Nonlogical Logic: 1=3 is Still Logical

[kanzure]

Logic is a great concept, having proven data support ideas. Can't there be a "logical logic"? Yes, because [our] "logic" is "logical" itself. 1=1. That's logical, because we say that 1 is existing, and then we say it equals one. Which is true, so its logical!

Now what about nonlogical logic? Such as saying " 1 = 3". Before, I said "1=1". We call that logical because we have "1" as "1" in our minds...which is where I've come up with this. Can't we all be wrong, and have "1 thing" actually be "3 things"? It's nonlogical to our understanding of logic, but it is still logical because we can not prove that our language is correct.


Err..right? Is there other examples of "nonlogical logic"? [Edit] Chaos? (just trying to spark some ideas)

[Extra]
1=3. It's wrong by our mathematical system, but that doesn't mean its not logical, does it?

 

[confutatis]

Logic is just one aspect of our minds, just one particular way of thinking among many. You can't think logically in most situations of your life, because in reality you're never sure what you're dealing with. There are many cases when what you think is "1" also appears to be "3" and logic will take you nowhere.

 

[Mentat]

Originally posted by kanzure
Logic is a great concept, having proven data support ideas. Can't there be a "logical logic"? Yes, because [our] "logic" is "logical" itself. 1=1. That's logical, because we say that 1 is existing, and then we say it equals one. Which is true, so its logical!

Now what about nonlogical logic? Such as saying " 1 = 3". Before, I said "1=1". We call that logical because we have "1" as "1" in our minds...which is where I've come up with this. Can't we all be wrong, and have "1 thing" actually be "3 things"? It's nonlogical to our understanding of logic, but it is still logical because we can not prove that our language is correct.


Err..right? Is there other examples of "nonlogical logic"? [Edit] Chaos? (just trying to spark some ideas)

[Extra]
1=3. It's wrong by our mathematical system, but that doesn't mean its not logical, does it?

Kanzure, I think the problem lies in the definition of "logic" that you seem to be working from. There is nothing "illogical" about 1=3, it is perfectly logical, it just doesn't necessarily make sense. Common sense does not equal "logic".

 

[Dissident Dan]

1=3 is not logical. Hold one rock in one hand and three rocks in the other. Count them.

First hand : "tet" (arbitrary counting sound)
Second hand: "tet" "tet" "tet"

Nope. Not the same.

When people think about making statements such as "1=3", they think about it linguistically. But you can't just think about it linguistically. 1 and 3 are symbols for actual things ("this many" and "that many").

 

[Gara]

1+1 = 10, 10+1 = 11, 11+1 = 100

hows this for logic?

 

[confutatis]

Originally posted by Gara
1+1 = 10, 10+1 = 11, 11+1 = 100

hows this for logic?

There's nothing illogical about 1+1=10, or 1+1=3, or 1+1=sausage. The point of logic is that all different ways of writing the same thing must be perfectly equivalent. Thus 2=1+1=5-3=8/4=...

10=1+1=101-11=1000/100... perfectly logical.

 

[Jeebus]

I believe that logic has to follow a certain structure or semantic structure of events and thus 'logic' becomes the 'logical'. When you try to put something in illogical format, it no longer follows the notion of logical form. It has to be played at a significant role in theories of meaning for natural languages. That's logic.

 

[Grev]

All I want to say is: Crap.

I learned a new thing today everybody!

Now I can argue with my friends. >=)

 

[darkmage]

We cannot be correct in saying that 1=3 unless we change the rules by which we make our statement (which we can't). Logic is based around rules and any statement which breaks the rules is logical, but it is simply a false staement.

 

[verty]

Saying that '1 = 3' is to say a false statement. The truth value of that statement is 'false'. We can judge it using logic, because we know what '1' represents and what '3' represents and what '=' represents. Using logic, we can make a judgement about that statement, that it is false. The statement itself isn't logic, but what we use to judge it is.

 

[darkmage]

Verigo: Yes, that is the best way to put it. I agree, but isn't a "logical statement" a statement which can be evaluated via logic? I know the statement itself is not logic, but it could be described as a "logical statement" becuase we use logic to evaluate it. Maybe this is a matter of opinion.

 

[verty]

darkmage, we can evaluate anything using logic. I would say that a statement is logical if we can logically evaluate it to be true. If it is unspecific, or lacking in information, I wouldn't call it logical.

We wouldn't normally talk of logical statements, but rather logical arguments, where we go from some initial premises and, though the use of logic, come to some conclusion. If the logic used in formulating that argument was correct, I would call the argument logical.

 

[Gara]

1+1 = 10, 10+1 = 11, 11+1 = 100 is binary. :)

 

[loseyourname]

I think you have effectively shown that you must specify both the language and the number system you are operating with, then we can evaluate your statement. If, in order to be considered true, it must defy logic, then it is illogical. It is also untrue. If it is true in accordance with logic, then it is logical.

 

[Moonbear]

Sure, 1=3 is logical if there is no definition of what these numbers represent. Numbers are just a shortcut. Without further explanation, they are an abstract concept, not a concrete amount. 1 coin = 3 coins (1 quarter = 2 dimes + 1 nickel). 1 rock = 3 rocks (1 30-kg rock = 3 10-kg rocks).

 

[olde drunk]

in the old DOS days there were commands a=c or c=b which were logical. without parameters any equation is logical. once we establish the subject and ground rules, an otherwise logical statement maybe false and illogical.

peace,
olde drunk

 

[Imparcticle]

1+1 = 10, 10+1 = 11, 11+1 = 100

hows this for logic?

