Garry G wrote: ↑Mon Apr 15, 2019 12:58 am

Scott Mayers wrote: ↑Sun Apr 14, 2019 11:23 pm

The relation of the etymology of "contingent" is 'con-'(with) + 'tangent' (touch), and I believe the past logicians chose it in light of something that is 'touchable' is sometimes and untouchable at other times. So it fits with how you are using it colloquially in the same way. Something that doesn't "have" be be true is one that is either one exclusively but minimally something that has been touched (ie sensed) at least once AND at least untouched at least once. Otherwise they'd be essentially always true or always false.

Thank you for that. Both interesting and informative.

I'm still unclear of even your OP to be using the four values when what you are thinking is more likely:

"Tautology", rather than 'true'. While they are related, 'true' is an individual assignment of comparative fitness, but with the other terms of 'contingency' you use, those are not comparable. Tautology, contingency, and consistency, are comparisons of whole formulas and relate to the outcomes of all possible values. If you insist on 'contingently true', it is more appropriate as:

"Contingent" unqualified. There is no such particular non-contingent claim and so is unneeded. What is ALL true or ALL false for all values is what 'non-contingent'' means. Thus, IF you are meaning the value of all possibilities, whether true or false for particular values, A contingent 'truth' if you insist on it has to mean "Contingent AND True". This is because a non-contingent truth is just either all true or all false, concepts already exhaustively defined as either a 'tautology' (meaning 'always true'), or Inconsistent (always false).

I don't get the example distinction you gave in the examples for what is non-contingent. If you meant that given you goldfish can't speak any language, the statement is simply not true AT PRESENT but may be in some other place, you MAY mean "Contingent but false" rather than non-contingent. If something is not presently true but still may be, you are meaning to speak of possibilities. The classifications you have are confusing.

When using 'truth' values among other values, they should relate: x is 'true', x is 'not-true', x is 'true and not-true', x is 'neither true nor not-true'. If you are using 'degrees', these then use numbers that propose some percentage of something 'true in x versus not-true in x' and these can have multiple values.

So I need to ask you to tell me if you are opting to describe values of INDIVIDUALS or GROUPS. You seem to mix them together.

I need to determine your definitions and the common principle of collected values they share in kind. Try the genus-specie definitions to both the particular values you use AND to the collection. This may help clear some of this up.

Gary G wrote:
Scott Mayers wrote: ↑Sun Apr 14, 2019 11:23 pm

Depending on what your need to design some logic for color though requires more information. All you technically need is one of those wheels, assign the background as 000 in the additive (adding white light). Then you have an '8-bit' code for those colors. I'd need to know more to understand if what you want to use that for? How are you relating this to "material implication"?

the reference to basic colour theory in post 7 was an attempt to illuminate a point about how to interpret Boolean values correctly. It is an analogy to help explain why this system has three values that are true. I then followed up with an appeal to consistency. so the appeal to colour theory does not exist on its own.

This is how the analogy works: RGB primary colours are the complements i.e. 100, 010, 100. The minimum value 000 in colour theory is black and black denies the presence of light. Shine red, green and blue light on a wall and white light is produced. So the primary colours are property of white light. the absent of light i.e. the minimal value black, is their denial. Taking white as an analogy we look to interpret true = 11. the values 01 and 10 become primary value for true analogous to RGB primary colours in colour theory. So we require an interpretation of 10 and 10 that leaves both properties of truth while also remaining complements and denying the minimum value false. and that is how we get three values that are true and one value that is false.

This is a bad example for describing boolean variables without clarity on those definitions above. And note too that while Boolean algebra is extended to multivariables, it is NOT a multivariable algebra.

Gary G wrote:
Scott Mayers wrote: ↑Sun Apr 14, 2019 5:09 pm

I'm not sure what you meant about the '2' and your example. That happens to be my "(2)" above as relayed by Lemmon's text along with that (1), not Russell.

I was responding to:

Scott Mayers wrote: ↑Sun Apr 14, 2019 5:09 pm

(2) If given not-P, then you can conclude the conditional, if P then Q. [

-P ⊢ P → Q]

and I think the example:

Moe did not win the lottery then if Moe did win the lottery then he was never born
demonstrates why [

-P ⊢ P → Q] is a poor form of reasoning.

Okay, but I already gave such an example in that original post that is identical in form. The statement IS still 'valid'. It is just not 'sound'. The poverty of the meaning requires an extended logic. Propositional logic does not break into the propositions. Predicate calculus begins this in the first-order logic. These are not actually paradoxes. At least they are not real paradoxes OF THE SYSTEM. The "paradoxes" spoken of implication are only superficial about the soundness of the statements because we lack a means to assure the propositions are actually related. This has to be done outside the system as is the input premise values are assigned with respect to reality.

In fact, even your statement example can be true. "Moe did not win the lottery" is the given FACT going in. The conclusion is dependent upon it in the identical same way as the consequent of an implication is necessarily true if the antecedent is true. The consequent as a conditional only asserts that if, AFTER knowing it is not true that he won the lottery, we then try to assume he did, this would assure that we are not talking about the living Moe [thus is non-alive, unborn or dead]. The conclusion is a consequent of the given as a conditional and so the value of the conclusion is necessary to be true IF the given is true but may be false or true if the given was false.

What may be more clear might be to find a way to indicate the nature of Q to be a 'dummy variable' versus P.

It is similar to the "OR introduction" rule in Propositional Calculus. It says that Given P, then the statement, (P or Q) is true. The Q in this is a dummy variable that may or may not be true. But since we are given P, the statement, 'P or Q' is true by accident. This is not a statement about P and Q but about the RELATIONSHIP of the 'or' operations with respect to what is given.

If you want to (no one stops anyone), you CAN clarify this to avoid the problem by, say, italicizing Q, place brackets around it, or some other indicator. In computer science, this is often treated as a "don't care" value. AND, while it seems it serves no value, these dummy variables actually DO have functional value. For instance, if you are trying to make some component match the timing in parallel to another, you might add a 'dummy' variable (or constant in some places) that makes the timing of some quicker component 'buffer' to the second component's longer time.