I'll grant it was poorly worded. Sometimes we are uncertain until we have carried out the calculation.

So I'll say it this way: if you think you can prove that 2 + 2 = 5, and that 2 + 2 ≠ 4, then you don't yet understand the meaning of these symbols. It may be as simple as mixing up "4" and "5."

people (students mainly, because of the social circumstances) do disagree with conventional mathematics, all the way back to the beginnings of arithmetic — Terrapin Station

If you think that 2 + 2 might be equal to 5 rather than 4, then you have not yet learned what these symbols mean.

Okay, that was funny. Thanks for keeping your sense of humor.

Anyway, I have already given, in this thread, a reason or two to think math is quite different. There are more, but I guess that should wait for another thread.

I think if your approach to philosophy is such that there is nothing especially odd about mathematics, then you're doing it wrong.

Yeah, to even get at the concept of a unit that can be counted you need to learn to conceptualize things in a particular way. So it's basically noting a supposed uniformity a la "if you play the game of conceptualizing things this way, then you conceptualize things this way." — Terrapin Station

I think "play the game" is a little tendentious. There is uniformity, but we have no idea why. Maybe it's cultural, maybe linguistic, maybe it's hard-wired, maybe something else. Maybe evolution nailed it, and maybe it fucked us over. Maybe it's optional, maybe it's not. Maybe Davidson is right, and the very idea of competing conceptual schemes is incoherent. I don't think the dismissive description you give here quite captures the range of issues at stake.

No, no, I insist. — T Clark

I used to love going out to dinner with my Dad and his brothers, because when the check came, there was what I called "the dance of the 20's," as they each started tossing 20-dollar bills out and picking up each other's and tossing them back.

1+1=2 is essentially 5 arbitrary symbols strung together that we are taught in elementary school to accept by rote. Inherently it has as much meaning as any string of symbols. Without further meaning one can just stare at it with bewilderment​. It is when one starts applying meaning to it, e.g. one apple and another apple is two apples that we begin to inject relativism. — Rich

Of course, symbols like "1" and "2" and "+" aren't inherently meaningful, but I would say they acquire meaning for us when we are taught how to use them to do math, not when we apply them.

I also agree that application can be messy, but that takes the math end as settled, as given. The poster child for this is the sorites and friends.

[Bonus apple math trivia: apples are sized not by diameter or weight or something, but by how many will fit in a standard box, so 120's are smaller than 90's.]

Thanks for slugging it out with me. I'll get the check!

I would vote "duckrabbit."

What if the girl were standing alongside the bull, boldly starting down the future? What would the bull mean then?

at the level we are discussing, i.e. restaurant bills and similar situations, math is just arithmetic. It's trivial. The capital of Israel is complicated in the same way that me paying for your lobster when all I had was a hamburger is complicated. When human judgment gets involved, nothing is easy. This web site provides dozens, hundreds, of examples of that. We'll argue about anything. — T Clark

I'm going to keep saying, "except math." @Terrapin Station might assert that truth is whatever he says it is, in both the general and specific senses, but even Terrapin is not going to assert that 2 + 2 = 5, or, more importantly, something like "To me, 2 + 2 = 5, even if for you 2 + 2 = 4." Nobody ever says anything like that. Math is out of reach of all sorts of controversy, both in fact and in principle.

Let's consider the trivial notion that 1+1=2. It is five symbols strung together that is inherently meaningless. It has as much truth as covfefee. It is when one attempts to ascribes meaning to it that relativism floods in. — Rich

Do you have an example in mind of an alternative interpretation of "1 + 1 = 2"? Have you had experience with someone claiming "1 + 1 = 2" means something different from what you think it means? Relativism floods in a whole lot of places, but I really don't see it flooding in here. What does this math relativism you speak of look like?

