## 1033: "Formal Logic"

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JimsMaher
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### Re: 1033: "Formal Logic"

Yeah, considering wnn as a "should do" version of iff is just absurd IMO.

"Should do this, when and only when that"?
... far too subjective to carry consistent and logical truth values (not simply reasonable ones).

The if:while analogy makes some sense. Though I'm certain I don't understand the full ramifications of the analogy as it applies to this newfangled when-and-only-when contraption the kids can't stop tweeting about.

if : while :: IFF : WNN

while condition, execute code = continuous recursion of code until condition ceases
if condition, execute code = code

It goes back to the tense thing then ... it's a case of at what point in the condition is the state checked, the while and if are automatically checked once, but the while is also automatically checked again at end of the code. The if can loop if code tells it to, and the while might not loop the code at all but it will check that second time atleast.

Now, attempting to reconcile that analogy to the direct definition of wnn ... truth tables
(T is true, F is false, + is possible, ‒ is impossible)

A iff B = ?
A: T T F F
B: T F T F
? : + ‒ ‒ +

C wnn D = ?
C: T T F F
D: T F T F
? : + ‒ ‒ +

With what you've described, C=F and D=F would still be + and not ‒ ... even though eliminating vacuous truth here could be a useful accomplishment (vacu-ish truth?), I should focus on the task at hand ...
The goal here is eliminating the vagueness of the description by using other description ... encoding into a pre-existing operator, some other meaning, rather than simply precising the original statement.

"Honk once and only once iff you love formal logic" ... still doesn't say how long those annoying logic lovers should lay on the horn though.
"Honk wnn you love formal logic" ... I'm not sure if redefining formal logic isn't mutually exclusive to loving it. Depending on your definition of love. If that makes any difference.

jpk
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### Re: 1033: "Formal Logic"

Pfhorrest wrote: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".

But that's not what "while" does in any language I've used. "while (condition)" means "do this as long as the condition is true, and then stop". What you're talking about is more of an event handler. You want wnn to be a handler on a particular event: any time this event occurs, execute this code. This is a more complex event-driven model of programming, but it can be arranged, as long as you're capable of describing the events you're interested in. (that is, as long as the events you care about are part of the world that your model describes)

bmonk
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### Re: 1033: "Formal Logic"

JimsMaher wrote:. . .

* 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.

I can love another person without understanding them.
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careyhammer
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### Re: 1033: "Formal Logic"

Sometimes it is easier to love the less you understand.
DUCK!

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### Re: 1033: "Formal Logic"

ineon wrote: "There's coke in the fridge if you are thirsty"
I had to tell off my mum for saying, "There's extra dinner if anyone's still hungry." Now she says, "There's extra dinner if anyone's still hungry... and there's still extra if no one's hungry."
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DavidF
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### Re: 1033: "Formal Logic"

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.

To what extent is this sort of talk actually about formal logic, and to what extent is it more about interpreting language to see how it matches logic? Are you actually talking linguistics here? As far as I can tell, the folks who really get down and dirty with formal logic are the set theorists, the set-theoretic topologists, and the computer scientists. Have I left anyone out?

JimsMaher
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### Re: 1033: "Formal Logic"

DavidF wrote:As far as I can tell, the folks who really get down and dirty with formal logic are the set theorists, the set-theoretic topologists, and the computer scientists. Have I left anyone out?

Logicians.

Pfhorrest
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### Re: 1033: "Formal Logic"

DavidF wrote:
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.

To what extent is this sort of talk actually about formal logic, and to what extent is it more about interpreting language to see how it matches logic? Are you actually talking linguistics here? As far as I can tell, the folks who really get down and dirty with formal logic are the set theorists, the set-theoretic topologists, and the computer scientists. Have I left anyone out?

I was consciously discussing a mix of both, actually. Those two paragraphs you quote are addressing two separate issues: one, people claiming that there are no imperatives in formal logic, when "formal logic" is not some homogeneous thing and there very much are formalized imperative logics, even if there is no standard consensus on which if any is the right one; and two, some people seem not to understand the difference between present simple, continuous, and habitual tenses and aspects of verbs (subject verbs now and is done and stops, vs subject is now verbing and has been and will continue to be verbing, vs subject verbs sometimes every now and then), and how English grammar is often ambiguous between them.

We could (and I'll bet you someone already has) formalize such linguistic differences, if we liked, with a formalization of verb functions, a time-indexing function, and some kind of indexical quantification.

Let for(n,x,F(x)) be a generalized quantification function meaning that formula F(x) holds for some scope n of variable x; and let possible values of n include "all" (universal quantification), "some" (existential quantification), and "this" (indexical quantification), possibly among others.

