No abacus can do arithmetic. An abacus just sits there.
No backhoe can excavate. A backhoe just sits there.
A trained agent can use an abacus to do arithmetic, just as one can use a backhoe to excavate. Can you define “do arithmetic” in such a manner that it is at least as easy to prove that arithmetic has been done as it is to prove that excavation has been done?
I’ve watched mine for several hours, and it hasn’t.
No, you haven’t. (p=0.9)
Have you observed a calculator doing arithmetic? What would it look like?
It could look like an electronic object with a plastic shell that starts with “(23 + 54) / (47 * 12 + 76) + 1093” on the screen and some small amount of time after an apple falls from a tree and hits the “Enter” button some number appears on the screen below the earlier input, beginning with “1093.0”, with some other decimal digits following.
If the above doesn’t qualify as the calculator doing “arithmetic” then you’re just using the word in a way that is not just contrary to common usage but also a terrible way to carve reality.
I didn’t do that immediately prior to posting, but I have watched my calculator for a cumulative period of time exceeding several hours, and it has never done arithmetic. I have done arithmetic using said calculator, but that is precisely the point I was trying to make.
Does every device which looks like that do arithmetic, or only devices which could in principle be used to calculate a large number of outcomes? What about an electronic device that only alternates between displaying “(23 + 54) / (47 * 12 + 76) + 1093” and “1093.1203125″ (or “1093.15d285805de42”) and does nothing else?
Does a bucket do arithmetic because the number of pebbles which fall into the bucket, minus the number of pebbles which fall out of the bucket, is equal to the number of pebbles in the bucket? Or does the shepherd do arithmetic using the bucket as a tool?
I didn’t do that immediately prior to posting, but I have watched my calculator for a cumulative period of time exceeding several hours, and it has never done arithmetic. I have done arithmetic using said calculator, but that is precisely the point I was trying to make.
And I would make one of the following claims:
Your calculator has done arithmetic, or
You are using your calculator incorrectly (It’s not a paperweight!) Or
There is a usage of ‘arithmetic’ here that is a highly misleading way to carve reality.
Does every device which looks like that do arithmetic, or only devices which could in principle be used to calculate a large number of outcomes?
In the same way that a cardboard cutout of Decius that has a speech bubble saying “5” over its head would not be said to be doing arithmetic a device that looks like a calculator but just displays one outcome would not be said to be doing arithmetic.
I’m not sure how ‘large’ the number of outcomes must be, precisely. I can imagine particularly intelligent monkeys or particularly young children being legitimately described as doing rudimentary arithmetic despite being somewhat limited in their capability.
Does a bucket do arithmetic because the number of pebbles which fall into the bucket, minus the number of pebbles which fall out of the bucket, is equal to the number of pebbles in the bucket? Or does the shepherd do arithmetic using the bucket as a tool?
It would seem like in this case we can point to the system and say that system is doing arithmetic. The shepherd (or the shepherd’s boss) has arranged the system so that the arithmetic algorithm is somewhat messily distributed in that way. Perhaps more interesting is the case where the bucket and pebble system has been enhanced with a piece of fabric which is disrupted by passing sheep, knocking in pebbles reliably, one each time. That system can certainly be said to be “counting the damn sheep”, particularly since it so easily generalizes to counting other stuff that walks past.
But now allow me to abandon my rather strong notions that “calculators multiply stuff and mechanical sheep counters count sheep”. I’m curious just what the important abstract feature of the universe is that you are trying to highlight as the core feature of ‘arithmetic’. It seems to be something to do with active intent by a generally intelligent agent? So that whenever adding or multiplying is done we need to track down what caused said adding or multiplication to be done, tracing the causal chain back to something that qualifies as having ‘intention’ and say that the ‘arithmetic’ is being done by that agent? (Please correct me if I’m wrong here, this is just my best effort to resolve your usage into something that makes sense to me!)
It’s not a feature of arithmetic, it’s a feature of doing.
I attribute ‘doing’ an action to the user of the tool, not to the tool. It is a rare case in which I attribute an artifact as an agent; if the mechanical sheep counter provided some signal to indicate the number or presence of sheep outside the fence, I would call it a machine that counts sheep. If it was simply a mechanical system that moved pebbles into and out of a bucket, I would say that counting the sheep is done by the person who looks in the bucket.
