it would be of no use. — Janus

It has been of use though because all of the examples of addition you have used so far in your life have been consistent with some quus-like rule. If you could have used that rule so far, then clearly it could have been of use.

It isn't really about intentional use anyway. The premise is that you have been using the addition rule for the whole of your life and you know it intimately. Then someone comes a long and questions: "How do you know you are not actually using quadditon? give me a justification of this."

Use is not so much relevant in that you would have to demonstrate that you are in fact using the "useful" rule, and that somewhere a long the line the future you are not going to give an answer that other people might find totally inconsistent with addition (but consistent with the "useless" rule). How can you demonstrate that you are not going to do that and you are in fact using the "useful" rule?

It's not dogmatism: I'll change my mind — Janus

I don't mean dogmatism in the sense of you not changing your mind, I mean dogmatism more in how it is used here:

https://en.m.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

You are defending the use of addition over other rules without demonstrating it. Your main justification so far seems to be that anything other than addition is arbitrary, but that in itself seems dogmatic. What do you mean by arbitrary other than that is just what you are used to, what seems natural... just what feels right? That seems to be dogmatism in the sense of the above wikipedia article.

If you can demonstrate that some rule could always yield the same result as addition and yet differs from it in the very part of it that does so. So, for example quaddition is exactly the same as addition up to any sum that does not exceed 57. — Janus

Again, its not about the difference between the two rules - we know they are different. It is about whether you can justify that a single rule you have been using is addition and not quaddition.

It may be easier to think about it analogous to how theories compete in science. For instance, Special relativity and Newtonian mechanics are very obviously different. But from our perspective on earth right now it may not be apparent which one is correct because they yield more or less the same results in our everyday context. We need an experiment to demonstrate one is the case and not the other.

I am therefore asking for your experiment about this. Asking me to demonstrate that quus always yields the same result as plus yet is also somehow different is an impossible contradition. They are just different. Yet, in our difficulty in figuring out whether the laws of nature are obeying Special relativity or Newtonian mechanics, would you also ask me to demonstrate that Newtonian mechanics gives different results yet is also the same as Special relativity? No, because that isn't relevant. We know they are different models; the question is which one is being instantiated right now on earth, which has to be demonstrated by experiment.

For the quus example, where is the experimental demonstration that you have been using addition and not quus (and then not any other type of quus-like overlapping rule)?

Edit: I hope this last part has addressed your arguments in the sense of saying that your arguments are erroneous and not relevant to the problem just like how trying to demonstrate that Special relativity is both somehow the same and different to Newtonian mechanics is not relevant to the question of whether Newtonian or Special relativity is actually the case on earth. Only an experiment can differentiate the two, which is also what you have to analogously/metaphorically provide to differentiate quus and plus.

The connection is that: it is only in the context of public language as we use everyday, in a way that must be consistent with other people's language usage, that we find notions of rules and definitions determined - because we are checked by public consensus.

The point of the private language argument is that: without these checks, language seems redundant and there does not seem to be an inherent need for people to characterize the things they see in the world, or rules they apply, in one specific way or another (as illustrated by Kripke's quus rule-following paradox). Wittgenstein seems to suggest that giving things determinate labels via a private language seems to have no contribution on people's behavior and cognizance of the world.

You are defending the use of addition over other rules without demonstrating it. Your main justification so far seems to be that anything other than addition is arbitrary, but that in itself seems dogmatic. What do you mean by arbitrary other than that is just what you are used to, what seems natural... just what feels right? That seems to be dogmatism in the sense of the above wikipedia article. — Apustimelogist

I'm not defending the use of anything, all I've been saying is that addition seems to me to be a natural development of cognition-based counting, and there is no reason to say that counting is any different in principle regardless of how many things are counted, or addition any different no matter how many things are added.

I understand the logic of counting and addition, and I also understand how the logic of addition is consistent with the logic of multiplication, subtraction and multiplication. Do you think the logic of quaddition is consistent with those or some equivalents?

