1033: "Formal Logic"

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Re: 1033: "Formal Logic"

Postby Whys » Fri Mar 23, 2012 6:20 pm UTC

Honk if you want the terrorists to win. :D
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Re: 1033: "Formal Logic"

Postby ctristan » Fri Mar 23, 2012 6:32 pm UTC

SirMustapha wrote:Thank you for explaining the joke in the alt text, Randall. I would never get it otherwise.

(NOTE: This is completely sarcastic)


I don't think it's really explaining the joke so much as complaining about people who honk when he stops for a pedestrian on the street and giving a valid use for such a bumper sticker. The alt-text doesn't even really explain what formal logic is or what IFF means, so I'm still not sure how it was explaining the joke.
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Re: 1033: "Formal Logic"

Postby Turing Machine » Fri Mar 23, 2012 6:39 pm UTC

Pfhorrest wrote:There actually are formal imperative (and deontic, which may or may not be the same thing) logics.

And present-tense verbs are ambiguous as to whether they mean occasional or continuous action; if we know that Bob swims, do we know that he always swims, non-stop; or just that he sometimes swims, now and then? How about if Bob lives? Or if he owns something? If he eats? We judge from context because the grammar does not explicitly mark it.

It works just the same with imperatives. If you tell someone to eat green vegetables, are you telling them to always eat green vegetables? Continuously, non-stop? Or, eat green vegetables whenever they eat? Or just, eat green vegetables sometimes, maybe frequently?

So, it-is-imperative-that(you honk <-> you love formal logic) could very well (and contextually, given what honking means, probably does) mean that, if you love formal logic, you should sometimes honk (for instance, now, when you read this sticker), and that if you were for any other reason to honk, you should do so only if you love formal logic.

It does not mean that everyone who loves formal logic should continuously honk so long as they love formal logic.


Imperatives don't have truth values.

Deontic logic is not a logic of imperatives. Its modal operators do not say "do the right thing" but "it is mandatory to do the right thing" or "it is permissible to do the right thing." Those two statements can have truth values; imperatives cannot.
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Re: 1033: "Formal Logic"

Postby Turing Machine » Fri Mar 23, 2012 6:42 pm UTC

Re: the duration of honking:

First, as I said, imperatives don't have truth values. If you want to restate this as a simple declaration, hey, that works!

Second, tense logic exists! You can add tense operators to your logic to say things like "at all future times and at all past times, a person honks IFF he likes formal logic".
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Re: 1033: "Formal Logic"

Postby SamSam » Fri Mar 23, 2012 7:06 pm UTC

ineon wrote:and why statements like "There's coke in the fridge if you are thirsty" don't make sense


You're the guy who still answers "can you pass the salt?" with "yes I can pass the salt" and then doesn't do anything, aren't you?

Kids normally work out that there's a separation between the strict literal meaning of what's said and what's actually being meant at around the age of five or six. For a little while, they find this hilarious. Then most kids grow out of it.

"There's a coke in the fridge" has an additional, social, meaning to it. It means "I'm inviting you to take a coke from the fridge." Most of us are not robots and understand this, just as we understand "do you want to go out to dinner with me" to be an invitation, not just a request for information ("sure, I'd love to." "Very interesting... so you want to go out to dinner with me..."). With this additional layer of meaning, the quote above makes perfect sense.
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Re: 1033: "Formal Logic"

Postby CodexDraco » Fri Mar 23, 2012 8:12 pm UTC

Or it is a quantum fridge and the existence of the coke depends entirely of your level of thirst. Then it makes perfect sense.
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Re: 1033: "Formal Logic"

Postby ahammel » Fri Mar 23, 2012 8:24 pm UTC

SamSam wrote:
ineon wrote:and why statements like "There's coke in the fridge if you are thirsty" don't make sense


You're the guy who still answers "can you pass the salt?" with "yes I can pass the salt" and then doesn't do anything, aren't you?

He appears to be the guy who is pointing out that the concept of "if" in English does not always related to the concept of a conditional in formal logic. There are applications of this knowledge beyond juvenile word play.
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Re: 1033: "Formal Logic"

Postby TheGrammarBolshevik » Fri Mar 23, 2012 8:25 pm UTC

Turing Machine wrote:Imperatives don't have truth values.

