I see. Your argument is that if you're against abortion, you should be in favor of unrestricted sex. And that conclusion you do not block because, in your view, no one wants that.

Doesn't it make you wonder, though, why no one wants that? Isn't there some reason to think that might be relevant? I can see how you might think that's beyond the scope of your argument, but this is exactly where lots of people confronted with this argument will land.

I am inclined to believe that (1) Al did possess at least some justification (even if weak) — Arkady

The word "justification" is unfortunate, because in ordinary usage it admits of degrees, the same way you might talk about having a lot or a little evidence. In the JTB theory it's supposed to be binary, I think.

Gettier cases always feel to me like magic tricks or confidence games. You're elaborately given the opportunity to verify things that don't matter, and then forced to draw conclusions you know you shouldn't. Meanwhile there's all sorts of crap going on behind the scenes.

I think this distinction does not really exist and is a fallacy based on failure of intuition. — sackoftrout

I appreciate your response, but I still don't understand the argument.

The Roman Catholic Church has traditionally taken exactly the option you suggest, to be against abortion and contraception. Did you intend to block this response somehow?

On the other hand, there are many people in the world (including many American Catholics) who use birth control but are anti-abortion. Doesn't that count as evidence that many people share the moral intuition you say does not exist?

Now that I think of it, the willingness of people to put the economic wellbeing of the currently living ahead of the environmental wellbeing of future generations, suggests this intuition, or bias, is well entrenched, if not always helpful.

You're close, @Arkady, if readers will tend to have an intuition that this doesn't count as knowledge, but they'll think that because they'll feel the belief isn't really justified.

I don't think you need most of paragraph 3 of you're just trying to build a Gettier case. You just need "Bob in fact stole the money."

Your case seems to turn on whether Al's belief was really justified, whereas Gettier cases usually try to make this airtight. This may be case of epistemic luck, but it feels more like, "I'll bet it was him" than the Gettier type.

Without deliberate intervention in this system, many more children would be born. Conversely you can say that rational human interference has prevented the natural trajectory towards consciousness for many systems. — sackoftrout

I think this is the weakest part of your argument. Surely we make a distinction between an actual, existing entity already on a trajectory toward consciousness, and only possible or potential entities (a fortiori not on any trajectory to anything).

I agree that science is a continuously expanding domain - gobbling up other disciplines, even art and music, like a hungry shark in the middle of a shoal of fish. Its rational basis and clever use of math has turned it into a formidable tool to understand our world, the universe itself. So, to some degree I'm in agreement with the OP that lack of scientific ''explanation'' does pose a serious problem for theism. — TheMadFool

I think this is a very nice point, but I would say science is a problem only for a certain sort of theism.

Here's a story: I recently had a used copy of Kant's first Critique with the occasional "I hate you Kant!" "Idiot!" etc. written in the margin by a frustrated undergraduate. This commentary was not related to, say, fathoming the transcendental unity of apperception--it wasn't related to Kant being hard. It was where Kant makes fun of the man who claims to know that God exists, and a few other places. (I wondered if these folks would hate Kierkegaard too.)

We all know Kant's deal--to set limits to reason and leave room for faith. But there is a certain sort of young Christian--I can't make claims about anyone else--who claims to know that God exists, that the Bible is His word, that Jesus is our saviour, and so on. I was raised a Roman Catholic and we never talked like this. It was always faith, not knowledge. You could talk intelligibly about a person's faith being tested, and so on.

So I would say that science is only an issue for you if see your religion as a matter of knowledge rather than faith. (Whether that's a recent or regional or denominational phenomenon, I can't speak to.) And not just knowledge by acquaintance--however your religion comes down on whether you can "know God" directly--but propositional knowledge. If you see your religion this way, you see it as on par with science, in competition with it, and these are the people, I believe, who see science--correctly!--as a threat.

On the other hand, @TheMadFool seems to be right about the broader cultural point, that the expansion of science in the last several centuries puts endeavors such as religion and philosophy both back on their heels, but mainly as matter of cultural prestige or something.

It seems odd to me that you'd be so eager to say that "2+2" isn't identical to "4," yet you readily say that Joe's subjective experience is identical to Pete's (or at least some part of it is). — Terrapin Station

You're maybe not "eager," but let's say "comfortable" concluding that if Joe and Pete both assert that 2 + 2 = 4, then there must be something similar about the states of their respective brains.

I'd be happy to try to explain what I understand of Frege's philosophy of mathematics, if you'd really like me to, but honestly Frege's writings are a way better source than I am. Some of this stuff I struggle with.

I had no intention of converting anyone or "winning an argument." I stopped by because you were talking about something there's prior art for. Just offering a way of thinking about this stuff that you might find helpful. If you don't, no harm no foul.

If you find these sorts of questions interesting, then you really ought to read Frege. (If, on the other hand, you find them an annoying waste of time that gets in the way of doing more interesting stuff, then probably not.)

If "4" points at something, then so does "2". Clearly they point at something different. — Metaphysician Undercover

Sure, "4" refers to 4, "2" refers to 2.

I think Frege construes 2 + 2 as a function. "2" has a sense, and refers to 2. "+" has a sense, but doesn't refer to an object. You can put them together to make a function you could call "... + 2," which also has a sense, composed of the senses of "+" and "2," but no reference because it's incomplete--there's a gap. By putting an object where the gap was, you can get "2 + 2," which has a complex sense, and now has a reference, which is the value of the function, namely 4.