The other thing is that the logic of quaddition is the exactly same as the logic of addition up until its arbitrarily stipulated divergence regarding numbers over 57. There is no cognition-based logic to justify such an arbitrary stipulation, so I deem the whole thing a lame non-issue; I see no significance in it. And since no one seems to be able to tell me what the significance is, I will waste no more time on this unless someone does.

Thanks for trying, but none of that means anything to me I'm afraid.

I have addressed the thing you asked me to demonstrate, now I think you should try and address what I asked you to demonstrate.

You say you unddrstand the logic of addition; lay out for me that logic then and give me the facts that rule out that you will give a quus-type answer in future uses of addition.

all I've been saying is that addition seems to me to be a natural development of cognition-based counting — Janus

And why can't I just question whether you have been quonting all along instead of counting?

There is no cognition-based logic to justify such an arbitrary stipulation — Janus

There is nothing that logically forbids someone from just using quaddition either.

There is no cognition-based logic to justify such an arbitrary stipulation

You don't have a cognition based logic to justify it other than you are used to addition. Not really a justification imo... "it just is because it is and anything I am not familiar with is wrong"... That's how it sounds.

At the end of the day, in the thought experiment, the data so far is just as consistent with the use of quus as plus.

I deem the whole thing a lame non-issue; I see no significance in it. — Janus

Well the significance is that you can't seem to refute it. Its very simple to refute Newtonian mechanics - for instance: under such and such conditions, time dilation occur; time dilation is impossible in Newtonian mechanics; Newtonian mechanics refuted. You don't seem to be able to use logic to justify addition at all.

This whole thing deep down is about the relationship between words and the world. The question is something like: do words have a fixed one-to-one relationship with the things that exist in the world in a way that they are intrinsically related? Does our behavior and thoughts prescribed in a rigidly defined, top-down manner by words and definitions, as if meaning has some kind of essence to it?

The alternative is: no, there is not a one-to-one fixed relationship between words and the world. Instead, we make labels and place them where we please and there are no fixed boundaries that force us to label things one way or another. We can, in principle, place the boundaries any way we like. Meaning is not essential in definitions but inferred from our behavior and how we use words in a bottom up manner. Our intractably, complicated behavior comes first.

If you think about it in this sense, what is in question is not whether we use quus or plus... we have a certain kind of mathematical behavior that we use very well for our own ends, but there is no single way to characterize it or label it or put boundaries around it. This underdeterminism has no consequence for our behavior because as I said just now, the behavior comes first, directly caused by the intractably complicated mechanistic behavior of our brains. And as our brains are just neurons communicating, there is nothing inherently semantically characterizable in what the brain is doing because its just mechanistic physics and there is probably not even a single way for brains to do any given task it is capable of.

You say you unddrstand the logic of addition; lay out for me that logic then and give me the facts that rule out that you will give a quus-type answer in future uses of addition. — Apustimelogist

I have already said that the logic of addition is unlimited iteration; in principle we can keep adding forever. The logic of quaddition like rules diverges from this when it stipulates some hiatus or terminus at whatever arbitrary point.

As long as such a quaddition-like rule does not diverge from the normal logic of addition, then there is no discernible difference and hence no need to use a different name to signify that procedure.

This whole thing deep down is about the relationship between words and the world. The question is something like: do words have a fixed one-to-one relationship with the things that exist in the world in a way that they are intrinsically related? Does our behavior and thoughts prescribed in a rigidly defined, top-down manner by words and definitions, as if meaning has some kind of essence to it? — Apustimelogist

Of course, words don't have a fixed one to one relationship with the world. However, numbers do correspond to actual number as instantiated in the diverse and multitudinous world. Two is always two regardless of what word you use to signify the concept. In contrast the concepts /tree/ or /animal/ are not so determinate. So, introducing questions about ordinary language into a discussion of counting and addition is only going to confuse the issue.

but there is no single way to characterize it or label it or put boundaries around it. — Apustimelogist

I don't need to do that; I don't need to define some essence in order to know that I am counting or adding. I don't even need to define the rule because the logic of counting and adding accords with the logic inherent in the cognition of mutlitudinous things.

