# Re: Logics

```On 9/27/2011 5:28 AM, Jason Resch wrote:
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```

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On Tue, Sep 27, 2011 at 6:49 AM, Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:
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On 9/26/2011 7:56 PM, Jason Resch wrote:
```
```

On Mon, Sep 26, 2011 at 12:14 PM, Stephen P. King <stephe...@charter.net
<mailto:stephe...@charter.net>> wrote:

On 9/26/2011 11:52 AM, Jason Resch wrote:
```
```

On Mon, Sep 26, 2011 at 9:44 AM, Stephen P. King <stephe...@charter.net
<mailto:stephe...@charter.net>> wrote:

snip
Jason,

I really would like to understand how it is that the truth
valuation
of a proposition is not dependent on our knowledge of it can be
used to
affirm the meaning of the referent of that proposition independent
of us?

That sentence was hard to parse!  If I understand it correctly, you are
how a truth, independent of our knowledge, can confer meaning to
something
without us?
```
```        [SPK]
Essentially, yes.

```
```
Things unknown to anyone can have consequences which are eventually do
make a
difference to beings which are aware of the difference.  A comet
colliding
with the Earth and hitting a pond of unicellular organisms may have
drastically altered the course of evolution on our planet.  That such a
comet
impact ocurred is a fact which is either true or false, despite it being
independent of anyone's knowledge of it.  Yet it has perceptable
results.

```
```        [SPK]
The web of causes and effects is an aspect of the material
universe. I am
taking that concept into consideration.

```
```        Correspondingly, the existence of some mathematical truth (even if not
comprehended by anyone) can have effects for observers, in fact, it
might
explain both the observers themselves and their experiences.
```
```        [SPK]
Slow down! "existence of some mathematical truth"??? Do you mean
the truth
value of some existing mathematical statement? That is what I mean in my
question by the phrase "truth valuation of a proposition". Is a truth
value
something that exists or does not exist?

I am not sure what you mean by "exists" in this case so let me say this,
the state
of being true, or the state of being false, for the proposition in
question, was
settled before a human made a determination regarding that proposition.
```
```
[SPK]
Is the "state of being true" a physical state, like the "state of
having 10
units of momentum"?

```
If the object under consideration is a physical object, you might be able to say that. If the object under consideration is 17, I would say no.
```
Is there a "truth detector"?

```
There can be truth detectors, in some sense we may be truth detectors, but us discovery of a truth is not what makes it true.
```
Are you sure that "state" and "true" are words that go together?

```
I am at a loss for an english word that conveys the status of true or false. We have the word parity for the status of even or odd, for example, but I could not think of such a word that conveys the same for true or false, which is why I used "the state of being true or false".
```
AFAIK, true (or false) are values, like numbers. In fact logics can have
truth
values that range over any set of numbers. This puts truth valuations in
the same
category as numbers. No?

```
True and false can be represented by two different numbers, but I am not sure that makes them values in the same sense of numbers.
```

```
```
```
```            How does the sentence "17 is prime is a true statement" confer
implicit
meaning to its referent?

```
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or
```        non-existence, comprehension or non-comprehension makes no difference
to 17,
only what you could say we humans have discovered about 17.

```
```        [SPK]
Is the symbol 17 the same extant as the abstract number it refers
to?

No, as I mentioned to Brent in a post the other day, we ought not confuse
the label
for the thing.  Nor should we confuse our idea of a thing for the thing
itself.
```
```    [SPK]
OK, does not this imply that there are (at least) two separate
categories:
Labels and Things? What relation might exist between these categories?

```
Labels are a human invention to support communication of ideas, which you might say is yet another category of things.
```
```
The relation ship might be as follows: if I tell you to multiply 1200 x 1800, you could arrange 1800 rows of 1200 beans and count them all, or you could follow some simple rules of transformation applied to the labels '1200' and '1800' and have a shortcut to the answer, without having to do all that counting.
```

```
```        Do you believe that symbols and what they represent are one and the
same thing???

No, we can apply some simple rules to the symbols in certain way to learn
things
```
```    [SPK]
What relation might exist between the "rules" of symbols and the
"rules" of things?

I think I covered this above.

```
```        How does not the fact that many symbols can represent one and the same
extant
disprove this hypothesis? Is the word "tree" have a brownish trunk and
greenish
foliage?  What about the case where sets of symbols that have more than
one
possible referent? Consider the word FORD. Does it have wheels and a
motor?
What is the height of the water that one displaces when we might walk
across
it? There is a categorical difference between an object and its
representations
and the fact that one subobject of those categories exists is not proof
that a
subobject in another category has a given truth value. BTW, truth
values are
not confined to {True, False}.

For well-defined propositions regarding the numbers I think the values are
confined
to true or false.

Jason

```
--
```    [SPK]
Not in general, unless one is only going to allow only Boolean logics
to exist.
There have been proven to exist logics that have truth values that range
over any
set of numbers, not just {0,1}. Recall the requirement for a mathematical
structure
to exist: Self-consistency.

```
Okay, there may be other subjects, besides number theory and arithmetical truth where other forms of logic are more appropriate. For unambiguous propositions about numbers, do you agree with the law of the excluded middle?
```
Jason
```
```
```
I think this an assumption or another axiom. Consider the conjecture that every even number can be written as the sum of two primes. Suppose there is no proof of this from Peano's axioms, but we can't know that there is no proof; only that we can't find one. Intuitively we think the conjecture must be true or false, but this is based on the idea that if we tested all the evens we'd find it either true or false of each one. Yet infinite testing is impossible. So if the conjecture is true but unprovable, then it's undecidable.
```
Brent

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