April 9, 2009

It's so sought after, so can we say what it *is*??confused1 I define something's spirit by its true nature and my soul to be my true self so it stands to reason that I ought to have a working definition of truth.

Truth = fact = actuality =...= truth

This equation encapsulates the notion that if you chase the definitions offered for truth by a dictionary, you will eventually end up with truth again, thus not having made much progress defining truth.

I call such words atomic. ("Set" is another example.)

There is a lot I could say about truth such as it being a property that might be possessed/held/satisfied by an utterance in some language. A property of utterances. That means some utterances have this property and some utterances do not have this property. If an utterance has the property then we'd say that utterance is true; otherwise, we'd say the utterance is not true.

Normally, there would be axiomatic utterances to start with which are assumed to have this property, the property of being true. Some rules for inference are assumed such as modus ponens. These rules form a syntactic calculus from which more and more utterances will be said to have the property of being true. That brings us to one important fact about the property known as truth: If the axiomatic utterances are true then all utterances which are consequences (with respect to the rule(s) of inference) of those axiomatic utterances are also true. (This assumes the soundness of the rule(s) of inference.)

The above pretty much describes just the "tautologically true." Another important phenomena is *conditional* truth. Conditional truth is still a property that utterances might or might not possess but, as the name suggests, it is not simply true or not true for all time. A real simple example is the utterance, "the successor of X is 1." That utterance is true if, and only if, X is 0. What this means is that if the utterance is non-specific or has any ambiguity in it, it has the potential to be, at most, conditionally true.

Thus, utterances can be divided into three overlapping categories: the utterances which are true, the utterances which are conditionally true, and the utterances which are neither true nor conditionally true.

There is a simpler definition of truth that occurred to me recently which is the actual reason for this thread. Truth is that which can be *seen*. Now 'can' and 'see' are a bit unclear.. Can does not mean a human can but that something can. Seen is perhaps misleading because I'm not referring to eyesight; *apprehend* is closer to what I mean. To rephrase, the definition of truth that occurred to me is this: *truth is that which can be apprehended* (By something, including us humans).

How does this connect up with the utterances property? Well, we can say that an utterance with the property of being true can be apprehended BUT not all things which can be apprehended are utterances, meaning that the apprehended definition of truth is more inclusive in case that matters.

"it is easy to grow crazy"

September 19, 2009

"at1with0" wrote:A circle is a set of points.How do I observe any set?

Sets don't actually exist, do they?

Geometry exists. A circle can be defined with geometry.

The set concept leads to logical difficulties. :think:

http://en.wikipedia.org/wiki/S.....thematics)

...the notion of a "set" is taken as an undefined primitive...

Set theory axioms are inadequate for metaphysics.

April 9, 2009

http://en.wikipedia.org/wiki/Mathematic ... hypothesis

Our external physical reality is a mathematical structure.

http://en.wikipedia.org/wiki/Structure_ ... l_logic%29

The domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier (especially in universal algebra), or its universe (especially in model theory).

2+2=...?

"it is easy to grow crazy"

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