It depends on what the definiton of "1" is. "1" could represent 5 things in one case to make 1+1=10.
"1 thing" is made up of millions of counterparts (i.e. atoms etc.) so by saying "1 thing", your are referring to millions of counterparts which make up this "one thing". Therefore, 1 may = billions .
But I don't understand how your aforementioned examples (quoted from Gara) could be logical by our concept of logic.

 

[wuliheron]

Words only have demonstrable meaning according to their function in a given context. In other words, you can have nonlogic logic if you so choose, but if you want it to have any meaning to anyone else you must demonstrate it's meaning in a specific context.

 

[idontthinkright]

Just to chip in,In every illogical,impossible solution,will have a logical interior that is hidden within a question's process.Whether inter-affecting or related to the subject,or a piece of the question that isn't shown.Btw nice picture gara XD XD

 

[laserblue]

From the start there is clearly a confusion based on the use of the word logical for rational. All this about 1 rock + 1 rock = 2 rocks is rock logic. There are very defined boundaries. A sheep is or is not a sheep. It can't be sort of a sheep.
How about lateral thinking and WATER LOGIC?
If removal of tonsils is a tonsilectomy and removal of an appendix is an appendectomy, what do you call removal of a growth from your head?
There is also a view of logic in which it is generalized with a bayesian probability viewpoint by Professor Edwin Jaynes in PROBABILITY: THE LOGIC OF SCIENCE. In this view, deductive logic follows from probabiloity rules and involves statements with a probability of 1 while inductive logic involves the same rules but probabilities between 0 and 1.

 

[wuliheron]

Just to chip in,In every illogical,impossible solution,will have a logical interior that is hidden within a question's process.Whether inter-affecting or related to the subject,or a piece of the question that isn't shown.Btw nice picture gara XD XD

And the opposite as well if you look at it that way.

What distinguishes a question from an answer is ultimately attitude. Logic is built upon natural language, and natural language is built upon attitude. Thus attitude provides the single most important context for gaining insight into whether something is a question or an answer.

For example, if I say "That's Bad?" I might be sarchastic or sincere, and might also be using "bad" as a slang term for "good". Whatever the case might be, demonstrably the only reason the term "questions" has any meaning is because we attach meaning to it, we give it an emotional context. That is why my computer can never really ask sincere questions. The lights are on, but nobody is home.

 

[idontthinkright]

i agree with what wuli says,basically we govern the language due to our feelings or reactions.

 

[Gara]

It depends on what the definiton of "1" is. "1" could represent 5 things in one case to make 1+1=10.
"1 thing" is made up of millions of counterparts (i.e. atoms etc.) so by saying "1 thing", your are referring to millions of counterparts which make up this "one thing". Therefore, 1 may = billions .
But I don't understand how your aforementioned examples (quoted from Gara) could be logical by our concept of logic.

1+1 = 10, 10+1 = 11, 11+1 = 100 is binary. :)

as i already quoted heh :)

 

[Nicomachus]

blah blah blah. What are you all talking about? The statement 1=1 is axiomatic, in fact it is the law of identity, how can you say it cannot be determined using logic? Obviously 1=3 is completely illogical, it is axiomatically incorrect. I think you are maybe starting another thread about justifying logic but you cannot do that. Also, some of you are going on about this question using nominalism; no one likes nominalism because its pointless. Sure you can say "When I write 3 I mean this many hashes # and when I write 1 I mean this many hashes # so it is true when I write "1 many hashes = 3 many hashes," but its just jibber jabber. Also, someone mentioned computer programs that would pass variable statements such as "a=c" as if that were some paradox ... Obviously, there is nothing wrong with that, it is completely logical, actually. Oh well, I guess I don't see the method to the madness.
*Nico

 

[techwonder]

Let's resort to lambda calculus, shall we? That's where we start by defining what "true" is and what "false" is. Lambda calculus is the basis for all modern computer languages and is in fact logic put into (mathemtical) language.

1=3 is not just illogical it leads to absurdities. If taken at face value, how would you do calculations? Let's try: What comes after 4? Ohh, you just add 1. Alright, so I have 3+1=? 4 or 6?

The problem with these "illogical" statements (contradictions) is that you can prove anything if you allow true paradoxes and unfortunately if everything is true then everything is nonsense.

 

[Rasine]

i think of logic as being a box or a restraint on thinking. eveyone knows that phrase: think outside the box. you must realize that there is no box, then your mind will be free to all possibilities. our minds would fulfill their potionals becuase with this we will not automatically elimate the illogical sloutions and ideas, but our lives don't even make sense. how are we to say that logic is what can only exist if our very being is not?

 

[plover]

Wouldn't the question be resolved formally something like:

If 1 and 3 have their usual definitions as numbers and = has it's usual meaning of indicating numerical equality, then

1 = 3​

is a well-formed statement whose truth-value can be determined (i.e. it's false).

Non-well-formed statements (given the usual meanings for the symbols being used) would be things like:

• 1 =
• 3 5 + %

that have no definable meaning within the symbol system, so no truth value can be determined for them. (Note: these particular sequences could have meaning in some symbol system, but in the system known as 'arithmetic', as it is commonly defined, they do not.)

Does anyone know what entities formal logic actually applies the word 'logical' to? My impression is that the word actually refers to inferences, not to statements. Statements are merely well-formed or not.