Symbolic Logic

[Max™]

fuck logic in all of its forms, must math taint all of this world

BLASPHEMY!

I can say that I truly understand physics on an innate level, and I aspire to one day understand everything else at the same level as a mathematician does.

Those guys are awesome.

Also:
Set theory - Wikipedia, the free encyclopedia

I love that stuff.


And just to fuck with the logic-cowboys a little:

If Max™ posts this statement, he will NOT be telling the truth.

[isladar]

I love set theory until they make me do Venn diagrams. FFFF those things.

[Max™]

lol

That's just the part of Set theory you can easily touch.

The von Neumann universe concept is crazy.

Where a Set to be considered is only pure if it's members are all sets, and those members of it's members are sets, and so on.

Then you get into cardinality and such, which ALWAYS fascinated me though I'm only barely beginning to fully understand infinites and transfinites and such.

Cantor was a madman or a genius, I can't say for sure which, or if he wasn't both.


I don't think you can use the argument that it doesn't apply to thought against logic, that is a good thing, logic exists on it's own.


If anything, use Godel's argument.


If x + z = y + z
then x = y

Now this is a basic statement about arithmetic.

Let's apply codes for the statements as well, such that:

The code for "a" is 1.
The code for "b" is 2.
etc

If the code number for a claim is x, we can say "There is a number p, ending with the code number x, that passes the test for being the code number of a valid proof."


How far can you take this?

Why was Godel such a crazy scary smart mo-fo?

He wound up with this:

There DOES NOT EXIST a number p meeting the following condition:
p is the code number of a valid proof of this claim.

Let's consider it briefly... if it is true, then there is no number p which is the code for a proof of this claim. It would be a true statement about arithmetic, but you can't prove it by doing arithmetic.

What if it's false?

It claims that the number p is the code number of it's own proof, so to be false there would have to be such a number. So that number would encode proof of an acknowledged falsehood!

[Not Kuno]

Oh god I hated this class. Fuck truth tables. I had no clue what you guys meant until I saw that shit posted. Ung.

[Korietsu]

lol

That's just the part of Set theory you can easily touch.

The von Neumann universe concept is crazy.

Where a Set to be considered is only pure if it's members are all sets, and those members of it's members are sets, and so on.

Then you get into cardinality and such, which ALWAYS fascinated me though I'm only barely beginning to fully understand infinites and transfinites and such.

I hated that crap so much in my discrete math class.

Also, I love the shit out of truth tables, makes designing digital logic so much easier than designing the same system in analog.

Also, for shits and giggles.

Easiest logic ever. Carry Lookahead Adder.

http://upload.wikimedia.org/wikipedi..._adder.svg.png

[isladar]

So now, my question I'm given is:
1. No premise (intentional)
...
...
prove: A v ~(A ^ B)

I know it's generally the same thing, but I keep getting tripped up.

Okay, but this hasn't been directly answered yet, and I haven't jumped on it because I'm not sure what exactly they're asking for in this case. Do they mean "prove it's a valid statement"? "Prove it's a tautology"? Or is it one of these:

p -> q
~p
------
~q thangers, without the if/thens as the antecedent?

[edit] buh, I'm probably completely missing all of this.

[Korietsu]

Okay, but this hasn't been directly answered yet, and I haven't jumped on it because I'm not sure what exactly they're asking for in this case. Do they mean "prove it's a valid statement"? "Prove it's a tautology"? Or is it one of these:

p -> q
~p
------
~q thangers, without the if/thens as the antecedent?

[edit] buh, I'm probably completely missing all of this.

Its just proof the statement's formal validity. IE, go through the steps of how the statement was built.

[Max™]

Masturbating with a logic textbook will end up giving you paper-cuts and/or ink stains in/on your dick/giney.

[Bingbong]

fuck logic in all of its forms, must math taint all of this world

THIS^^

takes 17 lines to figure out that a light switch can be "On" or "Off"



fuck dimmers.

[Max™]

How many lines does it take to figure out that a light switch can BE?

Spoiler: show

http://farm4.static.flickr.com/3018/...2ce85f29_o.gif

[Darus Grey]

You seem to be approaching the question of its utility from a fairly narrow perspective lol I'm not able to address the particular points you brought up regarding the relation of logic to actual human thought (simply because it's beyond the scope of my own knowledge), but it's somewhat beside the point. Let me just point out a few things in your first post that I'd personally take issue with.



What premise would that be? If the suggestion here is that symbolic logic is a model for how actual thought takes place, I'd disagree that this is the premise at all. As I would regard it, the premise is more about the analysis of true propositions that derive their truth from their logical form, rather than by facts about the world. Now whether or not that premise is flawed is, I suppose, also a question that's open to debate, but recognize that the question itself is at least one step removed from how the human mind perceives and actually analyzes those propositions. Either way, this other question is an interesting and perhaps unresolvable one, not the kind you could just dismiss as flawed and move on.




I would also dispute that it's useless. For one thing, in mathematics, there are several fields with a lot of work going on in them for which this class would be an early introduction. But even if he's not interested in mathematics or computer science (or philosophy although you'll probably object if I lump that in here), it's still useful in that it works a person's mind in a way that will make it more natural to analyze arguments and rhetoric down the line, just as a side-effect. And we agree it's fun, although I'm more with woozie in that the problems were fun because of their puzzle-type nature, and not because--like you, apparently--one enters into it with a misconception of its value and utility in certain respects. Sure, if you think that studying logic is going to unlock the human mind (or allow you to prove any sentence in first-order arithmetic) you might be setting yourself up for disappointment, but that doesn't mean that the field or even a cursory study of it is without redeeming value.