Deontic logic is not a logic of imperatives. Its modal operators do not say "do the right thing" but "it is mandatory to do the right thing" or "it is permissible to do the right thing." Those two statements can have truth values; imperatives cannot.

I don't see the relevance of this. There can still be imperative logics; they would just be logics that preserve imperative-ness instead of preserving truth.
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Re: 1033: "Formal Logic"

Postby Turing Machine » Fri Mar 23, 2012 9:06 pm UTC

TheGrammarBolshevik wrote:
Turing Machine wrote:Imperatives don't have truth values.

Deontic logic is not a logic of imperatives. Its modal operators do not say "do the right thing" but "it is mandatory to do the right thing" or "it is permissible to do the right thing." Those two statements can have truth values; imperatives cannot.

I don't see the relevance of this. There can still be imperative logics; they would just be logics that preserve imperative-ness instead of preserving truth.


Imperatives don't have truth values.

Read it again. Maybe it will stick this time.
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Re: 1033: "Formal Logic"

Postby bmonk » Fri Mar 23, 2012 9:39 pm UTC

orangedragonfire wrote:The problem here would be that people who love formal logic would have to honk all the time. Forever.

Maybe we need to add "once" or "once per day when you see this statement"?

savanik wrote:Out of all the things I learned in college, formal logic is probably one of the most useful things I've learned for my daily job. I do a lot of info searching, and being able to know that NOT (A OR B) is the same thing as NOT A AND NOT B really helps me troubleshoot queries.

Irony: It was in a Philosophy course and didn't count for Computer Science credit. Neither was my second-most useful class, Human-Computer Interfaces, that actually taught me how to properly use a testing methodology for interface design. That was part of the Psychology subtrack.

Are you saying that the Computer Science track is not very logical?

ahammel wrote:
SamSam wrote:
ineon wrote:and why statements like "There's coke in the fridge if you are thirsty" don't make sense




You're the guy who still answers "can you pass the salt?" with "yes I can pass the salt" and then doesn't do anything, aren't you?

He appears to be the guy who is pointing out that the concept of "if" in English does not always related to the concept of a conditional in formal logic. There are applications of this knowledge beyond juvenile word play.


But, actually, as long as there is coke in the fridge, then "There's coke in the fridge if you are thirsty" is always true. (It's also true whenever you are not thirsty.)
Last edited by bmonk on Sun Mar 25, 2012 9:36 pm UTC, edited 2 times in total.
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Re: 1033: "Formal Logic"

Postby bmonk » Fri Mar 23, 2012 9:43 pm UTC

savanik wrote:Out of all the things I learned in college, formal logic is probably one of the most useful things I've learned for my daily job. I do a lot of info searching, and being able to know that NOT (A OR B) is the same thing as NOT A AND NOT B really helps me troubleshoot queries.

Irony: It was in a Philosophy course and didn't count for Computer Science credit. Neither was my second-most useful class, Human-Computer Interfaces, that actually taught me how to properly use a testing methodology for interface design. That was part of the Psychology subtrack.

Are you saying that the Computer Science track is not very logical?
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Re: 1033: "Formal Logic"

Postby theo1358 » Fri Mar 23, 2012 9:51 pm UTC

javahead wrote:IIF = infinite if ... wasn't a typo I don't think.

I, for one, do not care one way or another for formal logic.
So I shall never honk again, but it won't stop me extending various forms of the middle finger. And screaming; i'm good at that.


IFF <=> if and only if
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Re: 1033: "Formal Logic"

Postby mric » Fri Mar 23, 2012 9:56 pm UTC

Turing Machine wrote:
TheGrammarBolshevik wrote:
Turing Machine wrote:Imperatives don't have truth values.

Deontic logic is not a logic of imperatives. Its modal operators do not say "do the right thing" but "it is mandatory to do the right thing" or "it is permissible to do the right thing." Those two statements can have truth values; imperatives cannot.

I don't see the relevance of this. There can still be imperative logics; they would just be logics that preserve imperative-ness instead of preserving truth.


Imperatives don't have truth values.

Read it again. Maybe it will stick this time.

You can have formal logics that handle imperatives. For example, Anthony Kenny describes a wish-preserving structure for imperatives, and R.M. Hare (among others) puts forward the view that an imperative can be translated into truth-apt sematically isomorphic declaratives.

