that it wasn't true all along. Obviously!

The term itself doesn't denote that it has a result. — TonesInDeepFreeze

OK, so what in the expression "2+1" denotes that there is a result. Grand Minnow was insisting that the expression denotes a result. I don't see it in the signification. Now you're pretending to be someone else, so that your inconsistency is not so glaring. Grand Minnow can argue that a result is signified and Deep Freeze can argue that an operation is signified. How's that?

The usage "result of an operation" is an informal way of referring to the value of the function for the arguments. — TonesInDeepFreeze

A function is a process. Grand Minnow kept insisting that "2+1" does not signify a process. That's why I say there is inconsistency. But clearly an "operation" or "function" is a process, and that's what is signified with "+".

The "value" of the function is not signified, because it must be figured out by carrying out the operation which is signified. If I say add some sugar to water, and bring it to a boil, the value (result) of that operation is syrup. But I'm not telling you "syrup", I'm telling you the procedure to make it. To obtain that value, syrup, you must carry out the operation referred to first.

For a while, in order not to split hairs, I went along with your term 'process', even though you have not defined it. That was okay for a while, but I was concerned that it would cause confusion, since there are actually two different notions: (1) a function. (2) a procedure for determining the value of a function applied to an argument. (I did touch on this earlier.)

So I'm not going to go along with your undefined terminology 'process'. Instead I'll use 'operation' (meaning a function) and 'procedure' (meaning an algorithm). — TonesInDeepFreeze

OK, I'm fine with "operation", so long as you recognize that what is signified is a a procedure, or operation, and as you say, this is "a procedure for determining the value of a function applied to an argument". The value is not signified, the "procedure for determining the value" is what is signified. Do you agree?

Do you even know what the use-mention distinction is? I — TonesInDeepFreeze

Of course I do. In philosophy we use a different convention. I use " " to signify a concept rather than a physical thing. I'm trying to conform to your convention but I'm a bit sloppy and missed one. Call it a typo.

There are an infinite number of ways to refer to the number 3. That doesn't mean they don't refer! Your argument is so daft! — TonesInDeepFreeze

Here's your inconsistency. You distinctly said "2+1" refers to "a procedure for determining the value of a function applied to an argument."

Now it's my turn to ask you, do you understand the difference between a procedure (function, or operation), and an object? Aristotle demonstrated a fundamental incompatibility between these two. A procedure cannot be an object, and an object cannot be a procedure because of this fundamental incompatibility. If "3" refers to the number three, and this is an object, then the procedure for determining a value, referred to with "2+1", cannot be the same thing as what is referred to with "3".

No he doesn't. If he does, he's wasting precious billable seconds. Instead, he just goes ahead to add the numbers. — TonesInDeepFreeze

Have you ever seen a ledger? Every account must be stated and balanced. Call it redundancy if you want, but there must be no room for error.

Are you serious? Are you trolling? — TonesInDeepFreeze

Of course I'm serious. You just told me there is an infinite number of ways to say "2+1", and I assume an infinite number of ways to say "3+1", so I ask you what distinguishes one from the other? Why is "3+1" not just another one of the infinite ways of saying "2+1"? That you do not answer means that you do not know.

No, the term '500+ 894+202' already denotes 1596. — TonesInDeepFreeze

Here is your inconsistency. Above, you said things like "500+ 894+202" denote "a procedure for determining the value of a function applied to an argument", which I accept. Now you are claiming that it actually signifies the value. What you say now is clearly false, because the procedure must be carried out before that value is derived.

It's just that the accountant doesn't know that until he performs the addition. The term doesn't start denoting only upon the knowledge of the account. The term doesn't spring into denotation every time some human being or computer somewhere in the world does a calculation. — TonesInDeepFreeze

What the person knows, is that "500+ 894+202" signifies the operation required to determine the value. Your claim that "500+ 894+202" represents the value is nothing but a misrepresentation. And, if you proceed in a philosophical argument with that misrepresentation of what "500+ 894+202" is known to signify, you are guilty of equivocation.

Two points. (1) You stated falsely about my motivation. (2) You outright fabricated a quote to make me look like I said the exact opposite of what I have been saying.

(1)

Now you're pretending to be someone else, so that your inconsistency is not so glaring. — Metaphysician Undercover

* I said at the very top of my last post that I am Grandminnow. I'm not pretending anything. And you lied by claiming that my motivation is to make anything less glaring.

* You have not shown any inconsistency.