The basis of Symbolic Logic is from the Greek Notion that human thought was a manipulation of symbols, this is why it's called symbolic logic, and why it uses symbols. This was simply considered true until the 1960s, at the time alternate testable theories started popping up and interest in testing classical logic was renewed. The only tests that could prove it, was those using classical logic to prove for itself. Which as Lakoff pointed out(MWLB; Preface), was circular logic.

The problem is that it really makes no sense. All the rules and laws of symbolic logic are work-arounds for flaws in the system, because the system itself is flawed.

This is easily apparent when you start converting symbolic logic into real language and then use semantics to see if they match up, and of course, they don't. Also vice-versa

So in the end, the only situation it works for consistently is when all the components of a problem remain symbolic. Which makes it useless for any practical application. It certainly has a lot of man hours put into refining it, but if I just made up some bullshit system right now, based on the idea that thoughts were infact different types of candies, it would hold the same scientific validity of symbolic logic, because they're both based on false premises.

[Denchi]

Ok, so help me out now.

1) Show that the argument is valid in SD

(E ⊃ T) & (T ⊃ O)
O ⊃ E
________________

(E ≡ O) & (O ≡ E)


2) Prove that each of the following is a theorem in SD

(A & A) ≡ A

I can do derivations till the cows come home, but I missed 2 classes last week due to swine flu and I’m just having a hard time understand what they’re even asking.

[Denchi]

1 (E ⊃ T) & (T ⊃ O)
2 O ⊃ E
________________

3 E ⊃ T 1&Elim
4 T ⊃ O 1&Elim
5 E ⊃ O 3,4 Hypothetical Syllogism
6 --- E Assumption
7 --- O 5,6⊃Elim
8 --- O 7Reiteration
9 --- E 2,8⊃Elim
10 E≡ O 6-9≡Intro
11 O≡E 10Comm
12 (E≡O) & (O≡E) 10,11&Intro

(E ≡ O) & (O ≡ E)


There I tried.

[Suiram]

Ok, so help me out now.

1) Show that the argument is valid in SD

(E ⊃ T) & (T ⊃ O)
O ⊃ E
________________

(E ≡ O) & (O ≡ E)


2) Prove that each of the following is a theorem in SD

(A & A) ≡ A

I can do derivations till the cows come home, but I missed 2 classes last week due to swine flu and I’m just having a hard time understand what they’re even asking.

If you can do derivations then you're fine. When they say show an argument is valid in SD they just mean show that there's a proof beginning with the premises (the sentences above the line) and ending with the conclusion (the sentence below). When they say show that it's a theorem they mean to derive the sentence without any premises.

[Denchi]

1 (E ⊃ T) & (T ⊃ O)
2 O ⊃ E
________________

3 E ⊃T 1&E
4 T⊃O 1&E
5 E ⊃ O 3,4 Hypothetical Syllogism
6 (E ⊃O) & (O⊃E) 2,5&I
7 E≡O 6Equiv
8 O≡E 7Comm
9 (E ≡ O) & (O ≡ E) 7,8&Intro

seems better. Although I'm not sure if I can use Commutation on "If and Only If?" It makes sense that you could.....

[Suiram]

seems better. Although I'm not sure if I can use Commutation on "If and Only If?" It makes sense that you could.....

When you said that stuff about "SD" I recognized that you had the book that I used a number of years ago in my own introductory symbolic logic course so I busted it out and looked at the inside cover, and it looks like there isn't a rule for commutation with the biconditional (even though it'd be perfectly valid) so you might want to just unpack it, commute it, and repack it, to be safe grade-wise.

[Denchi]

yeah... same book lol. Cool thanks for the help. yeah I'll have just add a step or two to be safe.

[Woozie]

If Max™ posts this statement, he will NOT be telling the truth.

Nice try, but my head was built with paradox-absorbing crumple zones.

[Suiram]

yeah... same book lol. Cool thanks for the help. yeah I'll have just add a step or two to be safe.

You might want to also be careful that you're allowed to use the rules of replacement, since they specify SD and not SD+ (unless this has changed in subsequent editions of this textbook). Obviously the one is not stronger than the other (in the sense of what is provable) since using a rule like commutation or equivalence just abbreviates a longer derivation with your introduction/elimination rules. But the problem may want you to go through all the motions (this is something only you can know because it depends on what your instructor said regarding the assignment).

[Woozie]

I don't think I understand your argument, DG.

In physics, we use different types of symbols just to represent abstract phenomenon. For example, fields were invented by the human mind as a way to understand how objects can interact at a distance. No one meant to imply that there were actually arrows sitting out in space that planets reacted to. Yet, our math was (is) based on the idea that this is the case. Physicists know that this isn't the case in our own minds. These representations are just tools we use to represent what can't really be represented.

Why wouldn't logic be the same way? pv~p is true whether or not we are using symbols. The symbols are nothing more than our way of representing this rule. The truth of pv~p isn't based on it's notation at all; the notation is just a convinient way of expressing what technically can't really be expressed.

Edit: And as for whether or not it's useful, I don't see how that's even up for debate. If math is useful, then propositional logic is automatically useful, even if it's wrong. At my college, we can't even take any upper level math courses until we take FOAM, which starts out with propositional logic, which is eventually upgraded to set theory and the basics of advanced calc/abstract algebra/topology. Anyone who hasn't taken FOAM is at a disadvantage in these classes. Our intro to logic course is a seperate course than FOAM, but they cover the same things.