It is true, though, that I'm rapidly running out of room here as I back into this corner. There are controversies that relate to the "higher mathematics" that Terrapin has doubts about, and there are controversies about the foundations of mathematics. There are philosophical differences about what I guess we'll have to call the "interpretation of mathematical symbolism." But these are really quite different from issues like what the capital of Israel is, whether I said I'd arrive at 7 or 8, whether Oswald acted alone, etc. And the goal is almost never some sort of relativism--it's usually still the nature of the one mathematics that's at stake. (We're getting farther afield here, which I suppose is my fault, but not to worry, because we're nearing the edge of my "expertise" too.)

It is also true that I cheated a little in my last post. The evidence most people actually rely on for the basic facts of arithmetic is either "That's what I learned in school," or "That's what the calculator/computer says." But if you consider the possibility of debate, which is what we're interested in here, there is always an effective decision procedure to determine whether a mathematical statement is true or false. That's true for mathematics bottom to top. What counts as a proof changes as you move from bottom to top and back, but the core remains the same: an effective decision procedure. So I had this in mind as the ultimate backstop for arguments over mathematics, whether or not it's actually accessible to the people who happen to be having the argument. So there's evidence and there's evidence.

So to get back to splitting the check and such: only an effective decision procedure, even if it's just a calculation on your phone, can settle mathematical arguments--no effective procedure, no truth--but an effective decision procedure is always available to settle any such dispute. (Until Fermat's Last Theorem was proven, no one knew whether it was true. Now we do.) There's no room to debate what to count as evidence, or how to interpret the evidence, and so forth. I guess people sort of know that, though maybe not explicitly, so they just don't argue about math the way they argue about other questions of fact. There's no point. There is also no room for "my math" and "your math," "math as I see it" and "math as you see it," etc.

For the purpose of this thread, it might be worthwhile to characterize other fields of argument by how they differ from mathematics.

PS: Should have said this too: Note that mathematicians have never argued about whether Fermat's Last Theorem is true. They might argue about whether it was likely to be true, whether it was likely we would ever have a proof, what approach might work, and so on, but there was universal acceptance for the method of deciding whether it was true: show us the proof. What other field has that kind of unanimity?

Math questions are easily answered without conflict not because they are special, but because they are, at this level, trivial. They are matters of fact like the capital of France or the number of ounces in a pound. We used to argue about that type of thing all the time. Now, with iPhones, calculators, and Google, we can't do it anymore. — T Clark

That's an interesting view. I still think you're wrong, but now I'm intrigued by this idea of math as fact.

Why do I think you're wrong? Well, you got the capital of France readily, but what's the capital of Israel? For almost any fact you can think of, there's probably someone out there who denies it.

I'm really glad you brought this up though, because I think I have an idea now why math is different. What counts as a fact, what we assert as true, is intimately related to what counts as evidence for it, and people can predictably disagree about evidence and its interpretation, and some of those debates are just unresolvable.

But think about math. The connection between a mathematical fact and the evidence for it is really quite different from everything else.

That of course is not an argument about the math, it's an argument about "what's fair."

Look at the way you guys are arguing over the definition of "relativism," and compare that to your behavior when it comes to math. Suppose you were having this argument over dinner and then split the check. It might take a few tries, but you would agree on an answer within minutes, after arguing for hours about the definition of a single word. — Srap Tasmaner

Yes, we could split the bill with few issues. We could just as easily agree that it was morally or ethically wrong when Tim Wood snuck off without paying. Absolutism vs. relativism doesn't really change much on a day to day basis. — T Clark

I think you're right about that last point, and that's worth looking at closer.

I think you're wrong about the other bit. It's just as easy to imagine one of you excusing him and one of you not, for all sorts of different reasons. But it's inconceivable that you would have different "points of view" about the math.

4 is greater than 3 by definition, not mathematics. — T Clark

One of us is missing the point, maybe it's me. We're exposed to lots of definitions, and people argue about those definitions, except when it comes to mathematics.

That disagreement is socialized out of them. — Terrapin Station

That may be. School and home try to socialize kids in all sorts of ways, but this is the only one that sticks universally, so far as I can tell.

it's simply a factor of how humans (and perhaps persons in general--it might not be limited to humans) tend to think about relations on the most abstract level. — Terrapin Station

That also may be.

I have no opinion to share at the moment on why it is so. My point is only what I said: mathematics holds a unique position.

