This is the Realm of Simply Beautiful Art

user21820

09:53

@amWhy At the risk of stirring up the pot, I'd like to say that I think we all agree on some basic moral principles (like not to intentionally commit premeditated murder), and that the principle is neither a factual statement nor a logical rule. What I think @shredalert was conveying, which I personally also believe, is that when we want to convince another person of something we perceive as correct, then we typically benefit from first laying out a deductive system, formally or not.

user400188

Morning @user21820

user21820

If the other party agrees with our system, which would include not just the logical deductive rules but also axiom (schemas), then we are good to go. If not, then we would have to deal with the disagreement at that level first, before we even try reasoning within our preferred system.

@user400188: Hello there! Nice to see you here. =)

shredalert

Morning all. @user21820 But look at civilisations like the Aztecs, they had ritual sacrifice, and it was morally fine for them. But to us those practices are not morally right.

Because we have differing principles/rules.

user21820

A moral rule such as the one you brought up could be represented by an axiom saying "It is good for society if everyone followed XXX." Of course, "good" and "society" and "followed" and people would also have to be axiomatized.

shredalert

We murder animals and plants in a premeditated way everyday. Just humans is an exception, and that exception is a principle/rule in itself.

user21820

09:59

@shredalert Since you want to bring it up, I actually am of the view that your claim is false. Namely, any society that has ritual sacrifice is not moral and they know it. Also, there will be exceptions in most societies, but usually only the dominant views get recorded in history.

shredalert

I'm not saying I disagree that people shouldn't be murdered. But, this is where I'd claim I am philosophising, in a different culture, at a different time morals and ethics are relative.

user21820

@shredalert As for animals, I don't actually want to discuss it since it is a sensitive issue, but personally I do not eat meat for moral reasons. Why do I distinguish between animals and plants? Because animals are conscious and I don't think plants are, so weighing the likely consequences, it is better to eat plants than to starve.

shredalert

But we have personal beliefs and views which shape our morals and ethics. For example I believe that rape, murder, sacrifice, paedophilia, etc. are wrong.

I'd put them in a small category called beliefs.

user21820

@shredalert I also claim that one can set up a moral framework that can be justified independent of culture and ideology.

I believe that you've also seen a bit of my moral views in a previous discussion in this very room. =)

user400188

@user21820 by " moral framework", do you mean principle? If so how do you distinguish principle from ideology?

user21820

10:05

By framework I mean a system by which I can quite systematically analyze arbitrary moral claims and come to the (in my opinion) correct conclusions.

By principle I mean the usual meaning people ascribe to various things that they subscribe to or uphold.

By ideology I mean the way of thinking of people, which may or may not be illogical, and may not even be principles.

shredalert

That's the point I was trying to make last night @user21820, and @user400188. Even for morals we set up some sort of framework/system, and think it should be true regardless of time and culture.

user21820

@shredalert Yes precisely that's why I agree with your claims last night, though I go further and claim that I can justify a certain distinguished system over others.

So that morality is no longer a purely subjective matter.

I believe it's a very objective matter, and that most people don't realize it.

shredalert

Someone once told me dogmas are a bad thing, but we have dogmas about rape and no one argues with that. So Dogmas can be a good thing.

I think some dogmas are actually a sign of progress of civilisation

I realise this might not be very relevant to the discussion, but I just wanted to let it out there.

user21820

So do you want to know my justification that a particular system of morality can be justified?

shredalert

Sure, I'm interested to read about it.

user21820

10:11

Okay a bit self-referential there.. Lol..

user400188

Its more or less what we do here when we jump to and from meta systems. So I don't think many will find it strange.

user21820

Basically, we make some fundamental assumptions. First, that it is good to have stability. This could be left vague, or defined in a system stability sense, or more precisely using information theory, but the details merely bog down the idea. The simplest analogy is physical stability (attractive fixed point).

I explicitly list it as an assumption because for sure some joker will disagree, even though his/her very existence is supported by stability preserving laws of physics.

I hope "joker" is mild enough not to be offensive. =D

shredalert

@user21820 good one. lol

user21820

Now this assumption breaks the symmetry between "good" and "evil", metaphorically speaking.