Nothing new regarding this is emerging from you, so I think we are done.

I have already said that the logic of addition is unlimited iteration; in principle we can keep adding forever. — Janus

But what do you mean when you say "adding" or "forever". How am I sure you don't actually mean "qu-orever" instead of "forever"?

The logic of quaddition like rules diverges from this when it stipulates some hiatus or terminus at whatever arbitrary point. — Janus

So what, this doesn't stop anyone using quaddition. It is both logically and literally possible to use the rule quaddition.

As long as such a quaddition-like rule does not diverge from the normal logic of addition, then there is no discernible difference and hence no need to use a different name to signify that procedure. — Janus

Yes, but equally someone could use that logic to say that quus should be preferred and there is no reason to use a different name of "addition" to signify it.

Two is always two regardless of what word you use to signify the concept. — Janus

How is this any different from saying that the image of the world I see is the same regardless of the boundaries I wish to draw on it and the way I wish to partition my concepts that describe it?

In contrast the concepts /tree/ or /animal/ are not so determinate. — Janus

But the image of a tree or an animal you see is determinate. Is the way you group different things as "trees" or "animals" much different from say describing things as prime numbers or odd and even or any other kind of mathematical concept? Can't addition, multiplication and subtraction all be grouped as operators?

So, introducing questions about ordinary language into a discussion of counting and addition is only going to confuse the issue. — Janus

No, because this whole issue is meant to be a generic property of all language. Quus was only given as a single example.

I don't need to do that; I don't need to define some essence in order to know that I am counting or adding — Janus

Okay, you know you're adding. But how do you know that what you are adding is not infact quadding, and how can you demonstrate that?

I don't even need to define the rule because the logic of counting and adding accords with the logic inherent in the cognition of mutlitudinous things. — Janus

How can you say it accords with anything if you can't define it, meaning how do you know that other rules don't also accord with the logic inherent with cognition.

Nothing new regarding this is emerging from you, so I think we are done. — Janus

I wouldn't be still saying anything if you would just give me what I want, but you can't. If you could, you would have done it literally days ago. You cannot actually resolve the underdetermination inherent in the problem. There is no way you can rule out using various different rules instead of addition without being dogmatic i.e. declaring that it is addition for no evidence or reason other than "you feel it", and because you can't even demonstrate you're actually adding, you cannot even demonstrate that what you feel is actually truly addition and not quaddition. And with your choice of dogmatism, equally someone else could be equally dogmatic and just declaring that they are using quus just because thats what "feels right". You can say they're wrong. But they could say you're just wrong, and there's no way to resolve it... which is I guess where we are at!

But what do you mean when you say "adding" or "forever". How am I sure you don't actually mean "qu-orever" instead of "forever"? — Apustimelogist

Forever means there is no limit in prinicple. What does "qu-orever" mean? Tell me that and I'll tell you whether I meant that.

I wouldn't be still saying anything if you would just give me what I want, but you can't. — Apustimelogist

I don't even know what you want me to give, since you apparently are unable to articulate it clearly.

and because you can't even demonstrate you're actually adding, you cannot even demonstrate that what you feel is actually truly addition and not quaddition. — Apustimelogist

C'mon man, this is total bullshit. I know what adding consists in, and if you could tell me precisely what quadding consists in then I could point to how it is different than adding. Inosfar as it is not different it is a moot point.

This is my last response unless you can explain exactly what you mean and want.

What does "qu-orever" mean? — Janus

I think it means, "Until you drop dead while adding 320 to 180 and only manage to say '5' before you keel over."

We will all stand around saying, "See, he was using quaddition!"