What route you go down partially depends on what you consider the negation of the imperative to be. If I say "shut the door", is the negation of the imperative "Don't shut the door", or is it "You may leave the door open"? If you consider the wish behind the instruction to be "I want you to shut the door", then the negation would be "It is not the case that I want you to shut the door" rather than "I want you not to shut the door".

That question about the treatment of the negative is critical to how to interpret the logic of the comic. Recast the statement "Honk iff you love formal logic" as "I want you to honk iff you love formal logic". For simplicity, I would present that as the conjunction of "You loving formal logic implies that I want you to honk" and "You not loving formal logic implies that it is not the case that I want you to honk". But an alternative reading of the negation would make the second part of the conjunction "You not loving formal logic implies that I don't want you to honk (i.e. I want you not to honk)."

The first approach provides no injunction on non-lovers of formal logic against their honking, only expressing the absence of a desire for them to honk. The second expresses an active request not to honk for the non-lovers of formal logic. The first reading has advantages in how imperative logics are formed.
Last edited by mric on Fri Mar 23, 2012 9:58 pm UTC, edited 1 time in total.
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Re: 1033: "Formal Logic"

Postby Pfhorrest » Fri Mar 23, 2012 9:58 pm UTC

Turing Machine wrote:
TheGrammarBolshevik wrote:
Turing Machine wrote:Imperatives don't have truth values.

Deontic logic is not a logic of imperatives. Its modal operators do not say "do the right thing" but "it is mandatory to do the right thing" or "it is permissible to do the right thing." Those two statements can have truth values; imperatives cannot.

I don't see the relevance of this. There can still be imperative logics; they would just be logics that preserve imperative-ness instead of preserving truth.


Imperatives don't have truth values.

Read it again. Maybe it will stick this time.

Try taking your own advice. And a class on metaethics.

If you're not trying to preserve truth, but instead whatever it is that imperatives convey, then it doesn't matter that imperatives don't have truth-values.

If it helps you wrap your head around it, you can rephrase any imperative in a superficially indicative form: "do x" => "you are to do x" or "it is imperative that you do x" or maybe "I order you to do x" or the like. What exactly the semantics of such sentences flesh out to is a big hairy problem (what are the truth conditions of "it is imperative that you do x"?), but you can then plainly see that you can logically conclude that an order to verb all nouns implies an order to verb this noun, and the like.

There is a similar big hairy problem about what the semantics of moral or deontic propositions are, and one proposed solution is that despite their superficially indicative form they are really hidden imperatives. There is no consensus in the field on this matter, which is why I said that imperative and deontic logics "may or may not" be the same thing.

My personal stance is that there are two types of proposition, indicative and imperative; the former proposes that something is (indicative copula), and the latter proposes that something be (imperative copula). What they convey are two different kinds of mental states: beliefs and intentions. I have a belief, I want to convey that belief to you, to impress it upon you and have you believe the same thing, so I make an indicative proposition to you. I have an intention, I want to convey that intention to you, to impress it upon you and have you intend the same thing, so I make an imperative proposition to you.

Logical relations hold between the states of affairs believed to be or intended to be; the addition of an attitude that "this state of affairs is the case" or "this state of affairs ought to be the case" has no impact on the logical relations between the states of affairs. But an attitude held toward one state of affairs implies the same attitude toward any state of affairs implied by the first. So indicative propositions can logically imply other indicative propositions, and imperative propositions can logically imply other imperative propositions. That imperatives are not true or false (but might rather be good or bad, on an imperativist metaethics) does not affect that in the slightest.
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Re: 1033: "Formal Logic"

Postby Harry Voyager » Fri Mar 23, 2012 10:16 pm UTC

Pfhorrest wrote:And for the military logicians out there: IFF iff you identify as friend, not foe.


Technically a positive response only implies a high likelihood that it is friendly. There is nothing intrinsically preventing those who are not friendly also responding positively to an IFF query, only their ignorance of the correct positive response.