(2)

You distinctly said "2+1" refers to "a procedure for determining the value of a function applied to an argument." — Metaphysician Undercover

I distinctly did NOT say that. And you put that misrepresentation in quotes to fabricate something I did not say.

I said that one notion of a process is that of a procedure for determining the value of a function applied to an argument.

And I say '2+1' does NOT denote a function nor an operation nor a process nor a procedure for determining the value of a function applied to an argument.

So stop right here. Go back to what I actually posted and see that I did not say, as you pretended to quote me, "'2+1' [refers to] a procedure for determining the value of a function applied to an argument."

If you don't then recognize that you fabricated a quote, then I won't know that I not talking with someone plainly dishonest and/or with real cognitive problems.

what in the expression "2+1" denotes that there is a result — Metaphysician Undercover

I addressed that already. The term '2+'1' denotes the value of the function + applied to the argument pair 2 and 1. It denotes the result of any computation of the function applied to those arguments. But it does not say within itself "there is a result". A term denotes an object (in this case, the object is the value of the function for the arguments, or the result of a computation of the function); a term is not itself a statement that there is a value or result.

'The father of Peter Fonda' denotes the value of the function (call it 'the father of function') applied to the argument Peter Fonda. That value is Henry Fonda.

'The father of Peter Fonda' does not itself denote the claim that there is value for the function.

A function is a process. — Metaphysician Undercover

As I mentioned, I'm not going to go along with your undefined terminology 'process'. Instead I'll use 'operation' (meaning a function) and 'procedure' (meaning an algorithm).

Grand Minnow kept insisting that "2+1" does not signify a process. That's why I say there is inconsistency. — Metaphysician Undercover

An inconsistency would be:

"'2+1' does not denote a process" and '''2+1' does denote a process".

But I never claimed that '2+1' denotes a process or operation or function or procedure.

So there is no inconsistency.

For about the seventh time now: '2+1' denotes the value of the function + applied to the argument pair 2 and 1. '2+1' does not denote a procedure nor a process (whatever vague notion of 'process' you probably have in mind. 2+1 denotes the RESULT of the procedure, not the procedure itself.

But clearly an "operation" or "function" is a process, and that's what is signified with "+". — Metaphysician Undercover

Yes, '+' denotes a function. But '2+1' does not denote the function. For about the eighth time now: '2+1' denotes the VALUE of the function for the arguments 2 and 1.

And rigorously a function is not a procedure. A function is a relation such that no member of the domain is related to more than one member of the range.

The "value" of the function is not signified, because it must be figured out by carrying out the operation — Metaphysician Undercover

I addressed that already. You skipped what I wrote about that and instead adduced an analogy that doesn't apply:

If I say add some sugar to water, and bring it to a boil — Metaphysician Undercover

Yes, that is a description of a process in the sense of a procedure (though, of course, only by analogy and not a mathematical procedure), and the result is syrup. But '2+1' is not a description of a procedure. A description of a procedure would be a statement of the recursive instructions for addition (and specifically for the inputs 2 and 1). '2+1' is not the name of a sequence of instructions. (Granted, in constructive mathematics, roughly put, there are notions of mathematical objects, such as numbers, being a construction. But we're not in that context, or to get to that context, you would need to understand a lot more about it.)

The value is not signified, the "procedure for determining the value" is what is signified. Do you agree? — Metaphysician Undercover

No, and see above and my previous posts.

Do you even know what the use-mention distinction is?
— TonesInDeepFreeze

Of course I do. In philosophy we use a different convention. I use " " to signify a concept rather than a physical thing. — Metaphysician Undercover

Use-mention is a convention in philosophy. It's not a different convention from that used in mathematics. And "concept vs. physical thing" is not it at all.

I'm trying to conform to your convention but I'm a bit sloppy and missed one. Call it a typo. — Metaphysician Undercover

You've been doing it over and over again. Not just typos.

do you understand the difference between a procedure (function, or operation), and an object? — Metaphysician Undercover

I am the one who has been harping on that difference.

Have you ever seen a ledger? Every account must be stated and balanced. Call it redundancy if you want, but there must be no room for error. — Metaphysician Undercover

You're babbling and again skipped my point. As I said, the accountant doesn't have to write '=?' or 'x' to add the numbers.

You just told me there is an infinite number of ways to say "2+1" — Metaphysician Undercover

Wrong. Use-mention again. I said there are infinitely many ways to denote 2+1, and '2+1' is one of those ways.

