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ChristianKl comments on What are your contrarian views? - Less Wrong Discussion
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The truth of a statement depends on the context in which the statement is made.
The full meaning of a statement depends on the context in which it is made.
Just to clarify, you mean that there is a context in which "0 = 1" is a true statement, which is not tantamount to redefining "0", "=", or "1"? That is, in some alternate universe, "0 = 1" is consistent with the axioms of Peano arithmatic?
In most cases the numbers that normal humans use don't follow strictly the axioms of Peano. Most of the time the dates of a month follow Peano. Most of the time the day after September 2 is September 3. But not always.
On a computer you can't store every natural number as specified by Peano with common integers.
If you start counting apples and get really many apples you suddenly have a black hole and no apples anymore.
I don't know enough about the philosophy of math to get really deep by we had lately someone writing posts about constructivist math that also contained the notion that there are no absolute mathematical truths.
In that case, it sounds like you're just not a math realist. There are plenty of people who believe that Peano arithmetic somehow exists on its own. Or possibly people who have a different definition of "exist" from me. It's hard to tell the difference. But I don't think disagreeing with that is all that unusual.
I'm not good enough at math to confidently answer that question. I'm good enough at math that I think that people want to debate whether or not something like infinite small numbers exist.
I don't care primarily about math. I see math as a tool. I'm happy that there are some people who build useful math and I'm happy to use it when convenient but it's not central for me.
I think this is uncontroversial if taken as referring to the following two things:
and controversial but not startlingly so if taken as referring to the following:
Are you intending to state something more than those?
There are some people who believe that there something called objective reality and you can check whether a statement is true in objective reality.
I say that a statement might be true in context A but false in context B.
I don't think you answered my question. (Perhaps because you think it's meaningless or embodies false presuppositions or something.)
Aside from the facts that (1) the same utterance can mean different things in different contexts, (2) indexical terms can refer differently in different contexts, and (3) different values and preferences may be implicit in different contexts, do you think there are further instances in which the same statement may have different truth values in different contexts?
(I think the boundary between #1 and "real" differences in truth value is rather fuzzy, which I concede might make my question unanswerable.)
Some concrete examples may be useful. The following seem like examples where one can avoid 1,2,3. Are they ones where you think the truth value might be context-dependent, and if so could you briefly explain what sort of context differences would change the truth value?
The fact that you claim to get 7 digits of accuracy by multiplying two 4 digit numbers is very questionable. If I would go after my physics textbook 1234 times 4321 = 5332000 would be the prefered answer and 1234 times 4321 = 5332114 would be wrong as the number falsely got 3 additional digits of accuracy.
A more exotic issue is whether times is left or right associative. The python pep on matrix multiplication is quite interesting. It goes through edge cases such as whether matrix multiplication is right or left associative.
Red is actually a quite nice example. Does it mean #FF0000? If so, the one that my monitor displays? The one that my printer prints? On is red not a property of an object but a property of the light and it means light with a certain wavelength? That means that if I light the room a certain way the colors of objects change. If it's a property of the object, what's when the object emits red light but doesn't reflect it? Alternatively red could also be something that triggers the color receptors of humans in a specific way. In that case small DNA changes in the person who perceives red alter slightly what red means. But "human red" is even more complex because the brain does comlex postprocessing after the color receptors have given a certain output.
If red means #FF0000 then is #EE0000 also red or is it obviously not red because it's not #FF0000? What do you do when someone with design experience and who therefore has many names for colors comes along and says that freshly spilled human blood is crimson rather than red? If we look up the color crimson you will find that Indiana University has IU crimson and the University of Kansas has KU crimson. Different values for crimson make it hard to decide whether or not the blood is actually colored crimson.
Depending on how you define red mixing it with green and blue might give you white or it might give you black.
I used to naively think that I can calculate the difference between two colors by calculating the Hamilton distance of the hex values. There even a W3C recommendation of defining the distance of colors for website design that way. It turns out it you actually need a formula that's more complex and I'm still not sure whether the one the folks gave me on ux.stackexchange is correct for human color perception. Of course you need to have a concept of distance if you want to say that red is #FF0000 +- X.
I also had lately on LW a disagreement about what colors mean when I use red to mean whatever my monitor shows me for red/#FF0000 because my monitor might not be rightly calibrated.
You might naively think that the day after September 2 is always September 3. That turns out not to be true. There also a case where a September 14 follows after a September 2. Some people think that a minute always has 60 seconds but the official version is that it can also sometimes have 61. It get's worse. You don't know how many leap seconds will be introduced in the next ten years. It get's announced only 6 months in advance. That means it's practically impossible to build a clock that tells the time accurately down to a second in ten years. If you look closer at statements things usually get really messy.
The US airforce shoot down an US helicopter in Iraq partly because they don't consider helicopters to be aircraft. Most of the time you can get away with making vague statements for practical purposes but sometimes a change in context changes the truth value of a statement and then you are screwed.
Multiplication: so this looks like you're again referring to meanings being context-dependent (in this case the meaning of "= 5332114"). So far as I can see, associativity has nothing whatever to do with the point at issue here and I don't understand why you bring it up; what am I missing?
