In order to express truth-or-falsity of the dynamical process, we have to make a continuous true-valued function, then in which there are a hybrid true-valued function well-formed by a state-dual T(P)=(a,b), where the a is partial-truth and the b is partial-falsity. Do you accept this definition? If not ,why?
If you have a function with continuous truthvalues, how would that differ from assignment of probabilities? For example, a proposition that has Pr 0.8 of being True also has Pr 0.2 of being False. Is anything gained by saying that any point on the real number line [0, 1] simultaneously represents both partial-truth and partial-falsity, which isn’t really needed for a continuous function? I think the notion of “partial” needs to be clarified and that seems to be a matter of how you characterize entailment relations. Is a partially-true proposition one that entails both a complete truth and a complete falsehood?
I‘m not entirely certain about how to understand the motivation behind your definition. So, I focus on the the notion of ‘partial truth’. This notion has been of some interest in the context of Truthmaker Semantics. Roughly speaking, a proposition P is true iff there exists a “truthmaker” T (a state of the world or a fact) such that T makes P true. In this context, the notion of partial truth can be spelled out as a truthmaker T that makes part of the proposition true. So, the proposition “It is rainy and windy.” is partially true if it is in fact rainy, but not wholly true (in the absence of wind), since it is a conjunction. The proposition “It is rainy or windy.” is made partially and wholly true by the fact that it is rainy, by virtue of the disjunction.
Maybe this goes in the direction you are interested in. If so, you may want to look into the work of Kit Fine (who is at the moment the driving force behind the development of Truthmaker Semantics, although many work on its development and on applications in philosophy and linguistics). In particular a paper that is available at Academia.edu called: A Theory of Partial Truth. I hope this helps.
to Karl Pfeifer,
Such as an example:
Propostion P: Tiger eat wolf generally, and wolf eat tiger occasionally.
The true-valued function T(P)=1, i.e. the proposition is truth.
Proposition Q: Tiger eat wolf.
The true-valued function T(Q)=(0.99,0.01), its means that the proposition is partial truth, true-valued function is 0.99, and is partial falsity, true-valued function is 0.01.
Because of contradiction in dynamical process, we have to take the state-dual to represent truth-or-falsity of this case.
This state-dual indeed entail a complete truth under some conditions and complete falsity under other conditions, i.e. T(Q)=(1,0) or T(Q)=(0,1).
Thanks for Kari Pfeifer and Sven Beecken.
Yaozhi Jiang I don’t understand your rationale and your examples are ambiguous.
RE: Proposition P: Tiger eat wolf generally, and wolf eat tiger occasionally.
RE: Proposition Q: Tiger eat wolf.
Your example is ungrammatical in that it doesn’t use articles, plural forms, or adjective pronouns (a kind of English quantifier).
What does "Tiger eat wolf" actually mean? Is it , for example, about a particular tiger (that tiger), some tiger or other, tigers in general, or about the species* of tiger. (Likewise for "wolf".)
The 1st conjunct of Proposition P is “tiger eat wolf generally”. This is somewhat better, since “generally” functions as a quantifier. But it is still not idiomatic English, so let’s rewrite it “tigers generally eat wolves”. This presumably means something weaker than (i) “all tigers eat wolves”, maybe (ii) “tigers will usually ("more often than not") eat wolves”. (i) would be completely-false if there exists at least one tiger that doesn’t eat wolves, whereas (ii) can be completely-true even if there are numerous tigers that don’t eat wolves.
The 2nd conjunct of your Proposition P is “wolf eat tiger occasionally”. This again is not idiomatic English, so let’s rewrite it as “wolves eat tigers occasionally”. Why should that be regarded as partially-true or partially-false at all? “Wolves eat tigers occasionally” means “sometimes wolves eat tigers” and that statement is not false on those occasions on which wolves do not eat tigers unless it is also the case that wolves never eat tigers.
So far I don't see an interesting role for your notion of partial truth or the function associated with it.
Also, you need to explain what "contradiction in dynamical process" means.
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* A statement about a species can be true even if it's seldom true of any individual member of the species. "Tigers eat wolves" in that context would just mean that tigers are the sort of animal that would eat a wolf if the opportunity arose, other things being equal.
to Karl Pfeifer,
It seems that both tiger and wolf maybe in plural form. In my original propositions both tiger and wolf are nouns for a category. The oringinal propositions means that tiger can eat wolf is not absolute, and under special conditions sometimes wolf can eat tiger. Of cause these propositions are simple examples, my paper titilled: atomic proposition and 1-order predicate function for dialectical logic will be preprint in researchgate as soon as my possible, about few days later, and then it will be published after acception, in the paper my opinions is partial-truth and partial-falsity are essential state by dialectical logic.
For this paper, critical comments are welcome.
Thanks for Karl Pfeifer.
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