And just for extra fun, there is nothing intrinsically preventing someone who is hostile to you correctly querying your IFF transponder, thus getting your IFF transponder to announce to them where you actually are, thus any given IFF query has a possibility of being one you do not actually want to answer.
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Re: 1033: "Formal Logic"

Postby JimsMaher » Fri Mar 23, 2012 10:23 pm UTC

{ People who know what Formal Logic is } = A
{ People who don't know what Formal Logic is } = B
A ∩ B = ∅
{ People who love Formal Logic } = C
{ People who don't love Formal Logic } = D
C ∩ D = ∅

You must know what something is to love it.
∴ C ⊆ A ∧ ~B
If you know what something is, you don't necessarily love it.
∴ D ⊆ A ∨ B

So, People who love Formal Logic know what it is, but not necessarily vice versa.
However, to read the bumper sticker and follow its instructions, a person must UNDERSTAND Formal Logic ...

{ People who understand Formal Logic } = E
{ People who don't understand Formal Logic } = F
E ∩ F = ∅
... consider the threshold for "understanding Formal Logic" as being that of sufficiently understanding the meaning of the bumper sticker in question.

If you understand something, you know what it is.
∴ E ⊆ A ∧ ~B
If you don't understand something, you don't necessarily not know what it is.
∴ F ⊆ A ∨ B

Since we are only interested in those who honk after reading the bumper sticker "Honk IFF you love Formal Logic",
we will only concern ourselves with the set of honkers ... I love Formal Logic.
A person can love Formal Logic and not honk after reading the bumper sticker ... I wouldn't.
Also, people honk all the time without reading that particular bumper sticker (figuring that it most likely doesn't yet exist IRL).

Anyway, back to the question at hand:
A person just honked after reading the hypothetical bumper sticker ... "Honk IFF you love Formal Logic".
* Supposing they understand Formal Logic, is it possible that they don't love Formal Logic?
Yes. Because E ⊆ A, and if you know what something is, you don't necessarily love it.

* Supposing they DON'T understand Formal Logic, is it possible that they DON'T love Formal Logic?
Yes. If you can't read the language, you can't follow the directions.
Ever try to read the foreign language sections of an Instruction Manual?

* Is it possible for someone to love Formal Logic and not understand it?
Yes. F ⊆ A and C ⊆ A.
Without further definition of love, it is therefore considered possible to love without understanding.
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Re: 1033: "Formal Logic"

Postby TheGrammarBolshevik » Fri Mar 23, 2012 11:06 pm UTC

Turing Machine wrote:
TheGrammarBolshevik wrote:
Turing Machine wrote:Imperatives don't have truth values.

Deontic logic is not a logic of imperatives. Its modal operators do not say "do the right thing" but "it is mandatory to do the right thing" or "it is permissible to do the right thing." Those two statements can have truth values; imperatives cannot.

I don't see the relevance of this. There can still be imperative logics; they would just be logics that preserve imperative-ness instead of preserving truth.


Imperatives don't have truth values.

Read it again. Maybe it will stick this time.

I did read it. That's why I acknowledged it but said that it isn't relevant.
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Re: 1033: "Formal Logic"

Postby Daggoth » Sat Mar 24, 2012 12:11 am UTC

Why would it cause constant honking?, the bumper sticker doesnt say "honk forever" it just says Honk.
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Re: 1033: "Formal Logic"

Postby Azshade » Sat Mar 24, 2012 2:09 am UTC

I have a bumper sticker that says "My dinosaur ate your Jesus fish". I like it because the people I want to understand it can. Whereas the problem with this bumper sticker is that the people who are honking the horns (I'd imagine) don't understand formal logic.
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Re: 1033: "Formal Logic"

Postby sngbrdb » Sat Mar 24, 2012 4:11 am UTC

`
Now I know why RM always draws stick figures :P


... and now for something completely different.


`
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Re: 1033: "Formal Logic"

Postby Pfhorrest » Sat Mar 24, 2012 7:31 am UTC

savanik wrote:Irony: It was in a Philosophy course and didn't count for Computer Science credit.

How is that ironic? Philosophy has been studying formal logic since before "computer" even meant a person who did arithmetic for a living. It was a philosopher who basically called for the existence of formal logic in the first place, saying "The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, to see who is right."

The same guy also invented infinitesimal calculus.

(No, not Isaac Newton).
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Re: 1033: "Formal Logic"

Postby Mirkwood » Sat Mar 24, 2012 8:43 am UTC

Daggoth wrote:Why would it cause constant honking?, the bumper sticker doesnt say "honk forever" it just says Honk.


