John Page

Nice.
Ah, "naturally" as "implicitly"?
That word natural again. Do you mean material? Arguably everything that we can conceive of exists, we merely need to be clear about the form of its existence and how it maps onto other parts of reality.
- but there are two F's, either they represent different things or they are considered the same or there is a recursive (self-referential) expression. Maybe I'm misiunderstanding you.
I think one needs to ask why the above exceptions are required and their impact on what we assume to be the inviolable nature of "truth".
Yes, the Tarski meta-language problem offered a solution but introduced infinite regression.

Cheers, John

jpbrooks

That's not what I meant. That is, I didn't mean to suggest that people who are not rational are Dialethic(?). Dialetheism is not the only view that (more specifically) undermines its own ability to be discussed rationally. So, in stating what I did, I was not providing a definition of the terms that I was using.

John, (we share the same first name, and I feel like I'm addressing myself) the problem is that if Dialetheism is adopted and applied consistently, even if we don't know whether it's true, any "argument" that you attempt to use to "defend" Dialetheism can be used by anyone with an opposing view to "support" their own view.

Perhaps I'm misunderstanding your position, but you seem be addressing a matter that is external to that of logic (truth, rationality, etc.). But if that is the case, then your inquiry can have no consequences that affect truth from a logical standpoint. You can't have it both ways. Either your position has nothing to do with the logical aspect of truth, in which case the way we understand and apply logic and truth to our views remains unaffected. Or it does relate to the logical aspect of truth and faces the problems associated with skepticism about truth.

The model seems interesting and may have some merit. But how could one know (or why would it even matter whether one could know) that it is an accurate model, on the basis of that kind of skepticism?

I'll be back later.

John Page

I understand. Do you believe a dialethic (dialethetic?) disposition implies irrationality?

Regarding your second point, I think we need to ask why things need to be true or false and why they need to be internal or external to logic. I am interested in the phenomenal aspects of truth in addition to formulation of these into systems of logic.

On the third point, the accuracy of any model, IMO, should be measured against the "real thing". It appears that truth is internal to the mind, in which case we need to know what drives our conscious notion of truth.

Cheers, John

jpbrooks

No, and I would further make a distinction between the "irrational" and the "non-rational". I would characterize the "Dialehic" disposition as being "non-rational", i.e., concerned about matters outside of the "sphere" of Logic and reasoning, rather than "irrational" in the sense of lacking logical or factual consistency.

These seem to be questions about the Phenomenology(?) (and/or perhaps Psychology?) behind the process of reasoning, This is undoubtedly an important area of study (and one that I have yet to pursue), but is external to the study of the role of truth within the subject of Logic. A reductionistic approach that eliminates one area of inquiry into the "nature" and function of truth in favor of another may be necessary in the short run for the further development of that particular area of inquiry as an independent "discipline", but, in the long run, is not very helpful in obtaining a comprehensive view of the subject matter.

I agree that our recognition and apprehension of truth (as a personal value) is internal and that it is perhaps important to know what drives our conscious notion of truth. The study of the internal aspect of truth is certainly an important area of inquiry. But in the real world, the internal and external aspects of truth are intertwined; not separated into unrelated "realms". And this means that the process of inquiry itself is amenable to the basic "laws" of Logic regarding truth.

John Page

Hi John:

I think this is where we diverge. You say "But in the real world....", whereas I am defining everying as part of reality. (Or, putting it another way, the universe - everything - is real therefore "the real world" is synonymous with the concept "universe").

Perhaps if you could give me an idea of what you mean by the real world (and unreal world) and how truths can be internal and external I might understand how you reach the position that this enables the logical process of inquiry.

Cheers, John

tk

John Page:
Agreed, that's a bad choice of a word. Maybe "necessarily" is a better word. Thus, I hold that truth is not necessarily contradictory.

Let me try to make myself clearer. Suppose we have

F(P) = ~P(P)
G = F(F)

The right hand side of the definition of F (which is "~P(P)") does not contain F itself, and neither does the definition of G (which is "F(F)") contain G itself. Although G contains F in its definition, however F has already been defined even before we tried to define G, so there's no recursion here.

(This is different from saying e.g. f(x) = f(x - 1) + x, where the right hand side of the definition of f also contains f.)

Even though the definition of G contains no recursion, yet if we try to evaluate G, we still get a dialethia. Clearly the issue is deeper than one of literal self-reference. One may say that it's because the definition of F contains terms that can potentially refer to F itself.

I guess the answer is partly suggested above: if we allow things to refer to themselves either directly or indirectly, then we can construct things from thin air and prove contradictions from them.

When Russell's paradox was discovered, the responses all took the form of arranging concepts in some kind of hierarchy or stratification: concepts are put in layers starting from some layer 0, and concepts in layer i are only allowed to refer to concepts in layers 0 to i - 1. (What about recursive functions? It can be argued that, even when recursive functions are defined, the domain of the function should be stratified in some way, so that f(x) only depends on f(t) for t at a `lower layer' than x.)

I think the restriction in first-order predicate logic, that arguments to predicates may not themselves involve predicates, can be thought of as a form of stratification. (Unfortunately, this restriction makes it difficult, if not impossible, to express things like "person X said P is true", for some general proposition P.)

