Im mostly on board with this until Act Three. I dont think mentioning norms and practices explains why we agree on novel cases, even without specifically communicating about them beforehand. The permissiveness in the case of the sonata doesnt help is with addition, where we agree there is only one right answer. De facto we learn norms about meaning from something like reinforcement learning, and that can no more/less beat the induction problem than linguistic deliberation can.
>You can bite the bullet and try to define a method for counting but eventually this chain will have to end and you’ll arrive at some term that can’t rely on any other.
I think the problem where a basic terms is defined in so that it creates an exception specifically when were adding 68 + 57, is avoided here by looking for specifically a context-free language of mathematics. For that, we have a good understanding of how an algorithm does it without any explicit represetation of "context-freeness".
Thanks for the input! An important part of Act 3 is that it denies that we do "agree on novel cases" with the kind of determinate force you're implying, or that we do "agree there is only one right answer" to a novel addition. I think that that appearance (and the problems it raises) is dissolved by redescribing the situation as us simply not disagreeing on novel cases and not diverging on the answers we give to novel additions.
Much of the time, the difference isn't palpable, but it matters when potential for disagreement does in fact occur. For example, in the history of mathematics, there were times when addition with negative numbers, zero and infinities was disputed. If we're saying that our norms for addition mean that we "agree on novel cases", then when the question of 1 + 0 comes along for the first time, we should agree at least on what our current practice of addition says about the question, even if we disagree on how to amend our definitions. But this is not how such situations work. Instead, 1 + 0 is simply undefined at the beginning because people were always operating on nothing more than a lack of disagreement for a range of more familiar cases.
I don't think I understood your point about context-freeness but the formalisations that are available with algorithms don't help with the core problem. Kripke is not worried about whether we can do addition or whether we can construct finite methods or devices that do it, he's worried about our grounds for saying that what a human/method/device/algorithm does is 'addition'. This is a problem of semantics rather than practice. The way we design algorithms already presumes a background of linguistic norms, it doesn't help settle the question of what those norms are.
>For example, in the history of mathematics, there were times when addition with negative numbers, zero and infinities was disputed.
I dont think this helps. I agree it makes more sense to say addition wasnt defined for those initially, but there still are potentially-infinite examples of addition of positive natural numbers, that we are highly confident we wont diverge on, and indeed will answer identically without knowing the others answer.
>Kripke is not worried about whether we can do addition
Neither am I. Im asking 1) How do I know we are very unlikely to diverge about addition of positive natural numbers? 2) How do I develop an addition-process thats unlikely to diverge from that of others, since I cant literally copy-paste it?
>I don't think I understood your point about context-freeness... The way we design algorithms already presumes a background of linguistic norms, it doesn't help settle the question of what those norms are.
Yeah, thats not what I mean. I think that 1) As per above, non-linguistic interaction cant establish norms from nothing any more than linguistic interaction. 2) Because of this, you already need to start out aligned, in some sense. 3) But obviously we arent born with the concept of addition. You need to acquire it from interaction somehow. 4) So we need to find a point on which its plausible we already are aligned from the start, and explain how we reach alignment on addition based on that.
And here I think context-freeness is a good candidate for something we might be aligned on prior to any active norm-making.
It's important to note the switch from any implication that "we know we won't diverge because we have the same understanding" to "we feel highly confident we won't diverge" - if the latter is the best we've got (and I think it is), it implies a fundamental difference in the kind of thing we've converged on.
So how do we get this confidence? Now that we've demoted knowledge to mere confidence, I see no reason to think that this question is different from asking how we become confident that we'll play a Beethoven sonata similarly. It's part of the psychological constitution of human beings to engage in similar activities in similar ways given similar circumstances and information. The generative quality of addition doesn't change anything - there are all sorts of unforeseen interpretative challenges that arise in playing music which people will agree on how to tackle without prior co-ordination.
The feeling that we need a formal underpinning, linguistic or not, ignores the contribution of biology. You ask "how do I develop an addition process that's unlikely to diverge, since I can't literally copy-paste it?" - you're an evolved ape with built-in cognitive biases and a specialty for behaviour imitation. Orangutans develop normative practices for fishing with sticks without language or concepts - language expands the scope of the practices we can co-ordinate but it doesn't fundamentally change how norms work.
Just to be clear, when you say "we aren't born with the concept of addition. You need to acquire it from interaction somehow," you're denying the thrust of Kripke's argument by assuming we do construct an addition concept. So although you said you were on board until Act 3, your issue is not that Act 3 is an inadequate solution per se, it's that you think the Kripkean skepticism of Acts 1 & 2 doesn't work and you (knowingly or unknowingly) want to reject Kripke's conclusion. For that to hold, there ought to be some facts about our practices that Kripke gets wrong and I'm not aware of any such facts.