If President Trump wants to claim that the crowd at his inauguration was bigger than the crowd at President Obama's, he can't just say, "I think 317,000 is more than 513,000." He has to say that the estimates of attendance at each event were wrong. Not only is that a good strategy, it's the only strategy because everyone on earth agrees that 513,000 > 317,000.

I brought it up because this thread was supposed to be about what happens when relativists and non-relativists argue. Well, one of the things that happens is that they agree on basic mathematics. They may disagree on where the numbers come from and what they mean. That might be ever so important to the argument. Not denying any of that.

@tim wood seems worried that there is no absolute truth that everyone accepts, and that not everyone even agrees there is such a thing. I'll grant that it's not what he wanted, but mathematics appears to me to enjoy universal acceptance.

Look at the way you guys are arguing over the definition of "relativism," and compare that to your behavior when it comes to math. Suppose you were having this argument over dinner and then split the check. It might take a few tries, but you would agree on an answer within minutes, after arguing for hours about the definition of a single word.

Unless you're curious that there's near universal acceptance of the definitions of terms? — Michael

Um, yeah. Math alone is treated as objective, as objectively true, by all parties to all arguments. That's ever so slightly an overstatement--I'm leaving to one side discussion of the foundations of mathematics. Outside of that vanishingly small exception, nothing even comes close to the universality with which mathematics is accepted.

Not even logic. Natural language is so complex, so much depends on context, on unstated assumptions, that people can argue endlessly whether A follows from B. They argue about the meanings of words. They argue about what words mean "to them," or what they "should" mean. They argue endlessly about what is and what isn't a fact. They argue about right and wrong and how you decide which is which.

But if an argument reaches a point where it's just a question of whether 4 is greater than 3, it's over.

There is something quite natural about the approach you took. I think for a lot of people, the argument for the existence of God has just one step:
(1) All this must have come from somewhere.
(2) God.
Your attempt to combine the cosmological and ontological proofs fills in some steps. It might be worth figuring out why that made it harder to get from (1) to (2).

One thing I find curious is the near universal acceptance of mathematics.

You can, of course, fake data, misrepresent data, tendentiously interpret data, and so on, and you can accuse someone you disagree with of the same, but there's no room for someone to say baldly, "In my view, 3 is greater than 4."

Whatever this is, it no longer looks much like a proof of the existence of God.

This is good stuff, Andrew. It's good to hear the thoughts of someone in the data trenches. I have a few more questions though.

I think there was a bit of special pleading in the influenza example. There's a "usually" thrown in with the predictive version that the causal version doesn't have. Surely the user of causal talk could be just as modest.

That "usually" made me wonder if we shouldn't try to separate the unpredictability of what we're talking about from the imperfection of our understanding of it. I had wanted to say there's a difference between saying, "Influenza is usually accompanied by fever, but we have no idea why," and saying, " Influenza is usually accompanied by fever, because [details]." But the "usually" itself could mean, "We don't know why it happens sometimes but not others," or it could mean, "There is some randomness to the way this process works, such that [details]." It seems worthwhile to keep those separate.

I just keep thinking that once you've given up this one big distinction, at least as an ideal to strive for, that all sorts of other meaningful distinctions will fall away too. I really like distinctions.

I don't have a horse in this race, Tim, and there is a certain sort of relativism I find worrisome, but I think we often have more to worry about from the absolutists. An ideology that is held to be above question can justify the most barbarous acts.

My point is that we don't need a notion of causality to obtain that understanding. Of course we can label the mechanism 'causality' if we want. But that does nothing other than add a superfluous label to a concept that was already perfectly clear. — andrewk

One use of the concept, though, is to help us weed out spurious correlations.

Mind. Blown.

Actually I just assumed that "Share" would bring up a selection of social media buttons like it does on loads of other sites, so I avoided clicking it.

Thanks also @Agustino. I guess that amounts to a sort of "back to the top of this post" function. Odd.

Thanks guys!

Along with reply, share, and flag, posts should have a link button, so you can refer to specific posts.