Forever means there is no limit in priniciple. What does "qu-orever" mean — Janus

You've just repeated a synonym for "forever" so how does that help? What does "no limit" mean and does any of this really help without specifying what exactly has "no limit"? That would be "adding" presumably so you're back to where you started and probably should characterize that to me first.

"Quo-rever" is just an analogous concept for forever, exactly like quus where all your uses of forever so far are consistent with it but it differs in some way. But tbh, forever or infinite seems so abstract it seems difficult to point to what you mean anyway: how exactly can someone show they are referring to the infinite? hence why when I asked what forever meant, you just replied with a synonym effectively. But again, the target here isn't really forever but addition. This explanation youve given is essentially "I am adding forever" but "adding" was what was in question in the first place so how is saying " I am adding forever" resolving the issue?

You could have meant " I am quusing forever"

Tell me that and I'll tell you whether I meant that. — Janus

Well I already told you that is irrelevant. This is just like the Newtonian vs Special relativity example I already gave. Its not about what you think you mean, its whether you can prove a fact of the matter about what you think you mean.

I don't even know what you want me to give, since you apparently are unable to articulate it clearly. — Janus

Whats so hard? Prove that when you use "addition" at any given time you don't mean quus or some other quus-like word. A fact that unambiguously shows that every time you say "addition" you cannot be meaning any of these other alternative phrases.

C'mon man, this is total bullshit. I know what adding consists in, and if you could tell me precisely what quadding consists in then I could point to how it is different than adding. — Janus

I think I will jist have to leave a quotation from Kripke:

"Let us return to the example of 'plus' and 'quus'. We have just summarized the problem in terms of the basis of my present particular response: what tells me that I should say '125' and not '5'? Of course the problem can be put equivalently in terms of the sceptical query regardIng my
present intent: nothing in my mental hIstory establishes whether I meant plus or quus. So formulated, the problem may appear to be epistemological - how can anyone know which of these I meant? Given, however, that everythIng In
my mental history is compatible both with the conclusion that I meant plus and with the conclusion that I meant quus, It is clear that the sceptical challenge is not really an epIstemological one. It purports to show that nothing in the mental history of past behavior - not even what an omniscient God would know - could establish whether I meant plus or quus.
But then it appears to follow that there was no fact about me that constituted my having meant plus rather than quus. How could there be, if nothing in my internal mental history or external behavior will answer the sceptic who supposes that in fact I meant quus? If there was no such thing as my meaning plus rather than quus in the past, neither can there be any such a thing in the present. When we initially presented the paradox,
we perforce used language, taking present meanings for granted. Now we see, as we expected, that this provisional concession was indeed fictive. There can be no fact as to what I
mean by 'plus', or any other word at any time. The ladder must finally be kicked away.

This, then, is the sceptical paradox. When I respond in one way rather than another to such a problem as '68+57', I can have no justification for one response rather than another. Since the sceptic who supposes that I meant quus cannot be answered, there is no fact about me that distinguishes between my meaning plus and my meaning quus. Indeed, there is no
fact about me that distinguishes between my meaning a definite function by 'plus' (which determines my responses in new cases) and my meaning nothing at all.

Sometimes when I have contemplated the situation, I have had something of an eerie feeling. Even now as I write, I feel confident that there is something in my mind - the meaning I attach to the 'plus' sign - that instructs me what I ought to do in all future cases. I do not predict what I will do - see the discussion immediately below - but instruct myself what I ought to do to conform to the meaning. (Were I now to make a prediction of my future behavior, it would have substantive content only because it already makes sense, in terms of the instructions I give myself, to ask whether my intentions will be conformed to or not.) But when I concentrate on what is now in my mind, what instructions can be found there? How can I be said to be acting on the basis of these instructions when I act in the future? The infinitely many cases of the table are not in my mind for my future self to consult. To say that there is a general rule in my mind that tells me how to add in the future is only to throw the problem back on to other rules that also seem to be given only in terms of finitely many cases. What can there be in my mind that I make use of when I act in the future? It seems that the entire idea of meaning vanishes into thin air."