Let at(t,P) be a time-indexing function mean that proposition P holds at time t.

Let V(s,o) be the proposition that some subject s performs verb V on (optional) object o.

If we want to say that you honk once just right now, then we would say "for(this,t,at(t,honks(you)))". If we wanted to say that you honk once just right now if and only if you love formal logic, we could then say "for(this,t,at(t,(honks(you) iff loves(you,formal logic)))".

Then, let us render all the verbs gerund, and require an indicative wrapper function to restore that meaning. So instead, we would say "there-is(for(this,t,at(t,honking(you) iff loving(you,formal logic))))", or in more natural (but stilted) language, "There is, at this time, you honking if and only if you are loving formal logic".

We can then replace that indicative wrapper function with an imperative one to get the meaning of the original sticker, formalized: "be-there(for(this,t,at(t,honking(you) iff loving(you,formal logic))))", or in more natural (but stilted) language, "Be there, at this time, you honking if and only if you are loving formal logic". ("Be there..." being an imperative phrase, like the "Let there be..." translation of the Latin "Fiat..." used for the commands the Abrahamic God supposedly gave to create the universe. Fiat lux. Let there be light. Be there light. c.f. "Saints be praised!", which might well be rephrased "Let the saints be praised" or "Be the saints praised").

Or, to standardize on prefix notation and get rid of that ugly infixed iff, we might say something like:

be-there(for(this,t,at(t,all-or-none-of(honking(you),loving(you,formal-logic)))))

Or, in slightly more natural but still horribly stilted language:

Be there, at this time, either all or none of the following states of affairs: you honking, you loving formal logic.
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### Re: 1033: "Formal Logic"

ahammel wrote:It also implies:
~(honk & ~you love formal logic)
~(~honk & you love formal logic)
~(honk xor you love formal logic)
(honk & you love formal logic) V (~honk & ~you love formal logic)

But I should stop. I've just had a nightcap and you really shouldn't drink and derive

The above is funnier than the comic. Without the comic I would not have read this. Drink and Derive. So, funny. I have read it before. I forgot. Thank you for the reminder. Funny stuff, that.
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severach
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### Re: 1033: "Formal Logic"

The self limiting aspect of honking is easily defined: "Honk IIF you love honking." That explains the average durations we see, 1/2 second for a hello, 3 seconds for "you idiot" and 7 seconds for "you almost killed me." See, I know how math class operates!

Now onto the real problem

IIF
IIF IIF
IIF IIF IIF

Can someone help me get to Seven Buffalos.

Tyrannosaur
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### Re: 1033: "Formal Logic"

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

CodexDraco wrote:Or it is a quantum fridge and the existence of the coke depends entirely of your level of thirst. Then it makes perfect sense.

No, sillies. It does make sense, and doesn't even have to be a quantum fridge. "There's coke in the fridge if you are thirsty" assumes you only care about whether or not there is coke in the fridge if you are thirsty. Which, although does make sense, is slightly inefficient. I prefer to say something like "There's coke in the fridge iff you are thirsty." You might have forgotten that humans are allowed to give false information. This implies that if you are thirsty, then there is coke and you are welcome to it. But if you are not thirsty, than you are not welcome to my coke dangit and besides I don't have any!

jpk wrote:
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".

But because the message of the bumper sticker is not imprinted on everyone's brains at the beginning of the universe, it does not have universal scope. It only has scope each time you read it, which is a single point in time, and can happen many separate times.

It's kindof like a stop sign. You only have to stop once every time you come across one, you don't have to stay stopped forever; even though condition (is at stop sign?) continues to be true.

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EDIT: Pushed "submit" instead of "preview" before finished with post. I'm sorry guys, I just came from slashdot.
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flyingferret
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### Re: 1033: "Formal Logic"

da Doctah wrote:
907Code-G wrote:Ah I forgot, xkcd is where I originally got my habit of using xor in conversations and intending or as an inclusive logic statement.

I've had this discussion about whether "or" in common discourse is inclusive or exclusive. Turns out it's both:

Exclusive: Mother to small child: "You may have one cookie or one candy bar before dinner."

Inclusive: Boss to employee: "If you show up to work drunk or naked I'll fire you."

I'd say the mother to small child example is actually the common "not and" usage - unless she has a thing about plying her child with precisely the right amount of junk food.

Coyne
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### Re: 1033: "Formal Logic"

kram2301 wrote:
Coyne wrote:Honk iff you don't honk.

Wouldn't it be slightly more paradox to say:
"Honk iff you won't honk."?

Now that you mention it, yes.
In all fairness...