So two examples: consciousness and pharmaceuticals.

As for the second, I would have guessed that if you asked most researchers, they assume there is always some definite mechanism at work, but we just don't know it is. There are practical challenges to figuring out what those mechanisms are (the complexity of the systems at work, the limits of our current technology, etc.) but does anyone think there's just nothing there to know? That correlation, and that at a pretty coarse level, is the best we'll ever be able to do?

I've got nothing for you on consciousness, but I wonder if you should give it so much weight. Consciousness is some pretty weird shit, as the natural world goes, isn't it? Hard cases make bad law.

So does your thesis of "conservation of properties," if we're calling it that, come down to a restatement of the first law of thermodynamics (with a nod to the second), once you've reduced everything to matter and energy? What does the argument look like stated in those terms?

You also mentioned genes, so there's an issue about information...

Okay. I thought you had been saying energy transfer is not causal.

Sorry--I was unclear.

In the typewriter example, there's no causal connection between what I do and what the typewriter does, right?

Is there any place in this description for the word "cause"?

Okay. So how do you see the connection between what I did and what the computer did? (Still just clarifying here, not arguing.)

I think the natural ground to look at is communication, since the relativist and friend are talking to each other, understanding each other's assertions, and so on. The question is how much mileage you can get out of that. It might be a lot.

I'm not quite convinced. Do we retreat to predictive talk just because of the difficulty of adequately specifying the ceteris paribus conditions in causal talk?

I expect many people believe that pressing the 'A' key should cause an 'A' to appear on screen, if everything works the way it's supposed to, but they know perfectly well that there are many things that can go wrong between keyboard and screen. Even a typical causal claim might involve a prediction that conditions will be normal, in some sense that may be difficult or even impossible to define.

You could then just absorb the causal claim into the predictive claim, but they are fundamentally different aren't they? Or are they?

I just caused that sentence to exist. It has the property of being composed of words; I am not composed of words. — Srap Tasmaner

Still an incorrect causal relationship. The words have a physical property (say pixels on the screen), and a meaning. The meaning of the words is caused by you directly, and they are also a property of you because you can think (i.e. you meant what you wrote). You are not composed of pixels, but the direct cause of the pixels is the computer, which has the ability to create these pixels. — Samuel Lacrampe

Just to be absolutely clear, you're saying that
(1) I created the meaning of the sentence, but
(2) the computer created what's usually called the "inscription" of it, the physical instance,
and
(1a) I was able to create that sentence-meaning because I can think (thank you), and
(2a) the computer is able to create the physical inscription of the sentence.

It's not my intention to hold you to details of the formulations given here. (Also not my intention to get into details about the example itself, about what a sentence meaning is, etc.) Just want to be clear what you're saying.

You also make the additional claim, I think, that
(3) I did not create the inscription, because
(3a) I can't.

Is that the gist of it? Change anything you like in the wording.

Yes. What you got from Hume, as summarized here, doesn't support the conclusion you draw, namely that everything we can conceive of must exist. (Hume didn't draw this further conclusion either, for what that's worth.)

Hume claims that
(1) any complex thing we can imagine is built up out of simple things, and
(2) any simple thing we can imagine is directly derived from our experience, as a faint copy, in fact.

If you accept these claims, you will reason thus:
(1) if I imagine something complex, then what I imagine has simple components;
(2) the simple components of what I imagine must be derived from my experience.

Hume doesn't suggest that the gold mountain we imagine must be real, only that we must have experience of gold and mountains.

Makes sense to me.

To send the PM somewhat anonymously you'd also have to create a shared mod account.

No, there's no notification. If there was an option for automatic notification, then we'd consider doing that, but we don't have that option. — Sapientia

Maybe it's rare enough the mods could just have a policy of sending the deletee a PM.

OTOH, that would probably invite debate, and a further policy like "We won't respond to PMs about post deletion" has an icky ring to it.

Erk.

Yeah but then there's lying. I think there were claims about military service that were demonstrably false. He may have done it just to mess with people he didn't respect, I don't remember.

One of Faulkner's hobbies was lying about his past, as I recall.