If a calculator does arithmetic, do the components of the calculator do arithmetic, or only the calculator as a whole? Or is it the system of which does arithmetic?
I’m still looking for a definition of ‘arithmetic’ which allows me to be as sure about whether arithmetic has been done as I am sure about whether excavation has been done.
Well, you do have to press certain buttons for it to happen. ;) And it looks like voltages changing inside an integrated circuit that lead to changes in a display of some kind. Anyway, if you insist on an example of something that “does arithmetic” without any human intervention whatsoever, I can point to the arithmetic logic unit inside a plugged-in arcade machine in attract mode.
Can you define “do arithmetic” in such a manner that it is at least as easy to prove that arithmetic has been done as it is to prove that excavation has been done?
Is still somewhat important to the discussion. I can’t define arithmetic well enough to determine if it has occurred in all cases, but ‘changes on a display’ is clearly neither necessary nor sufficient.
Well, I’d say that a system is doing arithmetic if it has behavior that looks like it corresponds with the mathematical functions that define arithmetic. In other words, it takes as inputs things that are representations of such things as “2”, “3“, and “+” and returns an output that looks like “6”. In an arithmetic logic unit, the inputs and outputs that represent numbers and operations are voltages. It’s extremely difficult, but it is possible to use a microscopic probe to measure the internal voltages in an integrated circuit as it operates. (Mostly, we know what’s going on inside a chip by far more indirect means, such as the “changes on a screen” you mentioned.)
There is indeed a lot of wiggle room here; a sufficiently complicated scheme can make anything “represent” anything else, but that’s a problem beyond the scope of this comment. ;)
Note that neither an abacus nor a calculator in a vacuum satisfy that definition.
I’ll allow voltages and mental states to serve as evidence, even if they are not possible to measure directly.
Does a calculator with no labels on the buttons do arithmetic in the same sense that a standard one does?
Does the phrase “2+3=6” do arithmetic? What about the phrase “2*3=6″?
I will accept as obvious that arithmetic occurs in the case of a person using a calculator to perform arithmetic, but not obvious during precisely what periods arithmetic is occurring and not occurring.
Anyway, if you insist on an example of something that “does arithmetic” without any human intervention whatsoever, I can point to the arithmetic logic unit inside a plugged-in arcade machine in attract mode.
… which was plugged in and switched on by, well, a human.
I think the OP is using their own idiosyncratic definition of “doing” to require a conscious agent. This is more usual among those confused by free will.
No abacus can do arithmetic. An abacus just sits there.
No backhoe can excavate. A backhoe just sits there.
A trained agent can use an abacus to do arithmetic, just as one can use a backhoe to excavate. Can you define “do arithmetic” in such a manner that it is at least as easy to prove that arithmetic has been done as it is to prove that excavation has been done?
Does a calculator do arithmetic?
I’ve watched mine for several hours, and it hasn’t. Have you observed a calculator doing arithmetic? What would it look like?
No, you haven’t. (p=0.9)
It could look like an electronic object with a plastic shell that starts with “(23 + 54) / (47 * 12 + 76) + 1093” on the screen and some small amount of time after an apple falls from a tree and hits the “Enter” button some number appears on the screen below the earlier input, beginning with “1093.0”, with some other decimal digits following.
If the above doesn’t qualify as the calculator doing “arithmetic” then you’re just using the word in a way that is not just contrary to common usage but also a terrible way to carve reality.
Upvoted for this alone.
I didn’t do that immediately prior to posting, but I have watched my calculator for a cumulative period of time exceeding several hours, and it has never done arithmetic. I have done arithmetic using said calculator, but that is precisely the point I was trying to make.
Does every device which looks like that do arithmetic, or only devices which could in principle be used to calculate a large number of outcomes? What about an electronic device that only alternates between displaying “(23 + 54) / (47 * 12 + 76) + 1093” and “1093.1203125″ (or “1093.15d285805de42”) and does nothing else?
Does a bucket do arithmetic because the number of pebbles which fall into the bucket, minus the number of pebbles which fall out of the bucket, is equal to the number of pebbles in the bucket? Or does the shepherd do arithmetic using the bucket as a tool?
And I would make one of the following claims:
Your calculator has done arithmetic, or
You are using your calculator incorrectly (It’s not a paperweight!) Or
There is a usage of ‘arithmetic’ here that is a highly misleading way to carve reality.