Why is "3+1" not just another one of the infinite ways of saying "2+1"? — Metaphysician Undercover

Another use-mention error by you.

you said things like "500+ 894+202" denote "a procedure for determining the value of a function applied to an argument" — Metaphysician Undercover

You did it again. You fabricated what I said.

You have it completely backwards what I said.

Your claim that "500+ 894+202" represents the value — Metaphysician Undercover

Yes, THAT is what I said. I said '500+ 894+202' denotes the value, not the procedure for determining the value.

This is probably around twenty times I've said it.

Now you got it right. So stop also fabricating that I said the opposite.

I distinctly did NOT say that. And you put that misrepresentation in quotes to fabricate something I did not say. — TonesInDeepFreeze

I apologize then, I misunderstood. I thought you meant that "2+1" could be interpreted as eithe of the following, (1) or (2).

For a while, in order not to split hairs, I went along with your term 'process', even though you have not defined it. That was okay for a while, but I was concerned that it would cause confusion, since there are actually two different notions: (1) a function. (2) a procedure for determining the value of a function applied to an argument. (I did touch on this earlier.) — TonesInDeepFreeze

Now I realize you are insisting that it is neither.

'The father of Peter Fonda' denotes the value of the function (call it 'the father of function') applied to the argument Peter Fonda. That value is Henry Fonda. — TonesInDeepFreeze

This is clearly incorrect. "The father of Peter Fonda" denotes that there is a person who has the position, the special relationship of being the father of the mentioned person, and this person who is the father of the mentioned person is your subject. It does not say that this person is Henry Fonda, so you cannot jump to that conclusion. If you knew someone named Henry Fonda, it would be a logical fallacy to jump to the conclusion that this man is the referred subject. You have not made the required logical connection, to determine that your subject is the same person as the one you know as Henry Fonda.

For about the seventh time now: '2+1' denotes the value of the function.. — TonesInDeepFreeze

This is false as well, and you just don't seem to get it. Take a look at your example of "the father of Peter Fonda". The thing which you claim as "the value", is clearly not signified, because the premise required to produce the logical conclusion is not stated in the argument. We need a further "unstated" (that's the way I use quotations, to signify special significance) premise to make your assertion a valid conclusion. In your example, the required premise might be "the person you know as Henry Fonda is the father of Peter Fonda". Then you can validly conclude that when some one says "the father of Peter Fonda", this is the person you know as Henry Fonda.

The thing which you seem to have no respect for, is the fact that "the father of Peter Fonda" does not refer to "Henry Fonda". This is very clear from the fact that one stated premise in a logical argument cannot refer to a conclusion. "Socrates is a man" does not refer to the conclusion "Socrates is mortal". That is because the expression does not include everything required to make that reference. Nor does "2+1" refer to the value signified by "3", because it does not include everything required to make that reference.

When we jump to a logical conclusion without stating the required premises, error is possible. You know someone named "Henry Fonda"; you jump to the conclusion that this is the man referred to by "the father of Peter Fonda", and mistake is possible. Rigorous logic seeks to exclude the possibility of mistake, not to create the possibility of mistake. The principles you are arguing for create the possibility of mistake by removing the need for the statement of premises. If some premises can be taken for granted, and not stated, as you seem to believe, then those premises cannot be judged for truth of falsity, and error is possible.

But '2+1' is not a description of a procedure. — TonesInDeepFreeze

Well, clearly "2+1" does not refer to a value. That is an invalid conclusion as I explained above. So, if it does not refer to a procedure, as I think it does, is it possible that we can find a compromise?

You are not recognizing the distinctions between terms and statements, terms and arguments, reference and inference, extension and intension, denotation and connotation.

Rather than composing lessons for you on the subject, I recommend:

https://plato.stanford.edu/entries/frege/ [Section 3]

https://plato.stanford.edu/entries/logic-intensional/

'Introduction To Mathematical Logic' pgs 1-68 - Alonzo Church

Are you going to address the points I made or not, Tones?

Do you apprehend the flaw in your example, and the difference between what "the father of Peter Fonda" denotes , and what "Henry Fonda" denotes?

Do you apprehend the flaw in your example, and the difference between what "the father of Peter Fonda" denotes, and what "Henry Fonda" denotes? — Metaphysician Undercover

The terminology here is incorrect--these two signs denote the same object, even though what they signify about that object is different.