Because now morality can be defined as the desire to preserve stability.

And since we assumed that stability is good, therefore morality thus defined is good.

Plenty of conclusions start following from this, though it's still not strong enough to reason about human society.

Do you see where I'm going?

shredalert

I'd put in a few dogmas about murder, etc., but yeah, I see where you are going.

Because one could say in some cases murder can further stability, so we'd need to protect against that.

user21820

10:20

In the case of murdering murderers who are quite apparently attempting to commit another murder, I actually think it's moral to do so.

Though I have careful caveats whenever I state such a thing.

See the last related discussion for example. =P

shredalert

Well, simple rules won't be enough, as we all probably agree, there need to be lots of thought out exceptions.

One thing that fascinates me is how the human mind can think and abstract about the physically impossible.

Going off on a tangent again. I know. lol

user21820

That's why I haven't got to that, and prefer to try to build the whole system as a well-founded whole.

Multiplicity of rules just doesn't work.

Next, we observe that stability can be interpreted as resilience and the tendency to return to a stable state after perturbation (this is similar to the physics definition), and it includes mental/emotional stability if we consider our mental processes to be part of what is good to be stable.

This intuitively lends credence to my 'careful variant' of the golden rule.

I won't claim that we can deduce the golden rule just like that, because clearly we haven't enough axiomatization to do so, but I'm too lazy to devise an explicit system to enable doing it!

user400188

I don't even consider if it is moral to murder murders. The rule for doing so wouldn't be moral, unless you could do it and correctly judge who is and isn't a murderer, in every case.

user21820

@user400188: I believe that everyone who follows my golden rule will not have much trouble, because they wouldn't be hasty to judge and would only act when they are certain, because they would never want to harm innocent people.

For example, if someone started shooting random people on the streets including young children, you can be nearly certain that that one is immoral and should be stopped, unless you think it's better to let many more people die.

So it would be morally justified for a police officer (or in their absence someone else) to kill that one to effect the desired (better) outcome.

I think that it is only people who do not follow my golden rule (in their heart) that are a problem, and so it's not my rule that is the problem anyway.

That said, I favour life imprisonment with acceptable living conditions over the death penalty, even for most murderers. It also follows from the same moral framework.

shredalert

I think most people would agree killing a murderer is only acceptable once we are certain they are the perpetrators and are still dangerous. And also the case where we see them openly shooting at people in the streets.

user400188

10:33

@user21820 I think in the same lines. Minus the golden rule which I haven't read yet.

user21820

@user21820 <- That's why over here I was careful to restrict to the case when a person is apparently going to attempt another murder, not at other times.

user400188

ah ok. I saw the word repeated twice instead of three times when I first read it.

user21820

Ah okay.

Hahaha.. reading fatigue.

=P

Anyway for ease of reference I can quote the main points from my version of the golden rule:

> Basically, we talk about conscious beings here. Don't ask me to define "conscious"; use your 'common sense'. We define a being to be moral iff it does not intentionally cause harm to moral beings, and minimizes harm to immoral beings. This is a recursive and not obviously well-founded definition, so it gives us conclusions in some cases and is inconclusive in others.

> Now "harm" is defined slightly differently in the two contexts. "harm to moral beings" is defined to be what those moral beings perceive to be harm to themselves. "harm to immoral beings" is defined to be what the being in question perceives to be harm to them. Namely, moral beings decide what is harm to them but immoral beings don't have that right.

> I welcome any probing or critique of my ethical framework, as I apply it in real life and wouldn't want to make ethical errors. Though rather tangential, I believe to a certain extent logical reasoning helps to dissect ethical frameworks for possible inconsistencies.

shredalert

Well, the parts open to interpretations are why we have things like supreme courts.

user21820

Yea.

shredalert

10:39

Assuming they, the supreme justices, are doing their job right, of course.

user21820

And hopefully the judges follow the rule hahaha..

user400188

I wonder sometimes how much mathematical logic a judge needs to learn actualy.

shredalert

I was watching a video by a logician last week, and I'll paraphrase: "When I was younger I wanted to become a lawyer so I took a class in philosophy. It consisted of logic and ethics. I thought that sounds like the two most important things for a lawyer. Now I know lawyers need neither logic nor ethics."

user21820

Just basic first-order logic? Enough not to make stupid logical fallacies.

shredalert

It was pretty funny lol

user21820

10:41

It's not true, that quote. Many judges have been fooled by fallacious arguments.

