# There exists only one opposite(from lack of a better word)

1. Aug 13, 2004

### Imparcticle

How do we know that there exists only one thing that is opposite to another thing?
For example, if you are composing an indirect proof, you would take the "then" statement and use its opposite to prove that the "if" statement is in fact true. But, what if there is a case where there are multiple statements that are opposite to one statement?

How do we know there isn't such a case? How do you prove there is only one opposite to something?

2. Aug 14, 2004

### wuliheron

According to the principle of identity, at least, if you are going to stick to the rules of formal logic.

3. Aug 14, 2004

### Imparcticle

Why do the formal rules of logic (are there informal rules?) only allow for one opposite? IF you believe this is true, how would you prove it?

4. Aug 14, 2004

### Crumbles

I have never come across a case where there are multiple statements that are opposite to one statement.

But the way I see it is you can only have one opposite because of the definition of the word opposite itself.

http://dictionary.reference.com/search?q=opposite

"Being the other of two complementary or mutually exclusive things"

Surely if you have an object A and you say an object B is opposite to A. But you also have an object C that is opposite to A, it would be understood that C is the same as B.

The only way I see of having two or more opposites to one thing is when you deal with more than one properties of that something. For instance a proton is the opposite of the anti-proton in terms of the type of matter but a proton's other opposite could also be the electron in terms of charge.

If you want the proton to have two opposites in terms of charge, it's not possible because anything opposite to +1 is -1. If anything else was opposite to +1, that would make it equal to -1

5. Aug 14, 2004

### Staff: Mentor

I think "opposite" is a bit vague. In formal logic, there are two terms, one of which may capture what you are looking for. Here are their definitions:
contradictory: Two statements are contradictory if they cannot both be true together, and cannot both be false together. An example is "this is red" and "this is not red".

contrary: Two statements are contrary if they cannot both be true together, but can both be false together. An example is "this is red", "this is blue", and "this is green".​
As you can see, contradictory statements divide the universe into two parts (A and not-A), so a given statement has but one contradictory. But a statement can have many contraries.

6. Aug 14, 2004

### plover

In formal logic, the opposite of (X) is (not X). On the other hand, the range of meaning that can be attached to the English word "opposite" is not restricted to this. Thus, there are situations which, as described in English, allow a concept to have several opposites. However, if (X) is a statement in English for which (A), (B), and (C) are plausible opposites, in most cases (not X) will be a necessary, but not sufficient, condition for (A), (B), or (C). (And other cases are similarly founded on the gap between standard usage and the definitions used by formal logic.)

(Note: This is more or less the same thing that Doc Al is saying. I was just taking "opposite" to always correspond to "contradictory"--as defined above--when used in the context of formal logic.)

Last edited: Aug 14, 2004
7. Aug 14, 2004

### tabloid

well first ask yourself how a 'normal' human being can ultimately 'see' his death;is that written in doctors books coz i wouldnt mind for a chek.

8. Aug 16, 2004

### Imparcticle

THANK YOU for that, Doc Al.
But is it provable? Can you give a formal proof proving that (A) is the opposite of (not A)?

9. Aug 16, 2004

### Staff: Mentor

And what would constitute a "proof" of that? Using what? Logic?

That the universe is divided into A and not-A is an axiom of standard logic. (There are others, I'm told.)

10. Aug 18, 2004

### Imparcticle

I see, I see. Definitions can't be proven....