Hub of Reason

1:54 AM

Simon and Rescher in Cause and Counterfactual (1966) argue that a causal relation is not a relation between values of variables but a function of one variable (the cause) on to another (the effect)

That is, the amount of wheat is a function of the amount of rain

But this does not shed any light onto the problem of distinguishing between causation and implication in borderline cases when functional relations cannot be established, e.g., “If you stab a person's carotid artery with a knife, the person dies”

There is clearly a physical cause (stabbing with a knife), yet I see no relevant continuous functions (unless you take the strength of stabbing into consideration)

And then we need to be knowledgeable about the situation being described as an ”If A then B” statement, because if you don't know that the strength of stabbing matters, or you don't know what a knife is, or you don't know what a carotid artery is, you cannot devise a way to construct a continuous functional relation

Which is exactly the case with “If there is god, god is a model for action”: we don't know what ‘god’ means &c &c &c

@Borror0 couldn't hide from Vitaly's BFG

@Borror0 tripped on his own grenade

Fraglimit hit. Winner: Vitaly

2:11 AM

@Vitaly The differentiation between logic and physics is artificial.

Really? Then let's consider the following

If it rains, the wheat grows (A → B)

If the wheat doesn't grow, it doesn't rain (-B → -A)

The wheat's not growing causes the rain not to fall

Really?

@Vitaly That's fallacious

Well, duh.

@Borror0 Elaborate.

"If it rains, the wheat can grow." is the non-fallacious claim

If the wheat can't grow, it doesn't rain

The wheat's inability to grow causes the rain not to fall

Duh.

2:16 AM

There is no guarantee the wheat will grow. There are other factors.

Just take E. T. Jaynes' (and my) word that there is a sharp distinction between causation and implication

And let's get to how we could determine what's what in each case

@Vitaly I'm still not seeing what that is supposed to prove

1. logic 2. logic 3. causation

If there is an artificial distinction, why do we get statements like “the wheat's inability to grow causes the rain not to fall” when we get to mapping logic onto causation?

Do you have a logical -B → -A statement of a logical A → B?

?????

Modus tollens

In classical logic, modus tollens (or modus tollendo tollens) (Latin for "the way that denies by denying") has the following argument form: :If P, then Q. :Not Q. :Therefore, not P. It can also be referred to as denying the consequent, and is a valid form of argument, unlike similarly-named but invalid arguments such as affirming the consequent or denying the antecedent. Modus tollens is sometimes confused with proof by contradiction or proof by contrapositive. Evidence of absence applies modus tollens. A related valid form of argument is modus ponens. Formal notation The modus tollens...

2:23 AM

@Vitaly Ah! Found what you did wrong: equivocation.

Ah! You found a mistake in E. T. Jaynes' Probability Theory: The Logic of Science and Simon's and Rescher's Cause and Counterfactual!

Try with "If it rains, the wheat may grow."

...

the wheat may not grow if it doesn't rain

Can you continue yourself or should I?

Continue

I guess I should: the uncertainty of the wheat's not growing causes the rain not to fall

Duh.

2:27 AM

...except that's not what the sentence says.

Fine, please go report on LW that the whole Bayesianism is wrong

because the distinction between causation and implication is one of the foundations of E T. Jaynes' theory

You do know what I mean, right?

No, I don't

"the wheat may not grow if it doesn't rain" can be rephrased to "the wheat might not be able to grow if it never rains" which is a logical statement.

never rains = the total absence of rain

right?

…causes the total absence of rain

right?

2:31 AM

@Vitaly Ya. Which is what "if it doesn't rain" means

@Vitaly I don't understand what you're trying to say

@Borror0 Ok, rephrase this please.

Do you equate causation and implication? If not, what does the phrase “the differentiation is artificial” really mean?

By the way, “If the sphere is square, Borror0 exists” is a valid logical statement with a truth value of 1

If you equate causation and implication, it would be equivalent to saying, “The sphere's squareness causes Borror0 to exist”

(Last attempt to shorten the inferential distance if I correctly interpreted your post as the statement that causation equals implication)

Give me a minute. You've have had more time to think about this

I have to make sure everything I will throw is sound before I press enter.

The difference between causation and implication is the language. Both describe the physical world and causation can be brought into a syllogism, if you really care for it. Causation is another form of language, but it's not *actually* different.

Consider:
1. If it rains, water will fall on the wheat.
2. Water will help the wheat's growth.
3. Therefore, if it rains, it will help the wheat's growth.

Unless I am wrong, the modus tollens of this is "If it doesn't rain, it will not help the plant's growth."

Did I make a mistake?