Logic should suffice for most things. Another thing they might need to learn is statistics.

shredalert

I should say that he meant the "need" part as a joke

user21820

Oh really haha okay.

shredalert

Because there are plenty of illogical and unethical lawyers

user21820

Exactly!

shredalert

It was in the tone of his voice

user400188

10:42

I think the same for politicians too. Unfortunately my best guess in "none".

shredalert

he chuckled a bit when he said that

user21820

Yea rulers also need logic, but sadly what we want is not always what we get...

Lol what a spelling error.

shredalert

A slip? lol

user21820

I'm too used typing "rules" and not "rulers".

user400188

I used principal instead of principle earlier.

shredalert

10:44

Which is why I'm sure everyone here will agree logic needs to be taught in secondary school.

3

Just basic stuff.

user400188

Yeah, at least in secondary education.

user21820

My statistics comment is because it's very easy to be misled by statistics, such as when 'experts in court' make certain statistical claims and the judges don't know all the technical details.

shredalert

I also believe financial education is another big thing that needs to be taught in secondary school.

If they are smart enough to learn about science they are smart enough to learn about basic finance.

user21820

Haha so are you saying they can learn it on their own?

shredalert

Well, it will be taught, of course.

user21820

10:47

Yea I think it should be taught as a matter of protecting society from the ills that come along with financial trouble.

That's the objective reason. The subjective reason is because teachers ought to care for their students period.

3

shredalert

Yep.

user21820

@amWhy: Hello and nice to see you here! I hope you don't mind my jumping into this interesting topic. =)

shredalert

o/ @amWhy @Mithrandir

I believe they're just waking up.

Mithrandir

Hmm? No, I've been online since over 4 hours ago

shredalert

Up early then

Mithrandir

10:53

It's 2PM, roughly

user400188

9PM for me. Afternoon @Mithrandir

Mithrandir

^_^

shredalert

Oh, I thought you were in the US for some reason @Mithrandir. My bad.

1159 here

user21820

@shredalert: So time to sleep for you?

shredalert

24 hours British time :P

almost noon

Wen1now

11:39

Who likes big numbers?

Mithrandir

@Wen1now @SimplyBeautifulArt does ;)

Simply Beautiful Art

11:56

o/

@Wen1now Oh yes, me!

Lol

@as4s4hetic Hello and welcome to my realm

user400188

o/ Welcome back @SimplyBeautifulArt

Simply Beautiful Art

o/

as4s4hetic

Hello! I'm just here to join the peanut gallery

Simply Beautiful Art

lol, okay

shredalert

12:13

Paraconsistent logic is the most confusing thing I've ever tried to understand in logic.

When your modal conditional can be true and false at the same time. And you need to check each world to verify if the conditional is true or false. breaks down in tears

Simply Beautiful Art

Hm, that does sound interesting.

user400188

"True and False at the same time" reminds me of quantum logic. There is no distributive law (other than that its all the same), so you can have things like A(B or C) then you cant simplify it further, because A does not distribute over the brackets i.e. "AB or AC"

shredalert

I'll give the gist of it

This is how we determine the truth of the modal conditional $A\rightarrow B$.
$A\rightarrow B$ is true iff:
(1) In every accessible world where A is true, so is B.
(2) In every accessible world where B is false, so is A.
$A\rightarrow B$ is false iff:
(3) In some accessible world A is true and B is false.
In consistent logic (something can only be true or false and not both at the same time) We don't need rule (2), but we need both (1) and (2) to show $A\rightarrow B$ is true in paraconsistent logic. And also, in paraconsistent logic $A\rightarrow B$ can be true and false at the same time.

This is all done to make sure we can't use explosion, $P\wedge\neg P,\therefore Q$ in our logic. Because in consistent logic you can imply anything from a contradiction. So if we had a contradiction it could imply 'I am a potato'.

