Let's first define what we mean by "logic" [1].
  

Merriam Webster Wrote:logic
play
noun  log·ic \ˈlä-jik\
Popularity: Top 10% of words
Simple Definition of logic

• [b]A:[/b] a proper or reasonable way of thinking about or understanding something
  
  
• [b]B:[/b] a particular way of thinking about something
  
  
• [b]C:[/b] the science that studies the formal processes used in thinking and reasoning
  

if we have a look at 1C, we can see that logic can be said to be a formal set of axioms by which we do our thinking and reasoning. The name we give to the logic of this universe is conveniently "logic". 

Let's look at "logical" [2].

Merriam Webster Wrote:logical
play
adjective  log·i·cal \ˈlä-ji-kəl\
Popularity: Top 40% of words
Simple Definition of logical

• [b]A:[/b] agreeing with the rules of logic : sensible or reasonable
  
  
• [b]B:[/b] of or relating to the formal processes used in thinking and reasoning
  

Now, let's hypothesize about an alternate universe. This universe would have its own logic (1C - ...the formal processes used in thinking and reasoning.) by which beings would reason within this universe, and for the sake of convenience, let's call it "goblygoop". Let's also give goblygoop a new entry: according to goblygoop, 2 + 2 = 5 is actually true. 

Now, the question is, "is goblygoop logical?". Initially it seems like it isn't, because according to 2A goblygoop needs to agree to the rules of 'logic' (our logic in this universe), which it doesn't. But obviously, that answer is relative to this universe. We can see that goblygoop does in fact conform with 2B, since goblygoop is the way in which thinking and reasoning would work in that universe. Therefore, goblygoop is a form of logic (1C) and it can be said to be logical (2B).




The list of "inb4's"

"But 2 + 2 = 5 is not true! Don't you know that it's 4?" - yes, according to our conditioned mind in this universe, that is the answer. But it won't be the same answer in goblygoop. 

"But 2 + 2 will always equal 4 no matter what." - no, that is a bare assertion. 2 + 2 didn't have to equal 4 in this universe. The mere roll of the dice made it so.

"But you're using our logic to prove their logic!" - no, my aim isn't to prove any of their axioms. I'm simply saying that an arbitrary set of axioms can by all accounts be considered "logical", even if that logic won't make sense here. It's all relative to the universe you're in.


EDIT: for the purposes of polling you guys, give kudos if you agree, or comment if you disagree.

I agree initially, but I haven't thought deep enough about this specific topic. It looks like it makes sense. If I ever care enough, I will ponder it more.

Quote:"But 2 + 2 will always equal 4 no matter what." - no, that is a bare assertion. 2 + 2 didn't have to equal 4 in this universe. The mere roll of the dice made it so.

Ok, this one I'm very iffy about.

(November 5, 2016 at 1:48 am)Irrational Wrote:

Quote:"But 2 + 2 will always equal 4 no matter what." - no, that is a bare assertion. 2 + 2 didn't have to equal 4 in this universe. The mere roll of the dice made it so.

Ok, this one I'm very iffy about.

You are iffy because it's a dumb idea.  That's because 2+2=4 isn't a rule or a set property-- it's simply a label.  If there were a universe where math worked differently, you'd just have different labels for whatever THAT reality was.  In any universe where there are 2 and 2, and the capacity to add, it will always be 4-- whatever you choose to call it. And if 2 + 2 = magic unicorn, then magic unicorn is just another representation of "4."

(November 5, 2016 at 2:38 am)bennyboy Wrote:

(November 5, 2016 at 1:48 am)Irrational Wrote: Ok, this one I'm very iffy about.

You are iffy because it's a dumb idea.  That's because 2+2=4 isn't a rule or a set property-- it's simply a label.  If there were a universe where math worked differently, you'd just have different labels for whatever THAT reality was.  In any universe where there are 2 and 2, and the capacity to add, it will always be 4-- whatever you choose to call it. And if 2 + 2 = magic unicorn, then magic unicorn is just another representation of "4."

But goblygoop giving them 5 is okay, or not?

(November 5, 2016 at 3:37 am)FallentoReason Wrote:

(November 5, 2016 at 2:38 am)bennyboy Wrote: You are iffy because it's a dumb idea.  That's because 2+2=4 isn't a rule or a set property-- it's simply a label.  If there were a universe where math worked differently, you'd just have different labels for whatever THAT reality was.  In any universe where there are 2 and 2, and the capacity to add, it will always be 4-- whatever you choose to call it.  And if 2 + 2 = magic unicorn, then magic unicorn is just another representation of "4."

But goblygoop giving them 5 is okay, or not?

That symbol '5' would still represent the concept 4, no?

(November 5, 2016 at 3:39 am)Irrational Wrote:

(November 5, 2016 at 3:37 am)FallentoReason Wrote: But goblygoop giving them 5 is okay, or not?

That symbol '5' would still represent the concept 4, no?

No, because to them that isn't logical, remember?

(November 5, 2016 at 3:40 am)FallentoReason Wrote:

(November 5, 2016 at 3:39 am)Irrational Wrote: That symbol '5' would still represent the concept 4, no?

No, because to them that isn't logical, remember?

I'm still not sure how you have arrived at that truth. Logically speaking (i.e. using the logic that we hold dear to), we can rule out the logical possibility of concept(2) + concept(2) = concept(5). As such, even if it was somehow true that logic is wrong in this case, it would be true despite our logic. But if it is true despite our logic, then I'm not sure how we can ever know it's true.

(November 5, 2016 at 2:38 am)bennyboy Wrote:

(November 5, 2016 at 1:48 am)Irrational Wrote: Ok, this one I'm very iffy about.

You are iffy because it's a dumb idea.  That's because 2+2=4 isn't a rule or a set property-- it's simply a label.  If there were a universe where math worked differently, you'd just have different labels for whatever THAT reality was.  In any universe where there are 2 and 2, and the capacity to add, it will always be 4-- whatever you choose to call it. And if 2 + 2 = magic unicorn, then magic unicorn is just another representation of "4."

l agree, 4 is a label for whatever is the sum of 2 and 2.
Maybe one should rephrase the question like this: could there be a universe in which intelligent beings cannot consistently set up the peano axioms?

A physics question as the next step: could there be a universe in which intelligent beings construct the natural numbers via something like the peano axioms, but those cannot be mapped to units of stuff in the world. We can assign the natural number 2 to a configuration of matter which is somehow grouped into two units (e.g two atoms, two balls), and if we take another of this grouping and employ our previous counting prescription for lumps of matter based on the peano axioms, will we get 2+2?

(November 5, 2016 at 3:57 am)Irrational Wrote:

(November 5, 2016 at 3:40 am)FallentoReason Wrote: No, because to them that isn't logical, remember?

I'm still not sure how you have arrived at that truth. Logically speaking (i.e. using the logic that we hold dear to), we can rule out the logical possibility of concept(2) + concept(2) = concept(5). As such, even if it was somehow true that logic is wrong in this case, it would be true despite our logic. But if it is true despite our logic, then I'm not sure how we can ever know it's true.

We can't arrive at that truth using our logic, because our logic only works in this universe. But in a universe governed by goblygoop, 2 + 2 does equal 5. They could ask the same questions about our answer being 4, or not?