Frege considers 4 a simple object. "4" is a name for 4 with a simple sense, but 4 also has infinitely many names with complex senses, but still the simple reference 4.

They do not reference the same entity though. — Metaphysician Undercover

"2 + 2" and "4" are, usually, different ways of referring to 4. They have different senses, but the same reference. For mathematics and logic, the reference is what matters, so identity is identity of reference, hence we say "2 + 2 = 4." That they have different senses, explains why an equation can be informative. "2 + 2 = 4" does not express the same thought as "4 = 4." (That's Frege's take, and I don't have a really good reason to disagree with him.)

And "thinking a proposition" is a state of an individual's brain, right? It is not a relation between the individual and an object, the abstract object that the proposition is, because there are no abstract objects.

So you'd rather be like one of those little girls crying about injustices around the world while sitting in their comfortable homes and doing nothing right? That's being a nice person right? Just sit back and say the right words, that will certainly fix the world up. Yeah that's certainly the way of fighting injustice. Condemning the Republicans... they must be rolling on the floor with laughter.

The world doesn't care about cries. The world only changes with actions. You or me or anyone can cry as much as we want about all injustices. The world itself is silent. And God only helps those who dare take action.

I don't see any proposals for action in this thread. All I see is crying about this and that. — Agustino

I think this is a false dichotomy. The choice is not between manning the barricades and being a whiny little girl.

One of the main things citizens do is talk to each other. If your government does something you disagree with, it is important to talk about it. That doesn't have to be some big public display. You talk to your family and friends, just like you talk about anything else you care about. There will likely be plenty of other people talking to their family and friends. Over time, public opinion shifts, and that matters.

It is important to keep ideas circulating, to keep talking. If you don't, the idea will be gone. One way you help keep a democracy alive is by being informed and keeping the level of discourse from falling. Some people will engage in more directly political activity, and they have to come from somewhere. You want them to come from an environment of careful thought, healthy debate and respect for the truth. If you were a dictator, you'd worry more about that than about the little armed rebellion your massive security forces easily put down. But imagine that out there, beyond the palace, they're all talking, it's impossible to stop, some of your own staff are probably talking.

Talk is important. Do it often; do it well.

The sky is filled with glowing blue dots.

I had always been a little uncomfortable using conditionals talking about cause and effect. Where the conditional shows up in this "deductive form," is it regular, old material implication?

I googled it -- I had forgotten about "Rayleigh scattering," that the small gas molecules will radiate the same wavelength they absorbed, so that's why the more-often-absorbed blue gets spread all around. (I used to get that backwards--thought it was blue because blue was the least absorbed.)

Anyway, "deductive form" something like what I did?

Oh my, no, not humoring you. I've enjoyed and learned from both sides in this argument. I only pointed out the misreading to give you a chance to reshape your response to Andrew, which I looked forward to reading.

Fair enough.

There are legal challenges currently working their way through the court system. But hey, why bother, amirite?

The explanations I have received, and have given, have been narratives, not mere references. The narrative (which as I have said, has the formal structure of a deduction that starts from premises that the explainee understands and believes, and proceeds by steps that the explainee understands and believes) will usually refer to many different phenomena along the way, with none of them distinguished from the others and having the special label 'cause' affixed to it. — andrewk

I'm nearly convinced but this part throws me a little, so I could use an example.

For the "why is the sky blue" example, you would do something like this?

1. Our atmosphere contains such-and-such gases, water vapor and dust.
2. If light strikes such-and-such objects, it behaves in such-and-such a way.
3. Thus when light from the sun enters our atmosphere, such-and-such happens and we see blue.

Is that the idea?

You misread@andrewk's last post. Those were examples of "here's the cause" explanations, not the sort of explanation he was advocating.

This is a tad hyperbolic and ignores the fact that Democrats attempt to do the same thing — Thorongil

Everybody does it, but it's well known that the GOP has turned gerrymandering into a way of life. It's easy to find sources: here's one.

As for voter suppression, if memory serves turnout was higher this election in every state in the South except one: North Carolina. Want to guess what the Republican legislature has been up to in North Carolina? There was even a memo from NC GOP bragging about how low black turnout was. Real commitment to democracy there.

Isn't the obvious modern correlate of "final cause" "purpose"?

I'm referring to identity in the 2+2 is identical to 4 sense. — Terrapin Station

Very funny.

The degree of widespread agreement about it is typically overstated. — Terrapin Station

Should have addressed this before...

Can you name me one business, government, non-profit, in fact any institution of any kind anywhere in the world today that takes an "alternative view" of basic math. (I say "basic math" because few institutions are concerned with, say, axiomatic set theory.)

For comparison, there are, particularly with the rise of data science, lively and valuable debates within what we could loosely call the "statistics community" over the interpretation of Bayesian and frequentist statistics, and the value of different approaches to different problem domains. There is also the so-called "p-value crisis" in the social sciences. In none of these cases is there debate about the math side of things--everyone agrees on that--but about how it's applied and how the results are interpreted.

Proofs are simply relative to the formal systems we set up. A proof in system x is simply a matter of a conclusion incorrigibly following in system x, per the definitions, inference rules, etc. that we've set up as system x. — Terrapin Station

Would you grant that this is a somewhat different way of establishing the truth of a proposition than obtains in, say, physics, history, politics, bar-room linguistics, etc.?

(Btw, my intention earlier was to be succinct, not "stern." I'm just an average joe, not a member of some cult.)

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.