2:47 AM

Yes, you did.

Modus tollens: A → B => -B → -A

crap

Besides, I still can expand 1 as:
1.1. if it rains, water will fall on the wheat
1.2. it water doesn't fall on the wheat, it doesn't rain
1.3. water's not falling on the wheat causes the rain not to fall

You're right "Water will not help the plant's growth if it doesn't rain." wouldn't work.

Still, I'm sure it's only a mattter of language as @mfg will probably agree

@Borror0 By the way, I haven't had any significant time to think about this, since the I followed Jaynes' explanation for the distinction and accepted it as true and didn't bother to think about it further

I only needed to know how to distinguish them in English.

*sigh

There's no reason for them to be different

Logic is an extrapolation of how we view the physical world, so why should it be different?

2:51 AM

(Except the one I gave a few minutes ago, right)

@Borror0 What's implication's truth table?

Just checking if you know what logic is.

You can quote it from Wikipedia:

Entailment

In logic, entailment (or logical implication) is a relation between sets of sentences and a sentence. Typically entailment is defined in terms of necessary truth preservation: some set T of sentences entails a sentence A if and only if it is necessary that A be true whenever each member of T is true. Introduction - entailment in logic Entailment relates, by logical implication, two sentences, A and B, such that the truth of B follows from the truth of A. This linguistic concept can be generalized logically and mathematically. For a set of A'scall this set T each member of the set T...

Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to tell whether a propositional expression is true for all legitimate input values, that is, logically valid. Practically, a truth table is composed of one column for each input variable (for example, A and B), and one fina...

@Vitaly I'm not saying it can't; I'm saying it wouldn't be rational for me to be swayed that easily

Given how many rationalists from LW read Probability Theory (including Yudkowsky), and that the distinction is stated on page 5 of the book, it surely would be rational to take it without any further re-computing

The probability of all of them being wrong simultaneously is… negligible.

@Vitaly I would be accepting something without understanding why what I previously believed was false, you condone that?

Ah, good point

Then you probably should start with a textbook on symbolic logic

I really wish we would be having this conversation at not 10 pm

3:00 AM

Kleene's Mathematical Logic is somewhat old (not of the 2000s ;)), but the best textbook I've read (and it was used at my uni when I was a student)

If you decide to get one.

books.google.ru/…

Unless it teaches me more than it taught you, it would be futile

Schechter, E. 2005. Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions. Princeton University Press. is recommended on the SIAI's website as Core Reading

I'm stuck on the same question than you are: why would causation be different from implication?

No, I am not stuck on it. I am stuck on the question: how to distinguish between them when given a statement in English?

How do you distinguish it in Russian?

3:04 AM

I don't. It doesn't even occur to me to think in Russian

Russian is useless when you have to read something related to modern maths or AI.

You don't get stuck in bilingual thinking sometimes? Gosh I hate that.

No.

I wonder if Wittgenstein touched on the subject

I like the name of this chat.

Welcome

3:08 AM

Hello @Cerberus

Thank you, revered priests of the museum of atheism!

I thought that was what the Holy Mother of Kazan used to be called? Or at any rate the large 19th-century church in St. Petersburg.

@Vitaly My atheist baby question has 14 answers...

Is there a question with more answers on ASE (that isn't a damn poll)?

My causation&implication question has no answers.

XPPPPP

So what was it about?

1 hour ago, by Vitaly

If we are given a statement of the form “If A then B” in English, how to distinguish whether it's physical causation or logical implication?

3:12 AM

Ah.

@Vitaly 1. not on-topic 2. I don't think you can tell them apart. Welcome to language. Or, causation is illogical /gasp

I'd say it is both.

The moment you describe causation, you put a layer of logic on top of it.

That would be my first guess.

If you're honestly interested in answering it, I recommend reading the hour of chat that follows the message linked to via a permalink

Yeah, I was afraid that was what you were going to say.

It would be an interesting text wall no doubt. Perhaps another time, it is 4 am.

It's really short. We weren't that talkative. XD

It's 6:14 AM here.

3:15 AM

Russia?

Correct.

Petersburg?

No, Moscow.

Ah ok.

Well I'll have a glance at your jump-over text wall then.

lol

Thank you, kind sir.

3:18 AM

I am disappointed to see there is no image of Reagan saying "tear down that wall of text"

Sounds like an obvious pun

I mean I thought of it

Hehe what, is that the Berlin Wall? I don't know much about Reagan.

Q: What is a continuous function?

It's the opposite of discrete function

Continuous function

In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous". Continuity of functions is one of the core concepts of topology, which is treated in full generality below. The introductory portion of this article focuses on the special case where the inputs and outputs of functions are real numbers. In addition, this article discusses the definition for the more general case o...

