I completely understand the desire to prevent irrelevant derailments on the thread, and I can see how diving into my epistemology could do just that. — Bob Ross
My concern was less with derailment, but not giving your theory its proper due when you're constantly trying to compare it to the d/a distinction. I've had time to build up the d/a distinction, then we've drilled into it. You have not been given the time to build your theory up, but are building it while comparing. That makes it very difficult for me to evaluate your theory fairly, while also trying to explain mine. In reading your reply, I see my suspicions were correct. Your definition of PoN was different from my understanding of it, and that's only because you haven't had time to let your own epistemology be explored and carefully constructed like I've had time to do here.
I do not mind at all exploring your epistemology here! Next post, feel free to get the last responses to the points I'll make here. I will not respond to them, but give you time to post your theory. You can use this spot as a draft if you would like before making your own post. Once I understand your theory, and get to ask my questions about it without the d/a comparison, we might come back to this later. You have had patience and curiosity with my proposal, the least I can do is return that favor. If this sounds like something you would like, I'll post my final points on the d/a distinction (for now!).
To keep it brief, my point is that my use of PoN is not meant as a logical construct like those, and its precise definition holds no immediate favoritism on the battle between paraconsistent vs consistent logical languages. I am defining PoN in the form of predicate-logic:
"a predicate cannot contradict its subject concept" — Bob Ross
Ah, I completely misunderstood this. I don't think this is called the principle of negation as often understood, but simply a consequence of language construction. First, lets break down what a predicate and subject are Feel free of course to amend my understanding of these definitions to fit your intention!
Subject - the "thing" being addressed in the sentence
Predicate - some type of assertion attributed to the subject in the sentence. An attribute, action, etc.
First, we can clearly see this is not more fundamental than discrete experience. This is a linguistic construct, whereas discrete experience requires no language, and is the foundation for language. One must be able to discretely experience to define a subject, and within my theory, you are able to define an essential or non-essential attribute of said subject. This is essentially a predicate; a further breakdown of the discrete experience of a subject into more discrete component parts. The "thing" is currently running. The "thing" is red. But I don't have to note that its running or red. The "thing" can exist as simply the discrete experience itself, unbroken and without any attributes but itself. Predicates are not required for subjects to exist.
Now if we are to note that properties are sub-discrete experiences of a subject, then by consequence we've constructed a system of distinctive logic that entails that a predicate is part of a subject. Thus we could propose that a predicate cannot contradict a subject, as that would mean we created attributes of a discrete experience that cannot exist on that discrete experience (the subject). But this does not predate the ability to discretely experience, it is built up from it. As such, "The predicate cannot contradict the subject" is not needed as a fundamental. It is a derived logic.
As for it being impossible that a predicate cannot contradict a subject, lets go further. What is the nature of a deduction? That the conclusion follows the premises. This also means that the conclusion does not contradict the premises. That the predicates do not contradict the subject. An induction is a conclusion that does not necessarily follow from the premises. This also means one possible type of induction is a conclusion which does negate the premises! I believe Dan is running right now. If so, it is distinctively implicit that Dan may in fact not be running right now. I look at Dan, and applicably determine he is not running. So here I have an induction who's resolved conclusion is that the predicate counters the subject. This was something I distinctively knew and held, despite reality showing otherwise. How does your epistemology handle the fact that inductions also implicate a predicate that contradicts the subject?
Let go even further. I applicably conclude Dan is running. But it turns out I made a mistake. It turns out this was Dan's twin that I was not aware existed. His name is Din, and he was the one running. Dan was also walking nearby with his back to us, and he turned around to let us know that was his brother when we yelled at "Dan" (who was Din) to turn around. Yet prior to Dan turning around, I distinctively and applicably knew that "Din" was "Dan" and that he was running. Barring the d/a distinction, was I not holding knowledge of a subject that had a contradictory predicate? Because the actual Dan was walking. In short, a Gettier type problem. How does your epistemology handle this?
The d/a distinction does not require the principle of subject non-negation (PSNN?) This is because I can distinctively know inductions, which implicitly allow me to distinctively hold knowledge of a sentence that could in application, have a predicate that contradicts a subject. Now, we can state that we distinctively know through deductions. This is true. But why should we hold to deductions over inductions? As I've noted, there is a hierarchy. But why is there a hierarchy? It is not because there is some necessary logical construct. It is because this logical construct gives us the best chance of survival, and actually understanding the world in a way where we can control or predict its outcomes accurately. Again, I do not see the PSNN as a fundamental. A nicely derived logic, but necessary for my epistemology.
Thinking further, someone could most certainly construct a distinctive knowledge that does not follow the PSNN. The construction of an all powerful God is one. All three omni's make this God. Despite a person being pointed out how that would be a contradiction, the person simply adds another property to God, "God can do all things, including holding predicates which are contradictory to its subject." Are we to say they do not distinctively know this? No, they distinctively know this, despite the predicate contradicting the subject. We can construct a separate distinctive logical system which would show this to be a poor distinctive bit of knowledge to hold, but we cannot deny that this is what they distinctively know.
I think this is similar to your green circles example.
It is perfectly possible to hold sincerely that something is A and not A without contradiction as long as the subject concept is not contradicted by the predicate — Bob Ross
Except for the fact that there are contradictory predicates. But if the predicates are contradictory in themselves, how does this relate to the subject? In the d/a distinction, I can claim I do not applicably know of any thing that is both existent and non-existent at the same time. But I can distinctively create such a thing in my mind. Which means I can say "There is a thing which is everything and nothing at the same time." and it be "possible" because I can create this in my mind. In your argument, these predicates do not contradict the subject. Whereas with the d/a distinction, I can demonstrate distinctively such a thing is possible, but applicably, it is something we cannot know. I do not have to concern myself to a linguistic game of predicates and subjects.