The reader is instructed to honk if (and only if) they love formal logic. After honking, they presumably still love formal logic, so they must honk again, and then again, ad nauseam. As someone else brought up, after sufficient honking they would stop loving formal logic, thus ending the terror of the honk.

Now, "honk once iff you love formal logic", that'd be better. If you see the bumper sticker again ten years later, though, you couldn't honk---you've already done it once.
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Re: 1033: "Formal Logic"

Postby JimsMaher » Sat Mar 24, 2012 9:23 am UTC

Maybe "Honk IFF you hate Formal Logic" would be more appropriate.
Given the general nature of the conclusions drawn here, the original seems to evoke more corrections and ire than woots and laughter.
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Re: 1033: "Formal Logic"

Postby Lode » Sat Mar 24, 2012 1:16 pm UTC

Wow, that is one UGLY car!
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Re: 1033: "Formal Logic"

Postby Michael.K » Sat Mar 24, 2012 1:36 pm UTC

Getting back to the topic of bumper stickers, people:

forth love if honk then

My favourite actual bumper sticker.

Unfortunately, the flavour of forth I had used endif, not then. :(
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Re: 1033: "Formal Logic"

Postby Daggoth » Sat Mar 24, 2012 4:48 pm UTC

"The reader is instructed to honk if (and only if) they love formal logic. After honking, they presumably still love formal logic, so they must honk again, and then again, ad nauseam. As someone else brought up, after sufficient honking they would stop loving formal logic, thus ending the terror of the honk."


It is not implied that you must honk forever if you continue to love formal logic after complying to the initial honk.

You read the bumper sticker (past tense)
You honk
You are done


Unless you somehow become locked visually onto the bumper sticker and can´t physically gaze anyway else. Even then you would only honk intermittently and once for every time you re-read the bumper sticker, not a single eternal honk.
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Re: 1033: "Formal Logic"

Postby Mirkwood » Sat Mar 24, 2012 7:39 pm UTC

Daggoth wrote:
"The reader is instructed to honk if (and only if) they love formal logic. After honking, they presumably still love formal logic, so they must honk again, and then again, ad nauseam. As someone else brought up, after sufficient honking they would stop loving formal logic, thus ending the terror of the honk."


It is not implied that you must honk forever if you continue to love formal logic after complying to the initial honk.

You read the bumper sticker (past tense)
You honk
You are done


Unless you somehow become locked visually onto the bumper sticker and can´t physically gaze anyway else. Even then you would only honk intermittently and once for every time you re-read the bumper sticker, not a single eternal honk.


Looking away from an instruction does not invalidate the instruction; you need not re-read the bumper sticker for you to follow the instruction, as you know the instruction exists and are thinking about it. (Much like "the game"; once you are introduced to it you always continue playing it, and often losing it, like now.) If you continue to know about the instruction, then you must honk if (and only if) you still love formal logic. I suppose you're right about the intermittent honking, though---a being with a reaction and processing time of zero would be doing one constant honk, but human limitations mean that it would in practice be a series of separate honks.
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Re: 1033: "Formal Logic"

Postby TheGrammarBolshevik » Sat Mar 24, 2012 8:32 pm UTC

Suppose I say "Honk." Do you need to honk forever in order to comply with my instruction?

If not, then why would you suddenly need to honk forever in order to comply with "Honk if and only if you love formal logic"?
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Re: 1033: "Formal Logic"

Postby jpk » Sat Mar 24, 2012 8:41 pm UTC

TheGrammarBolshevik wrote:Suppose I say "Honk." Do you need to honk forever in order to comply with my instruction?

If not, then why would you suddenly need to honk forever in order to comply with "Honk if and only if you love formal logic"?


Or even more basic: suppose I say "honk". Do you feel the need to comply with my instruction?
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Re: 1033: "Formal Logic"

Postby TheGrammarBolshevik » Sat Mar 24, 2012 8:42 pm UTC

Well, but I think what's at issue here is what it would mean to comply with the instruction, not whether anyone is actually bound to do so.
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Re: 1033: "Formal Logic"

Postby jpk » Sat Mar 24, 2012 9:12 pm UTC

TheGrammarBolshevik wrote:Well, but I think what's at issue here is what it would mean to comply with the instruction, not whether anyone is actually bound to do so.