>It's part of the psychological constitution of human beings to engage in similar activities in similar ways given similar circumstances and information. The generative quality of addition doesn't change anything
The odds of divergence are much lower with addition, and that changes something in my mind. Humans are only so similar, and that on its own is plausibly enough for the sonata interpretation, but not addition.
I do think that positing just bio-psychological similarity as the intial alignment is a viable fallback position, but that would still need to be "metabolised" by some sort of interaction/process to get the high reliability of addition.
>your issue is not that Act 3 is an inadequate solution per se, it's that you think the Kripkean skepticism of Acts 1 & 2 doesn't work.
I think 1&2 present real difficulties, which can be avoided only if we have something more to work with than in their setup. Im suggesting we construct the addition concept out of something else *which we also dont have according to 1&2*. Insofar as Kripkes solution boils down to "just agreeing" due to shared biology, I dont see how I reject 1&2 any more than he does.
I definitely think there are *some* concepts were born with, just not addition in particular. I dont see how 1&2 exculdes *all* concept constructions - surely once I *do* have some shared meaning, I can still define other things in terms of it?
As I said, I do think just biology as a backing is viable as a minimal position, and Im glad we did get to that - a lot of other pro-kripkenstein stuff insists on not admitting any backing. But its still open just how much human-specific biology mess plays into it in the end - for example, "sweet" would be very difficult for an alien to understand, probably impossible before modern chemistry, but I think we would understand each other about addition relatively well. It could well be that the relevant dispositions for that are simple, and then its not unrealistic we share them even with the alien.
Good question. I didn’t give strict definitions and, actually, I might want to find a better word than ‘consensus’ for what I was talking about.
If we’ve got a community that’s in the habit of doing x by doing y (e.g. adding by counting), a ‘convention’ would be explicitly agreeing to do so by following a rule of language (i.e. people say to each other “we do x by doing y” and then they do x by doing y), whereas ‘consensus’ (at least as I used it here) is simply doing x by doing y without disagreement about what we’re doing - there’s no rule which we follow in doing x.
On the consensus view, we’ll still say to each other things like “we do x by doing y,” but these statements function more like prompts than instructions because language can never describe completely what anyone actually does.
Does it help to note that the consensus about basic arithmetic seems frequently justified by our experience of interacting with the world around us, such as in being able to figure out how much flour will be needed to bake a cake large enough for all the guests?
Im mostly on board with this until Act Three. I dont think mentioning norms and practices explains why we agree on novel cases, even without specifically communicating about them beforehand. The permissiveness in the case of the sonata doesnt help is with addition, where we agree there is only one right answer. De facto we learn norms about meaning from something like reinforcement learning, and that can no more/less beat the induction problem than linguistic deliberation can.
>You can bite the bullet and try to define a method for counting but eventually this chain will have to end and you’ll arrive at some term that can’t rely on any other.
I think the problem where a basic terms is defined in so that it creates an exception specifically when were adding 68 + 57, is avoided here by looking for specifically a context-free language of mathematics. For that, we have a good understanding of how an algorithm does it without any explicit represetation of "context-freeness".
Thanks for the input! An important part of Act 3 is that it denies that we do "agree on novel cases" with the kind of determinate force you're implying, or that we do "agree there is only one right answer" to a novel addition. I think that that appearance (and the problems it raises) is dissolved by redescribing the situation as us simply not disagreeing on novel cases and not diverging on the answers we give to novel additions.
Much of the time, the difference isn't palpable, but it matters when potential for disagreement does in fact occur. For example, in the history of mathematics, there were times when addition with negative numbers, zero and infinities was disputed. If we're saying that our norms for addition mean that we "agree on novel cases", then when the question of 1 + 0 comes along for the first time, we should agree at least on what our current practice of addition says about the question, even if we disagree on how to amend our definitions. But this is not how such situations work. Instead, 1 + 0 is simply undefined at the beginning because people were always operating on nothing more than a lack of disagreement for a range of more familiar cases.
I don't think I understood your point about context-freeness but the formalisations that are available with algorithms don't help with the core problem. Kripke is not worried about whether we can do addition or whether we can construct finite methods or devices that do it, he's worried about our grounds for saying that what a human/method/device/algorithm does is 'addition'. This is a problem of semantics rather than practice. The way we design algorithms already presumes a background of linguistic norms, it doesn't help settle the question of what those norms are.
>For example, in the history of mathematics, there were times when addition with negative numbers, zero and infinities was disputed.
I dont think this helps. I agree it makes more sense to say addition wasnt defined for those initially, but there still are potentially-infinite examples of addition of positive natural numbers, that we are highly confident we wont diverge on, and indeed will answer identically without knowing the others answer.
>Kripke is not worried about whether we can do addition
Neither am I. Im asking 1) How do I know we are very unlikely to diverge about addition of positive natural numbers? 2) How do I develop an addition-process thats unlikely to diverge from that of others, since I cant literally copy-paste it?