Redness: yeah, again in some contexts "red" might be taken to mean some very specific colour; and yes, colour is a really complicated business, though most of that complexity seems to me to have as little to do with the point at issue as associativity has to do with the question of what 1234x4321 is.
So: It appears to me that what you mean by saying that statements' truth values are context-dependent is that (1) their meanings are context-dependent and (2) people are often less than perfectly precise and their statements apply to cases they hadn't considered. All of which is true, but none of which seems terribly controversial. So, sorry, no upvote for contrarianism from me on this occasion :-).
If you are in the object oriented paradigm 1234.times(4321) is something slightly different than 1234.times(4321)
In my map of the world I wouldn't formulate that statement, because you rate precision by an objective standard and I don't think that a single standard exists. Statements that people make are precisely the statements they make. My disagreement is about a fundamental issue and not simply about handling one example differently.
I guess you wanted one of those to be the other way around. In any case, that's commutativity not associativity, it has nothing to do with object orientation (you could equally say that times(1234,4321) and times(4321,1234) are different), and since it happens that multiplication of numbers is commutative it again seems like a total red herring.
I do? Please, tell me more about how I rate precision.
Which I think simply amounts to the fact that the same sentence may denote different propositions in different contexts, because meaning is context-dependent. Which I think is not at all controversial.
I may well be misinterpreting you, but in that case I think it's time for you to be clearer about what you mean. So far, all the examples we've had have been (so it seems to me) either (a) cases where meaning or reference is context-dependent but it's at least arguable that once the meaning is nailed down you have a proposition whose truth value is not context-dependent, or (b) just observations that life is complicated sometimes (September 1752, leap seconds, etc.) without any actual context-dependent proposition in sight.
As I remarked above, I'm not certain how precise one can make the distinction between context-dependent meaning and context-dependent truth value. But since (I think) intelligent thoughtful people are generally entirely unbothered by the idea of context-dependent meaning, any version of context-dependent truth value that can't be clearly distinguished from context-dependent meaning shouldn't be that controversial :-).
In python I can overwrite the times function of one element that means that different elements have slightly different times functions. As such it's important to know whether X times Y means that times is a function of the X or of the Y object.
But you might be right that associativity is not the right word.
When I see the word precision I see it has having a certain meaning that people at university taught me. You might mean something different with the term. What do you mean?
In the case of color my position lead to disagreement with other people on LW because I follow different heuristics about truth than other people.
There are many thoughtful people who put a lot of value in searching something like objective truth. Do you deny that proposition?
Nope. Because so far everything you've said seems perfectly compatible with "something like objective truth".
I appreciate that you consider yourself to be denying that any such thing is possible -- which is why I am interested in finding out exactly what it is you're claiming, and whether your disagreement with the seekers after objective truth is about more than terminology.
One of my pet theories is that colour terms are implicitly indexical, so I dont think that what you say departs from the uncontroversial cases.
Let's say you want to seed an AGI with knowledge.
Some humans get some gene therapy that turns their blood blue. Then the AGI reasons that those entities aren't humans anymore and therefore don't need to be treated according to the protocol for treating humans. Or it get's confused with other issues about 'red'.
The only way around this is to specifically tell the FAI the context in which the statement is true. If you look at Eliezers post about truth you won't find a mention that context is important and needs to be passed along.
It's just not there. It's not a central part of his idea of truth. Instead he talks about probabilities of things being true.
None of my Anki cards has "this is true with 0.994%" probability. Instead it has a reference to context. That's because context is more important than probability for most knowledge. In the framework that Eliezer propagates probability is of core importance.
That isn't an example where a truth value depends on context, it's an example where making the correct deductions depends on the correct theoretical background.
However I agree that quantifying what you haven't first understood is pointless.
The thing is that having freshly spilled blood turn out to be red is neither sufficient nor necessary to be a human.
For the AGI it's necessary to treat sentence that tell the AGI sufficient or necessary conditions from sentences that tell the AGI about observations. Those two kind of statements are different contexts.
We have plenty of smart people on LW and plenty of people who use Anki but we don't have a good Anki deck that teaches knowledge about rationality. I think that errors in thinking about knowledge and the importance of context prevent people from expressing their knowledge about rationality explicitly via a medium such as Anki cards.
I think that has a lot to do with people searching for knowledge that objectively true in all contexts instead of focusing on knowledge that's true in one context. If you switch towards your statement just being true in one context that you explicitly define you can suddenly start to say stuff.
When it comes to learning color terms I did have LW people roughly saying: "You can't do this, objective truth is different. Your monitor doesn't show true colors".
That was probably me. You can define colors objectively, it's not hard. That includes colors in a digital image given a color space. However what you see on your computer monitor may (and does) differ considerably from the reference standard for a given color.
If you are crediting an AI with the ability to undersand plain English, you are crediting it with a certain amount of ability to detect context in the first place.
How is that a contrarian statement? Obviously natural language is heavily context-dependent. So what exactly do you mean when you say that?
I'm not saying something just focused on natural language. I think it's true for any statements.
If you look at http://lesswrong.com/lw/eqn/the_useful_idea_of_truth/ there's no mention of context and how a statement can be true in context A but false in context B.