This brings me to...
Indeed, I have to (grudgingly) admit that anything we can think of actually "exists" in a sense. As for the form of existence, the strategy of stratification may provide an answer.

jpbrooks:
But what qualifies as "irrational", what as "non-rational"? I mean, any charlatan philosopher can easily claim that his philosophy lies `outside' the realm of logic, and thus shield his philosophy from critical review.

jpbrooks

True. Any charlatan could attempt to shield his philosophy from critical review in that manner, but I don't believe that such attempts would be successful. Philosophies are based on assumptions. And as long as those assumptions can be expressed as statements in a language that is intersubjectively meaningful, they are amenable to logic.

In contrasting the terms "nonrational" (I checked the dictionary entry, and no hyphen is needed) and "irrational", I simply meant to show that there is a difference between beliefs, claims, etc., that are based on (or closely related to[?]) aspects of consciousness (such as "feelings", for example), and beliefs, claims, etc., that are logically or factually inconsistent (such as the claim that physical objects with attributes that are truly, and not merely apparently, contradictory can exist in the real world) no matter what they are based on. And as I stated in my last post, I would characterize the "Dialethic" disposition as "nonrational" rather than "irrational". I don't find much wrong with the temperament of Dialetheism. I just can't accept the view as rational.

John Page

jpb:

But what is rationality? Example, some among us will consider the statement "No pigs exist" as perfectly rational and logical and the opposite of "Pigs exist".

I ask you, how can "no pigs" "exist"? If there aren't any then how can they exist? Here are other formulations to further illustrate the point: "No pigs are present", "God does not exist". In this way I might argue that these statements are dialethic.

So if the dialethic view is non-rational and propositional logic is rational, is the statement "No pigs are present" rational or not, and by what rule to you propose that I tell?

Cheers, John

jpbrooks

Sorry about the delay. Juggling commitments is keeping me busy.

I gave this matter some additional thought after I posted my first comment about the rationality of Dialetheism. I suppose that the general (and correct) meaning of rationality would be the quality or state of being "reasonable" (rational) which, as this article by Vuletic in the Secweb library (for example) illustrates, involves being able to provide (good) reasons for the position in question. I was using "rational" in the more narrow sense of not being logically or factually inconsistent. It is more narrow because a position that is inconsistent certainly has few "good reasons" for taking it (unless, of course, you view this matter from the perspective of Dialetheism).

And I would agree with them.

I think I understand what you're asking. (If you suspect I don't, feel free t correct me.) There is no actual inconsistency involved in your example because you are referring to the (non)/existence of two different things.There is a distinction between the state of being in which no pigs are in existence and the statement or proposition "no pigs exist" that (provisionally?) describes that state of being. The proposition about the nonexistent pigs exists.

Similarly, there is no (inconsistency) problem with these formulations.

It is "rational", as I stated before (according to my now admittedly too narrow definition of rational), because a statement is not irrational if it is not inconsistent. However, after reading Vuletic's article, I suppose it's better to use the term "consistent" instead of "rational" in the context of this discussion to eliminate confusion. So I stand corrected on that point.

John Page

jp:

Thanks for taking the time and trouble to respond.

It seems that we have a "self-fulfilling prophesy" here since you're judging dialetheism against pre-existing standards of logic that you use to test for rationality.
Let me try, with two more examples to show you why I think dialetheism can be considered reasonable.

First, and further to the "no pigs exist" example (where my real issue is with the concept that "no pigs" might even have a material corollary) let me introduce the "minus three little pigs". Have you ever seen minus three of anything? Of course, we can understand each other through the concept of math, and we can notice that soemthing is missing when our three little pigs are no longer in view, but taken literally "minus three little pigs" is nonsense (and therefore has no truth value). IMO dialetheism admits that this statement can be both true and false - we can consider it either way depending what we believe is a reasonable or rational interpretation of the statement. Conclusion: It is the observer that makes the "truth" judgement.

Second, how does the observer reach the truth judgement? Surely they must consider both the options and these may include "true" through "false" with "true and false" as a median value (which could also be called "neither true nor false", I guess). Thus, prior to making a "truth" judgement the observer's mind may set up opposite positions. Now I make a leap of intuition by suggesting that these positions are set up contemporaneously in the mind so they may be compared. When the "truth" judgement is made, this selection will be done from the available positions (*note below) the observers (subjective) frame of reference and the result, of course, may be either true or false.

Forgive me if the above is not totally clear, its the first time I've tried to write down my (subjective ) perception of what is actually going on in our minds. I think the dialetheic(?) approach encompasses the processes that are necessary for propositional logic to exist. My own firebrand is multi-valued logic where absolutely true and absolutely false are meaningless points, of course, this condemns me to being only partially correct - an inevitable result of being constrained by my own grey matter!

Comments welcome! Cheers, John

* note "Available Positions" can be considered similar to the set (S) in the Axiom of Choice where we are free to choose our truth using the function f(S). (Axiom of Choice. Let C be a collection of nonempty sets. Then we can choose a member from each set in that collection. In other words, there exists a function f defined on C with the property that, for each set S in the collection, f(S) is a member of S.)