In the same way that a cardboard cutout of Decius that has a speech bubble saying “5” over its head would not be said to be doing arithmetic a device that looks like a calculator but just displays one outcome would not be said to be doing arithmetic.
I’m not sure how ‘large’ the number of outcomes must be, precisely. I can imagine particularly intelligent monkeys or particularly young children being legitimately described as doing rudimentary arithmetic despite being somewhat limited in their capability.
It would seem like in this case we can point to the system and say that system is doing arithmetic. The shepherd (or the shepherd’s boss) has arranged the system so that the arithmetic algorithm is somewhat messily distributed in that way. Perhaps more interesting is the case where the bucket and pebble system has been enhanced with a piece of fabric which is disrupted by passing sheep, knocking in pebbles reliably, one each time. That system can certainly be said to be “counting the damn sheep”, particularly since it so easily generalizes to counting other stuff that walks past.
But now allow me to abandon my rather strong notions that “calculators multiply stuff and mechanical sheep counters count sheep”. I’m curious just what the important abstract feature of the universe is that you are trying to highlight as the core feature of ‘arithmetic’. It seems to be something to do with active intent by a generally intelligent agent? So that whenever adding or multiplying is done we need to track down what caused said adding or multiplication to be done, tracing the causal chain back to something that qualifies as having ‘intention’ and say that the ‘arithmetic’ is being done by that agent? (Please correct me if I’m wrong here, this is just my best effort to resolve your usage into something that makes sense to me!)
It’s not a feature of arithmetic, it’s a feature of doing.
I attribute ‘doing’ an action to the user of the tool, not to the tool. It is a rare case in which I attribute an artifact as an agent; if the mechanical sheep counter provided some signal to indicate the number or presence of sheep outside the fence, I would call it a machine that counts sheep. If it was simply a mechanical system that moved pebbles into and out of a bucket, I would say that counting the sheep is done by the person who looks in the bucket.
If a calculator does arithmetic, do the components of the calculator do arithmetic, or only the calculator as a whole? Or is it the system of which does arithmetic?
I’m still looking for a definition of ‘arithmetic’ which allows me to be as sure about whether arithmetic has been done as I am sure about whether excavation has been done.
Well, you do have to press certain buttons for it to happen. ;) And it looks like voltages changing inside an integrated circuit that lead to changes in a display of some kind. Anyway, if you insist on an example of something that “does arithmetic” without any human intervention whatsoever, I can point to the arithmetic logic unit inside a plugged-in arcade machine in attract mode.
And if you don’t want to call what an arithmetic logic unit does when it takes a set of inputs and returns a set of outputs “doing arithmetic”, I’d have to respond that we’re now arguing about whether trees that fall in a forest with no people make a sound and aren’t going to get anywhere. :P
Well, yeah. My question:
Is still somewhat important to the discussion. I can’t define arithmetic well enough to determine if it has occurred in all cases, but ‘changes on a display’ is clearly neither necessary nor sufficient.
Well, I’d say that a system is doing arithmetic if it has behavior that looks like it corresponds with the mathematical functions that define arithmetic. In other words, it takes as inputs things that are representations of such things as “2”, “3“, and “+” and returns an output that looks like “6”. In an arithmetic logic unit, the inputs and outputs that represent numbers and operations are voltages. It’s extremely difficult, but it is possible to use a microscopic probe to measure the internal voltages in an integrated circuit as it operates. (Mostly, we know what’s going on inside a chip by far more indirect means, such as the “changes on a screen” you mentioned.)
There is indeed a lot of wiggle room here; a sufficiently complicated scheme can make anything “represent” anything else, but that’s a problem beyond the scope of this comment. ;)
edit: I’m an idiot, 2 + 3 = 5. :(
Note that neither an abacus nor a calculator in a vacuum satisfy that definition.
I’ll allow voltages and mental states to serve as evidence, even if they are not possible to measure directly.
Does a calculator with no labels on the buttons do arithmetic in the same sense that a standard one does?
Does the phrase “2+3=6” do arithmetic? What about the phrase “2*3=6″?
I will accept as obvious that arithmetic occurs in the case of a person using a calculator to perform arithmetic, but not obvious during precisely what periods arithmetic is occurring and not occurring.
… which was plugged in and switched on by, well, a human.
I think the OP is using their own idiosyncratic definition of “doing” to require a conscious agent. This is more usual among those confused by free will.