As I explained, they do not denote the same object. One denotes the father of a person called Peter Fonda. The other denotes a person named Henry Fonda. That they denote the same object requires a further premise, that the father of Peter Fonda is the person named Henry Fonda.

Without that premise, the conclusion that they denote the same thing is invalid. And adding that premise is to beg the question. So the argument that they denote the same object is fallacious.

Again, this confuses denotation with signification. In any and every proposition about "Henry Fonda," we could substitute "the father of Peter Fonda" without changing the truth value. That is what it means for two signs to have the same denotation.

Again, this confuses denotation with signification. — aletheist

Denotation is a form of signification.

In any and every proposition about "Henry Fonda," we could substitute "the father of Peter Fonda" without changing the truth value. — aletheist

As I said, this is only the case if there is a premise which states that Henry Fonda is the father of Peter Fonda. But that is begging the question, which is respected as a fallacy.

Therefore the argument that "the father of Peter Fonda" denotes the same thing as "Henry Fonda" is a fallacious argument, by means of begging the question. The argument relies on assuming the conclusion.

Denotation is a form of signification. — Metaphysician Undercover

Completely wrong, denotation and signification are two different aspects of a sign, corresponding respectively to its object and its interpretant. This is Semeiotic 101.

Therefore the argument that "the father of Peter Fonda" denotes the same thing as "Henry Fonda" is a fallacious argument, by means of begging the question. — Metaphysician Undercover

I offered no argument at all, I simply stated a definition--if one sign can be substituted for another in any and every proposition without changing the truth value, then both signs denote the same object. This is also Semeiotic 101.

I have given you copious explanation. There's no point in me composing more explanation when it is better said anyway at the sources I offered you.

Completely wrong, denotation and signification are two different aspects of a sign, corresponding respectively to its object and its interpretant. This is Semeiotic 101. — aletheist

That's bullshit 101. In logic, there is no object, we have subjects. To denote is simply to be a sign of.

I offered no argument at all, I simply stated a definition--if one sign can be substituted for another in any and every proposition without changing the truth value, then both signs denote the same object. This is also Semeiotic 101. — aletheist

Then you're not addressing the issue we've been discussing. We've been arguing the truth or falsity of of a very similar principle. The "Fonda" example was provided as an argument for the truth of it. As I've shown, it's a fallacious argument.

We were arguing the truth or falsity of the principle of substitution, which is the basis of extensionality. It is claimed that if two signifiers signify things of equal value, they are exchangeable, therefore they signify the very same object. It is very clear to me that this is a false principle because "equal" is assigned according to some system of judgement, so only the properties deemed significant within that system are accounted for, and this is insufficient for the conclusion of "the very same object". I find it utterly amazing, and rather distressing, the number of people in this forum who cannot apprehend this simple fact.

Now you are arguing a slightly different form of that principle. "Truth value" is something judged. Propositions are stated. Predications are of subjects. So within a logical system "truth value" concerns what we say about subjects, not objects. Unless absolutely every property of a given object is stated (a task humanly impossible), so that an infallible judgment can be made, your proposed principle: "if one sign can be substituted for another in any and every proposition without changing the truth value, then both signs denote the same object" Is clearly unacceptable as false. You have not provided the means for closing the subject/object gap.

1. If irrational numbers don't "exist" I shouldn't be able to create a number that doesn't have a repetend [a repeating finite set of digits]

2. I can create a number that lacks a repetend e.g. 1.01001000100001...

Ergo,

3. Irrational numbers "exist" (I just gave you an example)[1, 2 Modus Tollens]

In logic, there is no object, we have subjects. To denote is simply to be a sign of. — Metaphysician Undercover

Logic generalized is semeiotic, the science of all signs--not just arguments, but also propositions and terms; and not just symbols, but also indices and icons. Subjects are the terms within propositions that denote their objects.

Then you're not addressing the issue we've been discussing. — Metaphysician Undercover

I never claimed otherwise, I was simply correcting a misuse of the technical term "denote." Again, "Henry Fonda" and "the father of Peter Fonda" denote the same object, even though what they signify about that object is different. If we were looking at a photo of the Fonda family, and someone asked me to point to Henry and you to point to the father of Peter, then we would both correctly point to the same person.

It is claimed that if two signifiers signify things of equal value, they are exchangeable, therefore they signify the very same object. — Metaphysician Undercover

This reflects more terminological confusion. What a sign signifies is not its object, but its interpretant.