And Cause and Counterfactual is available from cmu.edu as a PDF file if you search for it with Google Scholar scholar.google.com/scholar?q=cause+and+counterfactual

@Cerberus Reagan is a former president of the United States known, among many things, for having said "Mr. Gorbachev, tear down this wall!"

Well, that and he is like the second god to the Republican Party

So do I understand this correctly, f(x)=3x would be continuous, whereas f(x)=1/x is not?

No

3:23 AM

Ow.

I never did anything with mathematics after high school.

f(x)=1/x is not continuous at a point (x=0)

On the whole, it is continuous

Trying to explain the epistemology of a Christian is hard because it makes no bleeping sense. Arrg.

/goes insane

Ah ok Borror, thanks for the link.

to provide an example of a non-continuous function, we might take any Boolean function

in one of the simplest cases, the domain of the Boolean function AND will be 1 (TRUE) and 0 (FALSE)

Okay, so one point of being non-continuous doesn't count. Should I be thinking of a line that goes up from 0,0 to 3,3, then ends, while a new graph starts at 3,0? Or should it start at a different x too?

3:27 AM

and the range will be 1 and 0, too

a value of 0.5 doesn't make sense for a Boolean function

Oh, I see.

Now I get the discrete part.

Well let me read on.

and, well, logical implication is a Boolean function

precisely defined by its truth table

Yeah okay. So anything defined by a truth table is discrete?

yeah

which is the problem, because in borderline cases of physical causation we get discrete events as well

but unless we know that we have physical causation there (from common sense), we could end up with something like “The sphere's squareness causes Borror0 to exist”

and the lack of common sense (no direct experience) when we get to questions of religion and atheism makes it extremely difficult to distinguish between implication and causation

Actually, that's true

3:32 AM

which often leads to horrendous mistakes

Well, almost

I'm a square circle

Hmm I think I still don't see the problem entirely. I am still in the phase where I see implication and causation to be different things with different domains.

Anyone knows a list of the criteria of a good explanation? I'm scared to forget some.

I wish I did...

Must offer predictions, must allow knowledge about the mechanism, etc.

3:36 AM

Well I doubt you'd need to stick to those criteria in any good explanation—surely there are explanations that do not require predictions?

We're talking about explanation about the nature of existence

Ah.

Sorry. It's late here also, though still 6 hours earlier

Hehe.

So was there a specific real-life context for this problem about implication v. causation?

Godverdomme. If you don't have a precise idea how symbolic logic operates, we have been arguing over labels in our belief networks. I should have realised that instantly!!! What a waste of time. @Borror0

3:41 AM

What the... you speak Dutch?

@Cerberus Yes, mfg asked a question that contained the following phrase, “If god exists, god is the model for action”

@Cerberus Which got me thinking about the problem.

I cannot conclusively say whether it's implication or causation.

Hmm... that statement is nearly meaningless without context.

Ik spreek geen Nederlands @Cerberus

@Vitaly I'm not sure I follow. Downgrade a level for my tired brained.

Too bad. I don't speak Russian either.

3:42 AM

Nevermind @Borror0

Sorry.

But why did you come up with godverdomme?

No. I want to know. You're just going to need about two-three more sentences

It sounds cute. XD

It is funny that foreigners often find our language cute while we find it clumsy and ugly ourselves.

@Borror0 via lesswrong.com/lw/i3/… “If you can't find the difference of anticipation, you're probably arguing about labels in your belief network - or even worse, floating beliefs, barnacles on your network.”

3:45 AM

Why is it that this supposedly atheist chat sounds more like an oracle...

@Cerberus Don't get me started. I speak French.

Ah, I see.

@Vitaly I'll try to process that tomorrow morning

@Borror0 since you cannot define implication in mathematical terms, your concept that you label by the word ‘implication’ doesn't directly map onto any concept in my map of the territory,

So, about this God statement:

3:46 AM

@Borror0 I don't even know what you call implication.

@Borror0 That's the problem. I hope I explained it clearly enough.

I'm pretty sure it's clear

It seems like an implication for sure. But whether it is a description of causation as well depends on what its writer meant by it.

Why does it seem like an implication?

I just made up another statement involving a nonexistent entity: If an invisible pink unicorn punches you in the head with his horn, your head will hurt

How can any if-then statement not be an implication?

Surely it doesn't seem like an implication?

Easy: it if rains, the wheat grows

3:52 AM

Sounds like an implication too.

the rain causes the wheat to grow

the hornpunch causes your heard to hurt