I don't see why the former is an issue, unless the latter is settled in the affirmative. In any case, the answer to that question is trivial.
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Re: 1033: "Formal Logic"

Postby JimsMaher » Sat Mar 24, 2012 9:17 pm UTC

This entire discussion is trivial ... none the less ...
What does it mean to comply with any such instruction?

STOP sign: As you approach the sign, you stop ... once you've stopped, you the proceed. You don't stop forever. Having stopped for some reasonable interim, you have legally complied with the sign's instruction. Which was simply "Stop". There are more explicit regulations that accompany a STOP sign, which is just a trigger to follow those laws ... so maybe that's not the best example.

Well, the bumper sticker suggests nothing about duration. Honk. And supposing you read it once then look away, like any reasonable driver who is inclined to read bumper stickers in the first place. Then any duration of "honk" (singular) should be sufficient.

Be aware that certain jurisdictions have laws against honking, with fines attached. So, in such locations in order to comply with the bumper sticker, logically: one must break the law. And since this comic is available in those jurisdictions, XKCD is therefore promoting criminal activity!
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Re: 1033: "Formal Logic"

Postby jpk » Sat Mar 24, 2012 9:41 pm UTC

JimsMaher wrote:This entire discussion is trivial ... none the less ...
What does it mean to comply with any such instruction?



The problem that I think some people are having here is that they're getting confused about the difference between instructions and rules. A rule exists statically, and should be executed when its condition becomes true. An instruction exists as an instance, and should be evaluated once, when it is encountered. If the governing condition is true, execute the instruction. Note that we use iff logic by default here - if you do not in fact love Jesus and you honk at a car with a "honk if you love jesus" bumper sticker, you have not successfully complied with the instruction, despite what formal logic has to say about "if".


Be aware that certain jurisdictions have laws against honking, with fines attached. So, in such locations in order to comply with the bumper sticker, logically: one must break the law. And since this comic is available in those jurisdictions, XKCD is therefore promoting criminal activity!


Or would be if this sticker appeared in the xkcd store without appropriate legal boilerplate.
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Re: 1033: "Formal Logic"

Postby JimsMaher » Sat Mar 24, 2012 10:46 pm UTC

jpk wrote:The problem that I think some people are having here is that they're getting confused about the difference between instructions and rules. A rule exists statically, and should be executed when its condition becomes true. An instruction exists as an instance, and should be evaluated once, when it is encountered. If the governing condition is true, execute the instruction. Note that we use iff logic by default here - if you do not in fact love Jesus and you honk at a car with a "honk if you love jesus" bumper sticker, you have not successfully complied with the instruction, despite what formal logic has to say about "if".


Right, but the intrinsic logic of an instruction about formal logic should hold true for all logical permutations ... despite what Jesus says about love. Mostly good things, I hear. Wait, did Jesus ever have anything negative to say about love?

Anyway, so what you're saying is that if you honk, but not out of the prescribed love, then you have ignored (on some necessary level) the bumper sticker's command. I concur, to a point.

Consider intent.
Does a person have to understand the ramifications of their actions to be complying with an instruction? Say your car is stopped in front of a sign, if you don't know why you are stopping at a sign, or you just stopped randomly and it happens to be in front of a STOP sign ... are you disobeying the STOP sign's instruction? Well, OK I'm drifting from the IFF dynamic ...

Let's suppose a person loves Formal Logic and they honk their horn a few seconds after reading the sticker ... but not because of the sticker, rather it was to warn a pedestrian who was being dive bombed by a flock of sea gulls, and the driver was hoping to scare the birds. Would that honk be complying with the instruction? Supposing there was no thought to the sticker upon seeing the birds' attack.

Regardless of intent, I should think such honking would be more emphatic than if it were strictly out of the promotion of Formal Logic.
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Re: 1033: "Formal Logic"

Postby Pfhorrest » Sun Mar 25, 2012 1:56 am UTC

jpk wrote:The problem that I think some people are having here is that they're getting confused about the difference between instructions and rules. A rule exists statically, and should be executed when its condition becomes true. An instruction exists as an instance, and should be evaluated once, when it is encountered.


I think the bigger problem is that people are disagreeing about whether the depicted bumper sticker is issuing a rule or an instruction.