>I don't think I understood your point about context-freeness... The way we design algorithms already presumes a background of linguistic norms, it doesn't help settle the question of what those norms are.
Yeah, thats not what I mean. I think that 1) As per above, non-linguistic interaction cant establish norms from nothing any more than linguistic interaction. 2) Because of this, you already need to start out aligned, in some sense. 3) But obviously we arent born with the concept of addition. You need to acquire it from interaction somehow. 4) So we need to find a point on which its plausible we already are aligned from the start, and explain how we reach alignment on addition based on that.
And here I think context-freeness is a good candidate for something we might be aligned on prior to any active norm-making.
It's important to note the switch from any implication that "we know we won't diverge because we have the same understanding" to "we feel highly confident we won't diverge" - if the latter is the best we've got (and I think it is), it implies a fundamental difference in the kind of thing we've converged on.
So how do we get this confidence? Now that we've demoted knowledge to mere confidence, I see no reason to think that this question is different from asking how we become confident that we'll play a Beethoven sonata similarly. It's part of the psychological constitution of human beings to engage in similar activities in similar ways given similar circumstances and information. The generative quality of addition doesn't change anything - there are all sorts of unforeseen interpretative challenges that arise in playing music which people will agree on how to tackle without prior co-ordination.
The feeling that we need a formal underpinning, linguistic or not, ignores the contribution of biology. You ask "how do I develop an addition process that's unlikely to diverge, since I can't literally copy-paste it?" - you're an evolved ape with built-in cognitive biases and a specialty for behaviour imitation. Orangutans develop normative practices for fishing with sticks without language or concepts - language expands the scope of the practices we can co-ordinate but it doesn't fundamentally change how norms work.
Just to be clear, when you say "we aren't born with the concept of addition. You need to acquire it from interaction somehow," you're denying the thrust of Kripke's argument by assuming we do construct an addition concept. So although you said you were on board until Act 3, your issue is not that Act 3 is an inadequate solution per se, it's that you think the Kripkean skepticism of Acts 1 & 2 doesn't work and you (knowingly or unknowingly) want to reject Kripke's conclusion. For that to hold, there ought to be some facts about our practices that Kripke gets wrong and I'm not aware of any such facts.
>It's part of the psychological constitution of human beings to engage in similar activities in similar ways given similar circumstances and information. The generative quality of addition doesn't change anything
The odds of divergence are much lower with addition, and that changes something in my mind. Humans are only so similar, and that on its own is plausibly enough for the sonata interpretation, but not addition.
I do think that positing just bio-psychological similarity as the intial alignment is a viable fallback position, but that would still need to be "metabolised" by some sort of interaction/process to get the high reliability of addition.
>your issue is not that Act 3 is an inadequate solution per se, it's that you think the Kripkean skepticism of Acts 1 & 2 doesn't work.
I think 1&2 present real difficulties, which can be avoided only if we have something more to work with than in their setup. Im suggesting we construct the addition concept out of something else *which we also dont have according to 1&2*. Insofar as Kripkes solution boils down to "just agreeing" due to shared biology, I dont see how I reject 1&2 any more than he does.
I definitely think there are *some* concepts were born with, just not addition in particular. I dont see how 1&2 exculdes *all* concept constructions - surely once I *do* have some shared meaning, I can still define other things in terms of it?
As I said, I do think just biology as a backing is viable as a minimal position, and Im glad we did get to that - a lot of other pro-kripkenstein stuff insists on not admitting any backing. But its still open just how much human-specific biology mess plays into it in the end - for example, "sweet" would be very difficult for an alien to understand, probably impossible before modern chemistry, but I think we would understand each other about addition relatively well. It could well be that the relevant dispositions for that are simple, and then its not unrealistic we share them even with the alien.
What’s the diff between convention and consensus, shared attitude of a community? Soon as I ask that I say to myself, “Does it matter?”
Good question. I didn’t give strict definitions and, actually, I might want to find a better word than ‘consensus’ for what I was talking about.
If we’ve got a community that’s in the habit of doing x by doing y (e.g. adding by counting), a ‘convention’ would be explicitly agreeing to do so by following a rule of language (i.e. people say to each other “we do x by doing y” and then they do x by doing y), whereas ‘consensus’ (at least as I used it here) is simply doing x by doing y without disagreement about what we’re doing - there’s no rule which we follow in doing x.
On the consensus view, we’ll still say to each other things like “we do x by doing y,” but these statements function more like prompts than instructions because language can never describe completely what anyone actually does.
Does it help to note that the consensus about basic arithmetic seems frequently justified by our experience of interacting with the world around us, such as in being able to figure out how much flour will be needed to bake a cake large enough for all the guests?