." Again, "Henry Fonda" and "the father of Peter Fonda" denote the same object, even though what they signify about that object is different. — aletheist

Again, your argument that they denote the same object is fallacious. They may or may not denote the same object. They clearly signify something different, and we do not have the premises required to conclude that they denote the same object. Therefore your conclusion that they denote the same object is fallacious.

They clearly signify something different, and we do not have the premises required to conclude that they denote the same object. — Metaphysician Undercover

I agree that they signify different interpretants, but this does not preclude them from denoting the same object. It is a fact that Henry Fonda is the father of Peter Fonda, so by definition, it is also a fact that the signs "Henry Fonda" and "the father of Peter Fonda" both denote the same object. Someone who does not know the first fact would not know the second fact either, but that is irrelevant to their being facts.

I agree that they signify different interpretants, but this does not preclude them from denoting the same object. It is a fact that Henry Fonda is the father of Peter Fonda, so by definition, it is also a fact that the signs "Henry Fonda" and "the father of Peter Fonda" both denote the same object. Someone who does not know the first fact would not know the second fact either, but that is irrelevant to their being facts. — aletheist

I commend you for fighting the good fight against @Metaphysician Undercover. But here I find myself inclined to see his side of it. I might know who Henry Fonda is, but I might not know he's Peter Fonda's father. I can see @Meta's point that the "father of Peter" description conveys more information than merely saying "That's Henry Fonda."

Just as he claims that 2 + 2 conveys the idea of a process putting two numbers together in some way, which is different information than just referring to the number 4. He's wrong about that mathematically, but he may have a point about Henry and Peter.

A stronger example in natural language is Joe Biden and the president of the US. Joe is always Joe, but being president is contingent and others have held and will hold that office. Joe Biden has always been and will always be Joe Biden; but Joe Biden has not always been president and will not always be president. So these two statements are different somehow.

I agree that they signify different interpretants, but this does not preclude them from denoting the same object. — aletheist

As I said, they may denote the same object, but we do not have the premises required to conclude that they do. In logic we cannot assume other premises which are not stated. We have a person denoted as "the father of Peter Fonda" and we have a person denoted as "Henry Fonda". We have no other information. So the conclusion that they both denote the same thing is extremely unsound, because it is not derived from valid logic. It is invalid.

t is a fact that Henry Fonda is the father of Peter Fonda, so by definition, it is also a fact that the signs "Henry Fonda" and "the father of Peter Fonda" both denote the same object. — aletheist

In logic, assertions do nothing for you. They are proposals, propositions which must be judged for truth or falsity. TonesinDeepFreeze has been asserting that "2+1" denotes the same object as "3" does, in a similar way. They very clearly each signify something different. The only attempt by Tones, to support this conclusion with a premise, was a vague reference to extensionality. But a premise which states that two equal things are the same thing is clearly false, making that argument unsound, by having such a falsity as a premise. To say that the person denoted as father of Peter Fonda, and the person denoted as Henry Fonda, are equal, as human beings, does not justify the claim that they are the same person.

If you just keep asserting as a proposition "it is a fact that...", and you expect me to take that proposition as a premise for an argument, then you're wrong. I will not. You need to demonstrate the truth of it. Adding the emphasis "it is a fact" does nothing for your case. I am very certain that two things with the same value are not necessarily the same thing, as I can give you endless examples, so that is a false premise.

But here I find myself inclined to see his side of it. — fishfry

Fishfry! Never in a hundred years did I think I'd see this day. Let's go, I'll buy you a beer.

I might know who Henry Fonda is, but I might not know he's Peter Fonda's father. I can see Meta's point that the "father of Peter" description conveys more information than merely saying "That's Henry Fonda." — fishfry

The point is that "the father of Peter Fonda" gives different information from "Henry Fonda". The latter gives nothing, just the name of a person. The first expression also denotes a person, as well as the second expression denotes a person. But the information required to conclude that they are one and the same person is not provided. Even if we add the further premise, "Henry has a son Peter", the condition of reversibility, equality, is fulfilled, but we still cannot conclude that they denote the same person. There might be more than one Henry Fonda with a son Peter. Therefore there is still a possibility of error, which demonstrates why such conclusions are unsound.

I might know who Henry Fonda is, but I might not know he's Peter Fonda's father. — fishfry

Again, what anyone knows or does not know is beside the point. Since it is fact that Henry Fonda is the father of Peter Fonda, by definition (in semeiotic) the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object.