No, the point is the rule can never be determined, If he says 5, someone will just ask him to show he was using phlog-ddition!

I think it means, "Until you drop dead while adding 320 to 180 and only manage to say '5' before you keel over."

We will all stand around saying, "See, he was using quaddition!" — wonderer1

:lol: Yeah, that's about how seriously I take this nonsense.

You've just repeated a synonym for "forever" so how does that help? What does "no limit" mean and does any of this really help without specifying what exactly has "no limit"? — Apustimelogist

Any term can only be defined in other terms, so how does any term help? :roll: You know as well as I do what 'forever' in the context of 'addition can go on in principle forever'. You also know what 'no limit' means in the context of 'there is no reason to think there is, in principle, any limit to addition'.

Any term can only be defined in other terms, so how does any term help? :roll: You know as well as I do what 'forever' in the context of 'addition can go on in principle forever'. You also know what 'no limit' means in the context of 'there is no reason to think there is, in principle, any limit to addition'. — Janus

Well this is the point, nothing helps. You may say that "you know as well as I do" but if I interpret "forever" in a non-standard way that is consistent with your past usage of the word forever then whats not to say that you mean something else other than "forever".

Kripke says -

"Here of course I am expounding Wittgenstein's wellknown remarks about "a rule for interpreting a rule". It is tempting to answer the sceptic by appealing from one rule to another more 'basic' rule. But the sceptical move can be repeated at the more 'basic' level also. Eventually the process
must stop - "justifications come to an end somewhere" - and I am left with a rule which is completely unreduced to any other. How can I justify my present application ofsuch a rule,
when a sceptic could easily interpret it so as to yield any of an indefinite number of other results? It seems that my application of it is an unjustified stab in the dark. I apply the rule blindly."

We start with noting that there is a number so large, you've never dealt with it before, but in our challenge, we'll just pick 57. You've never dealt with anything over that. You and I are sitting with a skeptic. — frank

I think that this challenge is even less straightforward than we think it is and that the quoted portion must be evaluated first.

When one says that they've never dealt with a number over 57, does that mean that we do not know if addition will work when trying to add things to sums greater than 57? Or does it just mean that we haven't bothered to add that high but have the knowledge that addition will definitely continue to work?

This dilemma could allow for one or the other. I think that this challenge is interesting but the meaning of "you've never dealt with anything over that" seems to not indicate any clear constraints.

If it means the former, then the simple answer that mentions at the bottom of the first page does not apply. It does not matter if the rules of addition when handling sums over 57 must be consistent to preserve our knowledge of arithmetic if what appeared to be addition just stops working the way we think it would because really, we have been quadding - and this doesn't even mean the rules have changed as we have potentially been quadding this whole time. Or maybe addition sticks if we have knowledge that addition extends to (potential) sums that are greater than the greatest number we've ever encountered.

But I don't see that anywhere. So long as this uncertainty exists it seems to me we must side with the skeptic: you cannot prove that we can add 57 and 68 to 125, or that we haven't been quadding, because quaddition is one of an infinite number of equally valid rules that might dictate what happens when handling sums over 57 that could be consistent with the behavior observed when adding with sums less than 57.

Sorry Frank if you are over this thread already and have moved on.

When one says that they've never dealt with a number over 57, does that mean that we do not know if addition will work when trying to add things to sums greater than 57? Or does it just mean that we haven't bothered to add that high but have the knowledge that addition will definitely continue to work? — ToothyMaw

The thought experiment is pretty contrived to get the point across. I think he picks 57 for the sake of explaining his criteria for a rule-following-fact. But there probably is a number above which you've never added. Your knowledge of addition is not under threat. The aim of the thought experiment is to examine your intentions regarding past rule following.

Kripke admits that you would tell the skeptic she's crazy.

Well, I tried to contribute something. Thanks for the response, Frank.

:up: