I'm not seeing the relevance to deciding whether addition, subtraction, multiplication and division are basically derivable from counting operations. — Janus
Neither do I see a real significance in the distinction between "natural"and "artificial" concepts. — Apustimelogist
I don't see the phenomenological dimension of philosophy as "armchair speculation", but rather as reflection on what we actually do.
— Janus
Well thats more or less what I mean. — Apustimelogist
As I have already said, the quus issue has no relevance or consequence for people's ability to do things but I think if you are interested in notions of realism or whether we can have objective characterizations, problems like this are very interesting and central. — Apustimelogist
I think if you consider that quantitative abilities and counting might be primitive processes we cannot non-circularly decine then I would say actually, yes we are blind to these. — Apustimelogist
If you can't derive addition from counting then how are you proving you are doing addition? — Apustimelogist
inevitably evolve out of experience — Janus
Well, it's not what I mean. Armchair speculation I would class as metaphysics, not phenomenology. — Janus
I don't see the relevance at all, and no one seems to be able to explain clearly what it is, so... — Janus
We are not blind to considering how counting and the basic arithmetical operations can be instantiated using actual objects. This is not the case with quus. — Janus
You can derive addition from counting. Counting basically is addition. — Janus
has been saying that what these concepts mean and how they relate to each other is not trivial in a way that questions whether counting actually does much at all in this context. You want to use the example of counting tonshow you can get to what we deem thr correct answer but I think demonstrating your ability to meet a goal is not the same as specifying a description or meaning of what you actually did.— "Moliere
I think ultimately what is "natural" just boils down to something like an impelled preference and I don't see that as a valid way of arguing that something is somehow unique, correct or objective. — Apustimelogist
I don't really see how phenomenology is not another form of armchair speculation in a similar way. — Apustimelogist
The relevance for what? Its simply the issue of whether the descriptions you ascribe to behavior is uniquely determined as opposed to underdetemined or indeterminate. — Apustimelogist
I can demonstrate quus with objects just as well as I can with addition. — Apustimelogist
You keep mentioning objectivity, which has nothing to do with what I've been arguing — Janus
It's not mere speculation because experience is something we can reflect on and analyze. Metaphysics is not based on experience at all but on imaginative hypothesizing. — Janus
I don't believe you can. — Janus
I think in many ways reflecting on experience is just that though. I feel like people can have radically different views of what experiences are, what feelings are, what they actually perceive, and how do people make something of their perceptions other than by intuition? — Apustimelogist
Hmm, thinking about it, I think it might be difficult if your intuitions are set on counting rather that quounting. But maybe a quonter would find no problem with it. — Apustimelogist
I have been talking specifically about synthetic a priori knowledge of what is intrinsic to embodied experience: spatiotemporality, differentiation and the other attributes I mentioned. — Janus
If you have four piles of four objects then you have sixteen objects, three piles of three objects then you have nine, two piles of two objects you have four. This obviously cannot work with two objects, so I'm not seeing the relevance to deciding whether addition, subtraction, multiplication and division are basically derivable from counting operations. — Janus
But not the significance that know-how doesn't give a determinate know-that — Apustimelogist
Well, if they're not derivable from counting then your argument against quusing isn't really talking about the same kind of thing since you've outlined a procedure for deciding if someone is quusing by pointing out that we can count beyond the quuser. But if it's not counting then that doesn't really demonstrate that a person is adding or quusing. The operations are distinct, rather than reducible to counting. — Moliere
You could come up with a million absurd and arbitrary rules like quusing, and all I can say is "so what?". The logic of counting is inherent in cognition; even animals can do basic counting. And I see no reason not to think that basic arithmetic finds its genesis in counting. Give me a good reason not to think that and I will reconsider. — Janus
So maybe a more plain-language way of putting the question frank opened with (though I haven't read the text he's supplied, so I could be wrong): the skeptic might be asking how do you know the answer is not "the time is about 10:25" given that 125 divides into 12 10 times with a rough estimate of 25 minutes. — Moliere
I'd say that basic arithmetic's genesis is in abstraction more than counting. But whether that's a good reason or not is up to you. — Moliere
The challenge is about rule following, specifically about rule following activity that's now in the past. It's not an epistemic problem. It's not about what a person knows about which rule they followed. It's that there's no fact (a situation existing in the world) even in terms of mental states that satisfies Kripke's criteria for a rule-following-fact.
The idea of quadition was just to convey the problem. Kripke wasn't trying to do philosophy of math, although there have apparently been philosophers of math who were interested in it. — frank
My thoughts on it (so far) is that it fits pretty well with my belief that we aren't as rational in practice as we tend to think we are. I think some people would assume that means I end up a behaviorist, but I'd say they're making the same mistake again. They think their post hoc rationalizations are the way the world really is. It's not. — frank
I don't think I'd reduce rationality to rule-following either. — Moliere
I think what Janus's position amounts to is that there is a kind of fact, namely the familiar rules of arithmetic, which is the natural way to believe a person to be thinking about the question "how many?" — Moliere
I think some people would assume that means I end up a behaviorist — frank
Quaddition seems to arbitrarily countermand the natural logic of counting and addition; the logic that says there is neither hiatus nor terminus. — Janus
I don't believe arithmetic to be merely rule following, but I think it is something we get intuitively on account of its being naturally implicit in cognition. Some animals can do rudimentary counting, which means they must be aware of number.
So, it begins with recognition of difference and similarity, then gestalted objects, then counting of objects, and this basis is elaborated in the functions of addition, subtraction, multiplication and division. Mathematical symbols and the formulation of arithmetical rules then open up the possibility of endless elaboration and complexification. — Janus
Counting makes sense as a genesis of arithmetic. But is doesn't escape from the sceptical question. There is no fact of the matter that determines whether I have counted correctly - except the fact that others will agree with me. This reinforces me in my practice of counting, as my agreement with others about their counts reinforces their practice of counting. — Ludwig V
I hope that makes it clear how I see it. I'm happy for others to disagree, provided they disagree with things I actually think, and not some imagined position based on their misunderstanding. — Janus
If they don't make any difference, how are they alternative?It is therefore possible to use alternative concepts without any difference in behaviour. — Apustimelogist
There would only be a logic to countermand if there was a sensible definition of these things in the first place which specified the correct behavior without requiring prior understanding — Apustimelogist
What is fundamental to understanding concepts is not their definition, but knowing how to apply the definition. That is a practice, which is taught. Learning to count and measure defines number and quantity.I don't think you can give me a satisfying definition of counting or quantity, — Apustimelogist
There is a natural logic of these things. But we had to learn how to do it. It seems natural because it is a) useful and b) ingrained. "Second nature".the natural logic of counting and addition; — Janus
Here there's a few bases from which we could confuse one another: arithmetic as a practice, arithmetic as a part of our rational intuition, arithmetic as rule-following, arithmetic as it was in its genesis, and arithmetic as it is. — Moliere
There would only be a logic to countermand if there was a sensible definition of these things in the first place which specified the correct behavior without requiring prior understanding... and if rules like quaddition provided different outcomes to addition. — Apustimelogist
Counting makes sense as a genesis of arithmetic. But is doesn't escape from the sceptical question. There is no fact of the matter that determines whether I have counted correctly - except the fact that others will agree with me. — Ludwig V
I ask you to add 68+57.
You confidently say "125."
The skeptic asks, "How did you get that answer?"
You say "I used the rules of addition as I have so often before, and I am consistent in my rule following."
The skeptic says, "But wait. You haven't been doing addition. It was quaddition. When you said plus, you meant quus, and: x quus y = x+y for sums less than 57, but over that, the answer is always 5. So you haven't been consistent. If you were consistent, you would have said "5."" — frank
Hard to attain, at times. All we can do is re-state, try again, and all that. I read you as taking an intuitionist stance, as in mathematics is a part of our natural intuition that's even shared with other creatures, and so the skeptic has no basis because the skeptic is framing arithmetic in terms of rule-following when there's more to arithmetic than rule-following, such as the intuitive use of mathematics, whereas the skeptic's use is derivative of that (and so is an illegitimate basis of their skepticism, considering that the skeptic is undermining their own position in the process)
Let me know if that's close or not. — Moliere
There is a natural logic of these things. But we had to learn how to do it. It seems natural because it is a) useful and b) ingrained. "Second nature". — Ludwig V
If they don't make any difference, how are they alternative?
On the other hand, it is perfectly possible for two or more of us to get along quite well for a long time with different interpretations of the same concept or rule. The differences will not show themselves until a differentiating case turns up. This could happen with quaddition or any other of the many possibilities. Then we have to argue it out. The law, of course, is the arena where this most often becomes an actual problem. — Ludwig V
What is fundamental to understanding concepts is not their definition, but knowing how to apply the definition. That is a practice, which is taught. Learning to count and measure defines number and quantity. — Ludwig V
As stipulated the rules of quaddition do provide different outcomes: — Janus
My point here is the forward problem as described earlier. Even though quaddition has particular outcomes, someone can generate all of the behavior of addition and define it, have definitions, without using addition, even if they require a plethora of other concepts to make it work. And again, this all depends on people agreeing with all the necessary concepts which are required to make something like quaddition work. My understanding of all concepts is scaffolded on prior concepts and prior implicit understanding or abilities that have been learned by practise without definitions. — Apustimelogist
Even if you could come up with something, that wouldn't change the fact that addition is intuitively gettable, while the alternative is just some arbitrary set of rules that happened to work, and which would be parasitic on the gettability of addition in any case. — Janus
I think you can. If you can make up arbitrary rules like quaddition then you can think up infinite many rules which give describe all the same processing ability. — Apustimelogist
To you maybe. It might be totally unintuitive to a different kind of being. — Apustimelogist
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