Why are we assuming that quaddition has some weird exception clause? The notions are completely interdefinable, so this cuts both ways. Fom the perspective of the one doing quaddition, it is the one who was adding who didn't go on in the same way forever, but suddenly changed and started doing something different.
I'm pretty sure Tjump committed himself to the view that plants, grass, and treetops are NOT green. Because he's defining something green to be something that NEVER changes it's color. He even said at time 8 kajillion years from now the thing will still be green and that's what he means by a thing being green. So when Tree's die and their leaves turn brown, they were never green to begin with because green things stay green forver. When grass dies or even gets frozen over and turns a yellowish color before it springs back to life, it's not green. Because if it were green, then it would stay green forever without changing according to Tom. And those are just the obvious ones...I could do this with green apples, grapes, algae, etc. Literally anything that's green that will eventually change cannot be considered green. I wonder what color Tom would tell me the grass is if I pointed at it and asked him. It couldn't be green. Edit: I wrote this comment before Professor Brown addressed this. I unpaused after writing this and he immediately addressed it when talking about faded green things and the green apple. I should've waited to comment but it just seemed like such a hilarious entailment I had to pause and comment lol.
1:25:52: I think this one sentence from prof Brown really helped something click for me. On one hand, I can imagine writing software programs to do plus and quus, and for each operation, I could have the program output a tuple where one output is the mathematical output and a second output is literally the computer code that it ran. I had initially thought to myself, then, that it must be the case that we _can_ know what rule the system is following. However, the issue is that there are factors external to that rule itself that bears upon what rule it’s following. It seems related to the Turing halting problem, though not quite the same thing. For example, prof Brown used the example of a finite state automata to represent the possible states a calculator can be in. It is necessarily finite because the parts will inevitably wear out, or there are physical limitations on the device. On the other hand, at the bare-metal level, the “addition” operation is essentially just going to be some logic gates processing electrical signals. What the logic gates do _absolutely is_ a rule that is universal, and in one respect, we do know that’s what the gate is doing. However, the cause of the execution of the rule is not an _internal_ matter, it is an _external_ one, so the fact that justifies what rule the gate is following _cannot_ come from an internal place at all. I think I am starting to understand. Edit: I think the halting problem comparison may have been a little hasty. I still think there are some interesting similarities between the sorts of reasons that makes it difficult to determine when an algorithm is going to halt and the sorts of reasons that make it difficult to pin down what rule is being followed. However, at their core, the halting problem is more about recursive self-reference, whereas rule-following is more about internal/external justification. At least, that’s how I think I understand it.
How exactly does appealing to communal norms rescue one from this sort of extreme skepticism? By the same argument, how could you ever know what the community expects, or what anyone in it truly means. How do you even know which community you're in for that matter?
I’m by no means very savvy with rule-following, but I totally agree. I don’t really feel like the skeptical solution of relying on the community has ever felt very satisfying, I have always felt like and individual is still going to have the same issue even within a community, but also, what constitutes the community itself feels to me like a weak foundation - how does the community expand or contrast itself against another community then?
Tom admits that the PCB plus the externality (the hammer as he calls it), would be doing quadition. And then he says that without the externality, it would be doing addition. But doesn't this commit him to saying that no PCB ever does addition? Because to do quadition is to do addition up until a certain point. With this is mind, every single PCB will be destroyed at some point. Every person will die. Every machine will stop working. So Tom defines the PCB breaking as analogous to quadition, which would mean that no PCB ever performs the function of addition, since they will all break and will thus have all been doing quadition the entire time. And when I say quadition, I'm just using that rule because that's the one they are using in the discussion.
the argument seems to presuppose that there is one objectively correct and an infinite number of obectively incorrect ways a system could be working and i dont really see a reason to assume that. see "the purpose of a system is what it does"
Nooo! That's not how programming a computer or a calculator works at all! There is no lookup table like kids are learning multiplication from. This is _not_ how it works at all. The opposite is true. A very specific procedure is implemented in a calculator/computer. This procedure is called an algorithm. So yes, it is always the case that either addition is implemented (the calculator is running the addition algorithm) or quaddition is implemented (the calculator is running the quaddition algorithm). And it is perfectly clear, always.* Of course, someone who uses a calculator may not know the algorithm. Especially when he's adding the numbers for which the two distinct algorithms yield the same results. But it's only an epistemic problem - not knowing the procedure. And an analogous thing happens with us. If I learn one operation for adding numbers, I am following that rule that I learned. It's in my memory. I do not need to have many examples in memory. When I add numbers, I don't retrieve results from memory. Instead, I _perform an operation_ and what operation performs determines whether I'm doing addition or quaddition. I am conscious of the operation I perform. The higher levels of education is not an objection at all. The most you could say is that I'm doing a high-school level addition, and not university-level addition. But in neither case I would be doing any quaddition. *) Of course, one _can_ program a lookup table for a couple of operations like that. In fact, you can find code like that. But this is always done as a "programmer joke". But real hardware doesn't do that.
@WackyConundrum good point, we never said the world 'algorithm' but did use 'program' which is the same thing in this context. The program in the calculator will eventually output an E, and then you get the argument which I was giving in the discussion. It is not dependent on it being a lookup table (that was more about how elementary school kids learn), it is about whether you can tell what program is being implemented. As for you 'conscious awareness' of the operation, have you ever tried to add and made a mistake? If so how can you tell you added incorrect as opposed to implement some other operation correctly? (remember that the skeptical argument is applied only to your past behavior and the question is what about you makes it true that, in the past, you meant addition as opposed to quadition)
@@onemorebrown The only way of verification would be empirical verification. When I add 3 + 5 in my mind and get a result, I could verify what the number would be when I count 3 apples and then another 5 apples, for example. Another form of verification would be to use another operation of adding (writing on a piece of paper, say). And yes, in most cases we don't have 100% certainty. But that just means we are not omniscient / perfect. Just because we sometimes make mistakes, doesn't mean that we cannot perform a given operation in general. The "perform a given operation" is given through the intention of my knowledge of a particular operation (mechanism, procedure). As for whether I am able to tell what algorithm is being run, this question seems to suggest that there are mind-independent meanings of words, which is absurd, since language is a human project and concepts are mind "objects". So, of course language depends on society, time, and place. And of course concepts depend on the mind (concepts are _in_ minds, after all). So, the most I (and anyone else for that matter) can do is to intend to perform a given operation (as understood by me), and then act it out in the intersubjective world (behavior that is observable to others). I do not consider this to be a "skeptical" or "anti-realist" position. Concepts and rules are real - they exist in our minds.