I can see Meta's point that the "father of Peter" description conveys more information than merely saying "That's Henry Fonda." — fishfry

I have never denied this, but (in semeiotic) the information conveyed by a sign corresponds to its interpretant, not its object. If we were standing in a room with Henry Fonda--preferably back when he was alive--then we could point at him and truthfully say both "that is Henry Fonda" and "that is the father of Peter Fonda." Therefore, both signs denote the same object, despite signifying different interpretants.

As I said, they may denote the same object, but we do not have the premises required to conclude that they do. — Metaphysician Undercover

The only "premiss" required is the fact that Henry Fonda is the father of Peter Fonda. Someone previously unaware of this fact would learn that "Henry Fonda" and "the father of Peter Fonda" denote the same object upon being informed of it, but those two signs denoted the same object all along. Someone's ignorance does not affect the reality.

We have a person denoted as "the father of Peter Fonda" and we have a person denoted as "Henry Fonda". We have no other information. — Metaphysician Undercover

Again, in that scenario, I agree that we do not know that the two signs denote the same object; but that was never the scenario that I was discussing. I was simply pointing out that since I do know that Henry Fonda is the father of Peter Fonda, I also know that "Henry Fonda" and "the father of Peter Fonda" denote the same object. These are facts, not opinions.

To say that the person denoted as father of Peter Fonda, and the person denoted as Henry Fonda, are equal, as human beings, does not justify the claim that they are the same person. — Metaphysician Undercover

I never said anything about persons or equality. I merely made the point--which is utterly uncontroversial (in semeiotic)--that since Henry Fonda is the father of Peter Fonda, the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object, regardless of whether someone else knows it.

The point is that "the father of Peter Fonda" gives different information from "Henry Fonda". — Metaphysician Undercover

Again, I agree, the two signs signify different interpretants--i.e., convey different information--despite denoting the same object.

Fishfry! Never in a hundred years did I think I'd see this day. Let's go, I'll buy you a beer. — Metaphysician Undercover

Did you mean a beer? Or did you mean an alcoholic drink made from yeast-fermented malt flavored with hops? According to you they're two entirely different things :-)

The point is that "the father of Peter Fonda" gives different information from "Henry Fonda". — Metaphysician Undercover

I agree with you about this point of natural language. But I still disagree regarding 2 + 2 = 4, even thoug I do see the point you're trying to make.

The latter gives nothing, just the name of a person. The first expression also denotes a person, as well as the second expression denotes a person. But the information required to conclude that they are one and the same person is not provided. Even if we add the further premise, "Henry has a son Peter", the condition of reversibility, equality, is fulfilled, but we still cannot conclude that they denote the same person. There might be more than one Henry Fonda with a son Peter. Therefore there is still a possibility of error, which demonstrates why such conclusions are unsound. — Metaphysician Undercover

That latter is a bit disingenuous. If I say Socrates is a Greek philosopher, someone might object because they think I might have meant Socrates the cat philosopher. That's not really a good objection, if you fully qualified everything there would be no end to it.

Again, what anyone knows or does not know is beside the point. Since it is fact that Henry Fonda is the father of Peter Fonda, by definition (in semeiotic) the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object. — aletheist

Thank you. My granting of @Metaphysician Undercover's point is causing me to waver on 2 + 2 = 4. I need to read more of your posts so I can strengthen my backbone. Henry Fonda IS the father of Peter and that's that. There goes the beer @Meta was going to buy me, which according to @Meta is NOT the same as, "an alcoholic drink made from yeast-fermented malt flavored with hops."
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I have never denied this, but (in semeiotic) the information conveyed by a sign corresponds to its interpretant, not its object. If we were standing in a room with Henry Fonda--preferably back when he was alive--then we could point at him and truthfully say both "that is Henry Fonda" and "that is the father of Peter Fonda." Therefore, both signs denote the same object, despite signifying different interpretants. — aletheist

As you can see, @Meta has gotten into my head over the years. Must ... stay ... strong ...

The point is that "the father of Peter Fonda" gives different information from "Henry Fonda".
— Metaphysician Undercover
Again, I agree, the two signs signify different interpretants--i.e., convey different information--despite denoting the same object. — aletheist

Thank you for this clarification. Must remember it. Must not weaken. 2 + 2 = 4. Please don't take me to room 101.