Wen1now

Nice

shredalert

But that doesn't mean I am a potato of course, because a contradiction is never true so we just have the implication being true. A subtle point not to be missed.

user400188

12:33

what happens when we negate something in paraconsistant logic?

shredalert

If P is true and false $\neg P$ is also true and false.

otherwise it behaves as normal negation does

@user400188 I'm learning about if from section 11.5 of Sweet Reason.

user400188

Hmm Ill take a look.

shredalert

I'd recommend skimming 9.4 and 10.4 before you do, @user400188.

user400188

12:57

I went looking for those sections but got distracted by 11.1 . There is a figure at the top listing the "rules so far" . All of them are obtainable using the rules of Suppes, however I got stuck on $\lor\ Out$ .

I went back in the book to when its first introduced, but they appeal to the intuition that
"It’s saying that if you know that at least one of two statements is true, and both
statements lead to a third statement, then that third statement must be true."

This is nice to know, (and even helped with my proof a bit), but it didn't quite allow me to verify it with my rules.

That said I can verify it with my own made up rules. It wont be clear to anyone who isn't me however.

shredalert

You can show that rule is a valid argument using truth tables.

user21820

@shredalert For propositional logic, yes more or less.

user400188

yeah thats more or less what I ended up doing. I used simplification to show it was a tautological implication.

shredalert

The predicate rules are the ones which rely on 'common sense'

user400188

the thing is, I am unable to use a series of tautological implications to get there. I have to simplify it first then do it all in one go.

@shredalert I'm not surprised.

user21820

13:01

Well if you think really carefully about it, truth tables can't justify even propositional logic completely, because to use a truth table you need to be able to 'know' that you've listed all possible truth assignments, and then 'check' whether for every row you have that if the premises are true then the conclusion is true. So it looks like you already must know the semantics of first-order logic to use truth tables!

But yea, definitely go ahead and use truth tables to convince yourself of the validity of the rules. =D =D

Simply Beautiful Art

Oh hey, its @user21820

user400188

There was a proof in suppes that if something tautologically implies another thing, then its valid.

So if you do the truth table and find a tautology, you don't need to look for validness thereafter.

shredalert

Use the shortcut method we were discussing earlier, @user400188. You'll see if you make the conclusion of the $\vee\;Out$ rule false, you can't make the premises true.

user400188

ah your right

shredalert

I did that for all the rules just to make sure they were valid arguments. The only one you can't do it for is $P\Rightarrow Q\wedge\neg Q,\therefore\neg P$.

Because it's a philosophical argument

user400188

13:10

?

for me its a tautological implication

shredalert

Using the shortcut method to show the deduction rules in the book are valid arguments @user400188

user400188

oh I just meant that $P\Rightarrow Q\wedge\neg Q,\therefore\neg P$ is not a philosophical argument to me.

shredalert

You can't show that with truth tables.

user400188

why not?

shredalert

Did you try?

Simply Beautiful Art

13:13

lol

user400188

hmm ill give it a go

$P\rightarrow false$ simplifies to $\lnot P$ , so $P\rightarrow false\ |=\ \lnot P$ will be equivilent to saying that $\lnot P\ |=\ \lnot P$ .

Which is why I think it will work in truth tables.

shredalert

What I'm trying to say is that the only truth values we are using is false for A and B in $A\Rightarrow B$

Because $Q\wedge\neg Q$ is always false

And we are assuming $P\Rightarrow Q\wedge\neg Q$

user400188

I'm not quite sure what you mean

shredalert

I'm just trying to say that unlike the other rules this truth table just has one line

user400188

"the only truth values we are using is false for A and B in A⇒B" < this spesificly

It has four lines, its just that two of them dont affect the outcome of the implications.

shredalert

13:20

I'm just saying the setup which we are using, is making the result, a contradiction, always false

Because the logic is consistent, not paraconsistent

I think my previous claim saying you can't use truth tables is kind of not true. You can use a truth table but the consequent can never be true, is what I'm trying to say, because of the way the logic is set up.