I argue that it is issuing an instruction (that the verb "honk" is in the present tense, not a timeless, continuous tense), but that that instruction is conditional. The algorithm it would have you follow is this: "upon receiving this instruction, evaluate whether or not you love formal logic; if so, honk; else, do not honk." As "honk" by itself is usually taken to be an instruction, not a rule, that means honk once, now (upon receiving the instruction), not "honk continuously hence force."

A rule would more likely be phrased "honk when and only when* you love formal logic"

*(I hereby coin then term "whenn" to abbreviate this, if it doesn't exist already).

JimsMaher wrote:Let's suppose a person loves Formal Logic and they honk their horn a few seconds after reading the sticker ... but not because of the sticker, rather it was to warn a pedestrian who was being dive bombed by a flock of sea gulls, and the driver was hoping to scare the birds. Would that honk be complying with the instruction? Supposing there was no thought to the sticker upon seeing the birds' attack.


The "only if" part of the bumper sticker's command would say that such a person is permitted to honk, since they love formal logic. That they honked for some reason other than loving formal logic would thus be perfectly compliant with that part of the sticker. The "if" part obliges them to honk, since they love formal logic. But it likewise does not oblige a motive for honking.

Say I am jogging down the street and some mouth-breather shouts "Run Forrest Run!". (Yes, this happens sometimes). I was already running, and still am, and so am in compliance with their imperative, even if I would not have run simply because they said to do so.

On a highly tangential note, I think this distinction has a very important impact on political philosophy, in particular with regards to explaining philosophical anarchism, which is not any position on how society should be or what people should do, but rather the position that how society should be or what people should do is in no way dependent on what the state says about those matters, though it may be coincident with it. In other words, nobody is obligated to do as the state says, but the state may nevertheless say to do some things which are obligatory.

That is, the philosophical anarchist is saying that there may be some things which are obligatory, and if the state tells you to do them, you are required to obey -- but not because the state said to. Anybody else's command to do so would be just as compulsory, and you would be required to do it even if the nobody said so. The imperative force of the command is not determined by who commanded it, but by what was commanded. Authority is trustworthiness to issue commands iff they are obligatory, rather than commands being obligatory iff they are issued by an authority.

Rather like we take indicative propositions to be. Academic authority comes from being a reliable source of true indicative propositions, not the other way around; indicative propositions aren't made true by their being issued by an academic authority.
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Re: 1033: "Formal Logic"

Postby jpk » Sun Mar 25, 2012 2:41 am UTC

Pfhorrest wrote:
jpk wrote:The problem that I think some people are having here is that they're getting confused about the difference between instructions and rules. A rule exists statically, and should be executed when its condition becomes true. An instruction exists as an instance, and should be evaluated once, when it is encountered.


I think the bigger problem is that people are disagreeing about whether the depicted bumper sticker is issuing a rule or an instruction.

I argue that it is issuing an instruction (that the verb "honk" is in the present tense, not a timeless, continuous tense), but that that instruction is conditional. The algorithm it would have you follow is this: "upon receiving this instruction, evaluate whether or not you love formal logic; if so, honk; else, do not honk." As "honk" by itself is usually taken to be an instruction, not a rule, that means honk once, now (upon receiving the instruction), not "honk continuously hence force."

A rule would more likely be phrased "honk when and only when* you love formal logic"

*(I hereby coin then term "whenn" to abbreviate this, if it doesn't exist already).



That was exactly what I had in mind, I disagree with you in not a jot of this. I like "whenn", but it still allows for the rule/instruction confusion, unless it's defined to restrict itself only to the "instruction" context - in which case it sort of loses its purpose.
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Re: 1033: "Formal Logic"

Postby JimsMaher » Sun Mar 25, 2012 4:00 am UTC

Regarding "whenn" or might I suggest the alternate notation, "wnn" ...
It seems that the very nature of wnn, if replicating the pattern of iff, is as follows:

A iff B: Suppose A, then B ... Suppose B, then A; A is true if and only if B is true.
A wnn B: Suppose A, then B ... Suppose B, then A; A is true when and only when B is true.
¿ wnn ≡ iff ?

It superficially appears to be simply a matter of the minor change in the framing of the tense of the declaration.
Is there any way that wnn should be defined as being not logically equivalent to iff ?
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Re: 1033: "Formal Logic"

Postby imantodes » Sun Mar 25, 2012 7:20 am UTC

Is there any way that wnn should be defined as being not logically equivalent to iff ?


