# Re: Is Truth Mysterious?

*From*: herbzet <herbzet@xxxxxxxxx>*Date*: Tue, 13 Feb 2007 19:32:13 -0500

David Marcus wrote:

herbzet wrote:

I actually tend to agree with what you've been saying in this

thread, but I don't like to think about the Liar too much

because it just makes me want to hide under the covers and

weep quietly.

Did you read

http://www.davidmarcus.com/SemanticParadoxesAsEquations.pdf

?

Yeah, it seems consonant with what LauLuna is saying. If the liar

has no solution, i.e. cannot be consistently assigned a truth value,

then it would seem to be pseudo-proposition, a non-proposition,

however much it is a grammatically well-formed sentence.

I think "This sentence is true" is also a pseudo-proposition,

being totally void of meaning.

It seems there are a lot of grammatically well-formed sentences

that are bearers of neither meaning nor truth-value:

"A negative square root of Tuesday blushes isomorphically."

Pseudo-propositions have no more meaning than a mirage in

the desert has water. They're an illusion.

===============================================

For a different resolution:

"We now consider the equation

x^2 + 1 = 0.

Transposing, we have

x^2 = -1

and dividing both sides by x gives

x = -1/x.

We can see that this (like the analogious statement in logic)

is self-referential: the root-value of x that we seek must be

put back into the expression from which we seek it.

Mere inspection shows us that x must be a form of unity, or the

equation would not balance numerically. We have assumed only

two forms of unity, +1 and -1, so we may now try them each in

turn. Set x = +1. This gives

+1 = -1/+1 = -1

which is clearly paradoxical. So set x = -1. This time we have

-1 = -1/-1 = +1

and it is equally paradoxical.

Of course, as everybody knows, the paradox in this case is

resolved by introducing a fourth class of number, called

_imaginary_, so we can say the roots of the equation above

are +i and -i, where i is a new kind of unity that consists

of a square root of minus one.

What we do in Chapter 11 is extend the concept to Boolean

algebras, which means that a valid argument may contain

not just three classses of statement, but four: true, false,

meaningless, and imaginary."

"Laws of Form" by G. Spencer Brown, preface to the first

American edition [1972].

In Chapter 11 he goes on to consider Boolean expressions

"of degree < 1" which may be considered as infinitely

extended expressions. Some of those expression can be consistently

assigned the values "true" or "false", others must be

considered to have imaginary roots. This does not prevent

us from manipulating and equating these sorts of expressions.

I'm going to go hide under the covers for a while now.

--

hz

.

**Follow-Ups**:**Re: Is Truth Mysterious?***From:*David Marcus

**References**:**Is Truth Mysterious?***From:*LauLuna

**Re: Is Truth Mysterious?***From:*herbzet

**Re: Is Truth Mysterious?***From:*LauLuna

**Re: Is Truth Mysterious?***From:*herbzet

**Re: Is Truth Mysterious?***From:*David Marcus

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