So that choice for consistency is forcing us to conclude that P is false

I hope that makes a bit more sense

user400188

It makes a lot more

I didnt consider you meant "philosophical issue" in the sense that it depends upon which logic you are using.

shredalert

That's what I should have said

Because we've got a consistent logic, our truth table fixes only one truth value for $Q\wedge\neg Q$, so we're forced into the conclusion of $\neg P$.

user400188

@shredalert When you read $[A\rightarrow B\bar B]|=\bar A$ , do you see it as two separate things?

e.g. $[A\rightarrow B\bar B]$ as well as $|=\ \bar A$

I consider them as one, and when I make a truth table, I do it for $[A\rightarrow B\bar B]\rightarrow \bar A$

Ive got to go to bed now. Goodnight @everyone

shredalert

13:37

Night @user400188. If I read it right I see it as a single truth table

user21820

15:51

@user400188 @shredalert: Oops was away just now. It's correct that that argument can be proven to be logically valid via truth tables. Remember that logically validity is a notion in the meta-system MS, which itself is a classical system. MS can construct the truth-table with all possible truth assignments of P,Q, and show that in every row where "P⇒Q" and "¬Q" are both true, "¬P" is also true. This validates the argument, since every world satisfying the premises also satisfies the conclusion.

shredalert

Yeah, I realised the thing I said about not being able to show it with truth tables was wrong.

But I was trying to really say that we aren't left with much option as the contradiction is always false. So for the implication to be true, P must be false.

user21820

Yeap.

shredalert

@user21820 I'm going to resume The Two Towers soon btw.

Almost done with my last Hobb novel

user21820

It's also good to also see precisely why it works, namely that we are working in MS and every proof of validity essentially boils down to appealing to the classical logic of MS itself.

shredalert

Yeah. I think that's very important to remember.

user21820

15:55

That's why when you set up the inner system it seems circular; you define "A∧B" to be true exactly when A is true and B is true.

Okay have fun reading!

I'm going off soon.

shredalert

ty

user21820

See you!

shredalert

Have a good night. :)

user21820

Thanks =)

Zophikel

19:21

@amWhy I sent you an email :>)

amWhy

20:33

Hey, @SimplyBeautifulArt, @shredalert! \o/

shredalert

\o/

o/

\o

amWhy

@shredalert I sent two waves at once, one to you and one to @SimplyBeautifulArt

shredalert

Waves all around @amWhy

Mithrandir

🌊

shredalert

That a penguin? @Mithrandir

Mithrandir

20:36

No

It's a wave

amWhy

@Mithrandir Is it a "wave"?

shredalert

Oh

amWhy

@shredalert As a wave of water..... in the ocean, or big lake, which surfers seek out.

shredalert

Only to face wipeout. lol

Simply Beautiful Art

Oh, hello lol

amWhy

20:40

@SimplyBeautifulArt (1) Needs two close votes: math.stackexchange.com/questions/2348683/direction-sense, (2) Needs one more close vote: math.stackexchange.com/questions/2348585/angle-related-to-time

shredalert

I haven't used a close vote in weeks o:

by close vote I mean flag

gives my points away to everyone else

amWhy

On the first of the two, (1), I had even spent time trying to help the asker, and posted an answer I planned to be a CW post, but deleted my answer in the end; read comments below question.

shredalert

CW?

Simply Beautiful Art

Lol, I opened those two and then went to go do something, and then came back to them and thought "wow, these aren't good questions, why did I click on them?" only to realize I should've placed my votes lol

amWhy

@shredalert Get onto it, flag away

:38614237, CW: Community Wiki. There's a teeny box at the very bottom of all question and answer fields with a grey tiny box that one can click, labeled Community Wiki. I've usually used it to make explicit I wasn't after gaining points; i.e., more or less. You don't see it used a lot these days; it was used historically to also keep "Big List questions" open, if of high quality and informative, but turning them to CW so there's nothing in it for anyone except

shredalert

21:11

Ah, I see.

shredalert

21:42

Too tired to study atm. Just going to listen to music and read my novel, probably.

Simply Beautiful Art

Ah yes, I should get back to music...

shredalert

Electro swing? @SimplyBeautifulArt

Simply Beautiful Art

Yup

shredalert

More folk metal here.

Simply Beautiful Art

Lol, when you ask a question and it has 4 views in about 10 minutes, including the view of the person who posted it.

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$Mathematics$ This is the Realm of Simply Beautiful…