Yes: "iff" is an operator that applies to truth values; "wnn" is an operator that applies to rule compliance.

A iff B --> if A is true, then B is true, and vice versa.
A wnn B --> If A is true, you really ought to be doing B, and vice versa.

Examples:

1) A person is a bachelor iff that person is a man who is not married.

2) You can drive wnn you are not drunk.

"1" has a truth value. "2" does not. "2" does not indicate that driving while drunk is impossible, but that it is not permissible.
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Re: 1033: "Formal Logic"

Postby imantodes » Sun Mar 25, 2012 8:07 am UTC

Regarding this

The reader is instructed to honk if (and only if) they love formal logic. After honking, they presumably still love formal logic, so they must honk again, and then again, ad nauseam. As someone else brought up, after sufficient honking they would stop loving formal logic, thus ending the terror of the honk.


and similar statements along the same lines:

No duration is specified. Neither formal logic nor normal interpretation of natural language provide any justification for the idea that, when a duration is not specified for an instruction, we must assume that the duration necessary for compliance is eternal. As has been pointed out previously in this thread, anyone who has dealt with traffic signs or any other form of natural language instruction is, in fact, aware of this, whether willing to admit it now or not. The presence of "iff" in the bumper sticker changes nothing, since "iff" does not have any defined role in specifying durations for rule compliance. I can only assume this misunderstanding arises thus:

If we interpret the bumper sticker as a command to ensure that the proposition, "Honk iff you love formal logic," is true, well, truth has no duration, so we must honk so long as "you love formal logic" is true, and not honk so long as "you love formal logic" is not true.

However, this is silly. That isn't how commands or instructions work. "Close the door!" doesn't mean "ensure that the proposition 'close the door!' is true!" Commands don't have truth values. Compliance with a command is not a matter of ensuring that the command itself is a statement that is true. Something like "stop iff you are at a stop sign!" is no different; interpreted as a command, it just means "stop if you are at a stop sign, and don't stop otherwise". "Iff" does not mean "for eternity", nor does it mean "interpret this command as a proposition that you are obliged to ensure is true."

Now, suppose someone said: "Ensure that 'you are stopped iff you are at a stop sign' is true!" OK, now if you arrive at a stop sign, compliance with this command requires that you remain stopped for eternity. Similarly, if the bumper sticker said something like this: "Ensure that 'you are honking iff you love formal logic' is true!" well, you must honk continuously so long as you love formal logic.

OTOH, with the original bumper sticker, "honk iff you love formal logic", by honking continuously you would indicate to any observers that you do in fact love formal logic... but aren't very good at it.
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Re: 1033: "Formal Logic"

Postby Pfhorrest » Sun Mar 25, 2012 8:57 am UTC

imantodes wrote:
Is there any way that wnn should be defined as being not logically equivalent to iff ?

Yes: "iff" is an operator that applies to truth values; "wnn" is an operator that applies to rule compliance.

That's not how I meant it, at least. I meant whenn/wnn to be a subset of iff, more specific about the tense of the verbs involved.

For instance, take two completely indicative sentences (neither of which are true, but hey):

"People swim if and only if they are able to hold their breath under water."

This sentence does not necessarily claim that all and only people who are able to hold their breath under water swim constantly for the entire time that they have that ability. It might only claim that everyone who has that ability swims sometimes. The grammar by itself does not strictly mark which of those is the case, but from context we can assume it is the latter that is meant. (Not that that's true anyway; some people can hold their breath, but still never swim).

"People swim when and only when it is a warm summer afternoon."

This sentence unambiguously claims that people swim, always, constantly, and without fail, whenever it is a warm summer afternoon, and never when it is not. (This is obviously false as nobody swims all summer afternoon, every summer afternoon). It cannot be taken to mean only that people all swim on some summer afternoons, but not necessarily all of them, just sometimes, and never at any other time of day or year.

In computer programming terms, it's analogous to the difference between an "if" and a "while". "If (condition) { code block };" means "right now, evaluate condition, and if it returns true, execute code block, then stop and proceed to the next line", where as "while (condition) { code block };" means "continuously evaluate condition and continually execute code block any time it returns true, and don't stop unless explicitly told to".
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