Finally, I want to ask if a subject can hold two contradictory predicates, why can it not hold a predicate which contradicts its subject? If a thing can have the predicate of both being there, and not being there, then isn't the subject a contradiction in itself? Which again, we can imagine such a thing distinctively. At best we can only speculate that such a thing could be known applicably. If I can distinctively create whatever subject with whatever properties (predicates) I want any time, then doesn't that hold to the notion I've been stating this entire time? That is, distinctively, I can hold whatever system of logic I want. And I am not seeing the argument that convinces me that I cannot create a system of logic in which the predicate can contradict the subject.
Again, the only way to counter such a hold, is with applicable knowledge. By asking them to show that such a being exists, we can escape the fact that we can distinctively know almost anything we want/are programmed to hold. In applicable knowledge we use deduction, but again, we use deduction not because we need to, but because it is more helpful to our survival and outcome in life.
"The bread I am eating is purple"
Well, I am not eating bread. So I am neither eating bread that is purple nor bread that is not purple, because I am not eating bread. Therefore it is neither true nor false. Imagine I am eating cereal and I claim: — Bob Ross
I had to note I don't believe this is the case. This is a combined sentence, and we can break it down.
I am eating bread.
The bread is purple.
Both are false, I cannot see this as being neither true or false in application.
"this sentence is false"
I could simply concede that the liar paradox outputs {t, f}, which is essentially the same thing as defining a liar paradox sentence as having a property of being contradictory (just like being green and not green). — Bob Ross
Again, we can break the implicit combination down.
This is a sentence "This sentence is false."
The previous sentence is false.
That results in t,f. No paradox or indeterminency. I would argue that when one cannot break a sentence down into t and f, that is a weakness of sentence construction, not a revelation of knowledge.
You are subscribing your epistemology to LEM and PoN, most notably as described by classical logic. This rules out the actual applicable usages of paraconsistent, fuzzy, and first-degree entailment logic. My epistemology still accounts for these within their own respects. — Bob Ross
I never claimed my epistemology ruled these logical constructs out. If anything, I've noted repeatedly you can construct whatever logical system you want distinctively. Can those logics be used in application? If so, then they are fine. I think this is a situation again in which I do not fully understand your theory.
Thus I would conclude using the POI that what is distinctively known is what we discretely experience, and I would add the claim we could discretely experience both something, and its negation at the same time.
I don't think you can posit this unless you are redefining discrete experience: the subject concept necessitates, categorically, that it be distinct, which necessitates that one cannot experience both something and its negation at the same time in the same place. — Bob Ross
No, we just affirmed I could do this. Can't I say a thing is both green and non-green at the same time? That is indeterminency. I can distinctively know this. Can I applicably know such an indeterminency? So far, no.
A potential infinite, of the type I am describing, is not claiming "it could, or could not be", it is claiming that a particular finite operation would be infinite if given the sufficient resources to continue. For example, counting the positive integers starting at 1 is a potential infinite. This claim is not an induction whatsoever. — Bob Ross
I agree with your definition here. But we know this because the design of numbers allows this to be. Such a description is not necessarily meaningful for any designed system. What we can discretely experience is potentially infinite. What we can applicably experience is potentially infinite. Any formulaic system with an X variable will always be so. My question to you so I understand better, is whether your foundation is finite. The system of numbers is formed by symbols, addition, subtraction, and for our purposes, base 10 rules. Does your epistemology have a solid and unquestionable base that does not need potentially infinite regress?
This is why it is important to note the necessary inseparability of time and space, for the sentence "Space contains A and not A" does not violate predicate logic PoN, nor does "Time references A and not A at the same time": it's only when combined, the union of the two concepts, where the predicate contradicts the subject concept. — Bob Ross
I don't believe this is correct Bob.
Space contains A and not A
Time references A and not A at the same time
Therefore space and time contains A and not A, and references A and not A at the same time
So again, we have contradictory predicates to a subject. What might help is showing a genuine situation in which a predicate contradicts a subject, and why, without using the d/a distinction.
Mine contains no potential infinite regress.
I think it does. You can construct PoN and LEM based off of my definition of PoN, but cannot prove my definition of PoN without recursively using it. This is just like how you can't ever stop counting positive numbers granted enough resources and claim you've hit the last positive integer. — Bob Ross
I think I clearly did using discrete experience. If you discretely experience within another discrete experience, then that sub discrete experience is part of the bigger one. But we could also discretely experience that the sub discrete experience is not part of the bigger one. Perhaps it is a parasite, or foreign entity that we find not necessary to the greater experience. If the predicate cannot contradict the subject, can the subject contradict the predicate? What happens then if in my mind I reverse what the subject and predicate are? Claiming a predicate can never contradict a subject is a logical rule you have constructed after understanding what a subject is, and what a predicate is. It is not foundational.
If you would like to end the conversation in this discussion board here, that is totally fine! Sometime soon I will post a discussion board of my epistemology anyways. — Bob Ross
Coming back to this, I think it is simply needed that you construct your epistemology from its foundation at this point. I believe I don't fully understand your theory, as you've noted you define things different from what I think you are. Coming from me, I understand.
:) So until you really have room to build your theory, I think we'll be talking past one another. Again, feel free to respond to my points that I have made, and I will let you have the last word on those. Then, if you would like to continue, feel free to construct your epistemology here, even as practice before posting it on its own thread. I will address it without using the d/a distinction. If we get to a point where you and I both feel we understand your theory, then we may go back to those final points that you'll make. Great discussion as always Bob!