Again, what anyone knows or does not know is beside the point. Since it is fact that Henry Fonda is the father of Peter Fonda, by definition (in semeiotic) the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object. — aletheist

These are nonsensical assertions. You are asserting that it is a fact that these words refer to these objects regardless of how people use the words. The issue is whether or not "the father of Peter Fonda" and "Henry Fonda" necessarily represent the same object. That you can define them as representing the same object, and insisting that this is a fact, is irrelevant I don't see any point in discussing the soundness of a logical argument with someone like who, who simply insists that the conclusion is a fact, and that's all there is to it.

If you want to start with the premise, that Henry Fonda is the father of Peter, we can do that. But then the example is irrelevant to the question of whether "2+1" denotes the same thing as "3", because we are not starting with that premise. We are arguing whether or not this claim is true, or logically sound. So we cannot start with the premise that "2+1" denotes the same thing as "3" because that would be a fallacy of begging the question.

So, to make the example relevant, we must start with the two expressions, "father of Peter Fonda", and "Henry Fonda", and you need to demonstrate how they necessarily refer to the same object, without begging the question. Insisting that it is a fact is simply begging the question, and that is a logical fallacy. So your procedure up until now has been completely useless.

I never said anything about persons or equality. I merely made the point--which is utterly uncontroversial (in semeiotic)--that since Henry Fonda is the father of Peter Fonda, the two signs "Henry Fonda" and "the father of Peter Fonda" denote the same object, regardless of whether someone else knows it. — aletheist

Yes, yes, keep begging the question, it really doesn't bother me if you do. You're only fooling yourself.

That latter is a bit disingenuous. If I say Socrates is a Greek philosopher, someone might object because they think I might have meant Socrates the cat philosopher. That's not really a good objection, if you fully qualified everything there would be no end to it. — fishfry

Let me give you a more relevant example. Let's consider an experiment in quantum physics. Consider that a photon is emitted by an emitter, and a photon is absorbed by a detecting machine. Each instance involves an equivalent amount of energy, so the assumption is that the two are the same photon. Then comes the difficult task of determining the continuous existence of that photon between point A and point B, which is produced by the idea that they are the same photon. But there is no need to assume that the two are the same photon, likewise there is no need to assume a continuous existence of the photon between point A and point B. It is only this (what I call odd) way of looking at things, that if there is a quantifiable value here, then an equal value over there, these must represent the same thing, which promotes the idea of the continuous existence of a photon between these two point.

Henry Fonda IS the father of Peter and that's that. — fishfry

As explained above, to premise that "Henry Fonda IS the father of Peter" is no different from premising that "2+1 IS 3". But since what I am looking for is an indication that 2+1 really is the same thing as 3, some sort of logical argument, that's simply begging the question. So the issue is to demonstrate logically, how it is that the two distinct expressions "the father of Peter Fonda", and "Henry Fonda" both refer to the exact same thing, and how this is relevant to the case of "2+1" and "3".

As you can see, @Meta has gotten into my head over the years. — fishfry

You had me a little worried for a while there. :wink:

Thank you for this clarification. — fishfry

You are welcome, I am glad that it was helpful. :cool:

So, to make the example relevant, we must start with the two expressions, "father of Peter Fonda", and "Henry Fonda", and you need to demonstrate how they necessarily refer to the same object, without begging the question. — Metaphysician Undercover

Good grief, I never said that they necessarily denote the same object, I only said that they actually denote the same object. That is why I kept calling this a fact. If Henry Fonda were not the father of Peter Fonda, then obviously the signs "Henry Fonda" and "the father of Peter Fonda" would not denote the same object. What I mainly wanted to do was simply point out the difference between what a sign denotes (its object) and what a sign signifies (its interpretant).

Then the example is irrelevant to the issue we are discussing, that "2+1" denotes the same object as "3".

You joined the discussion a bit late, and seem to be missing the issue.

Then the example is irrelevant to the issue we are discussing, that "2+1" denotes the same object as "3". — Metaphysician Undercover

I have quite deliberately said nothing directly about that issue until now, because I was mainly interested in commenting on the other example that came up. Its relevance has to with the question whether "2+1" and "3" are likewise different signs that denote the same object despite signifying different interpretants. The problem, of course, is that we cannot even in principle point at something and say both "that is 2+1" and "that is 3." However, we can point at a collection of three apples and say both "that is 2+1 apples" and "that is 3 apples." Moreover, we can substitute "2+1" for "3" in any proposition without changing its truth value or in any equation without changing its result. What should we conclude from this?