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Most statement that are not mathematical equations have a truth value depending on time and often even more context. Mathematical logic should be generalized to cater for this.

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Gebhard Greiter, 2011

The most simple example of a paradoxical statement seems to be

If we assume

So, what is wrong here?

The problem here lies in what we think a statement is: Under a formal point of view, a state-

ment may be

for example cannot be assigned a truth value (

which person Alice exactly we are speaking. So, at least now, it is an

We see: Depending on the context

value v(

time, but may also contain definitions of the objects the statement refers to.

Formal logic usually ignores this fact, and so mathematicians see

such that v(

Now we prove that the statement

If not, a context

v(

In other words: One element

This equation however is satisfied neither by

1

What we have learned is: The fact that paradoxical statements exist is telling us that to have

only two truth values (

We also see that mathematical logic should be generalized to

no longer ignore the fact that mapping statements to boolean values is not enough:

Reality is mapping statements

The fact that mathematical logic as you find it in text books is ignoring context (especially

time) and knows only two boolean values, may be a consequence of the fact that at least

mathematical statements can only be

time we look at them:

Mathematical laws are valid in every context.

Other statements however do not have this nice feature - maybe not even statements that

describe physical laws: Researchers believing in String Theory are no longer sure that our

universe is the only one, and they tell us that, should other universes exist, the physical laws

valid there may differ from the physical laws valid in our universe.

Author's homepage: http://greiterweb.de/spw/

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