A wonderful write up as always Bob. No worry on the time, quality posts take a while to write! I have to think through my responses quite a bit at this point myself, as you often ask new questions I haven't considered before, and I want to mull my initial thoughts over before responding. Lets get to it.
Firstly, "distinctive knowledge" is "deductions". "Applicable knowledge" is merely referencing the means of achieving that "distinctive knowledge" (i.e. the transformation of an inductive belief into deductive knowledge--belief into knowledge) and, therefore, is unnecessary for this distinction you are trying to convey. — Bob Ross
I think it is important that this distinction remain. What I might have been missing is a third category.
Deductions are knowledge. The difference between distinctive and applicable are what was involved prior in the chain of reasoning. This mirrors the induction hierarchy, though I don't think one deduction is more cogent than another. Deductions without any inductions immediately prior are distinctive knowledge. Deductions concluded immediately inductions are applicable knowledge. I would not mind renaming the words within that distinction, but that distinction is absolutely key to breaking out of the previously failed theories of knowledge. I will see if I can show you why in our conversation.
First, to be clear, deductions are forms of knowledge. Inductions are forms of beliefs. But how we determine those inductions and deductions allows us a different approach. I think the problem is maybe I haven't clearly defined an abstraction. An abstraction is not a deductive conclusion from an induction, it is the formulation of the essential and non-essential properties of an identity. Within a solo context is a tool of your own creation, there are no limits to what you can, and cannot create in an abstraction. If you create limits, those are self-imposed limits.
For example, making a game. Imagine there are no people around. I invent the game called "Go fish" on my own. Did anything in reality force me to create those rules? No. Now, can I take a real deck of cards and play a game? That is an induction. Once I confirm that I can, or cannot play that game, then I have a new type of knowledge, the conclusion of an induction. That is something that needed to test reality, and either passed or failed.
Another way to view it is when you discretely experience the color "red". Not the word, the experience. Then you say, "That is 'something'". That construction of the essential property, and non-essential property of what 'red' is, is the abstraction, and fully in your creative control.
For all intents and purposes here, I am going to elaborate with a distinction of "categorical" vs "hypothetical" deductions (not married to the terms, just for explanation purposes). Although they are both deductions (and, consequently, their conclusions necessarily follow from the overlying principle and subsequent premises), they differ in the validity of the overlying principle itself. If a deduction was "categorical", then it is necessarily (categorically) true. — Bob Ross
Your categorical deduction fits the bill perfectly. I agree that is a deduction. But I'm not sure the hypothetical is an actual deduction. Let me point it out
However, if I am asserting this "hypothetically", then I am thereby asserting in virtue of hypothetically holding that it is true that all cats are green. — Bob Ross
"All cats are green". Is that by definition, or is that an induction? That is the fine line that must be clarified. If cats are green by definition, as an essential property, then that is what is distinctively known. If however, color is not an essential property of a cat, then its involvement in our logic does not result in a deduction, but an induction. This is because I am admitting to myself that if I found a red creature with the essential properties of a cat, I would still call it a cat.
However, if it was "hypothetical", then the conclusions are only true in virtue of granting the overlying principle as hypothetically true. This can be demonstrated (both of them) in one example:
1. All cats are green
2. Bob is cat
3. Bob is green — Bob Ross
This is not hypothetically if you are the one who has determined the definitions. Lets flesh it out correctly.
1. An essential property of cats is they are green.
2. An essential property of Bob is that they are a cat.
3. Therefore, Bob is green.
Including non-essential properties turns this into an induction.
1. An accidental property of cats is they are green. (Could or could not)
2. An essential property of Bob is that they are a cat. (Must be)
3. Therefore, Bob is green.
This is not a deduction. This is an induction because we've basically stated, "Cats could, or could not be green". We have deduced an induction based on our abstractions. And we can classify this type of induction using the hierarchy. If, as you implied, we've always seen green cats, but we are willing to accept a cat that could be another color, then this is a speculative induction.
So, we can abstract both deductions and inductions. And this abstraction is distinctive knowledge.
They are not applicable knowledge, because applicable knowledge only comes about after we have taken our abstracted induction, and deductively concluded the result.
if I define "glass" as having the essential property of being "(1) clear and (2) made from melting sand", then, assuming I didn't watch it get made, I can't assert that this pane in front of me is actually "glass": it would be an induction. — Bob Ross
True. Based on the context of your definition, you will never applicably know whether that is glass.
So, although I deductively discover the properties of the presumably "glass pane" in front of me, I do not deductively obtain that it is thereby "glass" (I inductively assert it is). — Bob Ross
Just to clarify, if you meant that you deduced that the glass was made of silica, clear, and for all intents and purposes, had all the non-essential properties of a window, but you could not find the one essential property "That it was formed through melting sand", then yes, you could only ever inductively know it as a window.
I would also like to briefly clarify that my square root of 25 example was meant as a "solo context", as it can be posited as either one (but I should have made that clear, so that's my bad). The dilemma is still there if we were to presume that I came up with the mathematical operation of the square root. I came up with it a year ago, by myself, and began memorizing the answers of the square roots of like 100 integers (or what have you). Then, a year later, I ask myself "what's the square root of 25?". I immediately assert it is "6" in reference to what I believe was what I memorized a year ago (in accordance with the mathematical rules I produced). That's an induction. — Bob Ross
This is such a good point! Lets walk through this. So at the time when you state, "the answer is 6", that's still distinctive knowledge and deduction. That is because what you experience remembering as the answer, is the answer. There's no one else to tell you that you are wrong. There's no other answer you can give, because that is what you remember.
Stay with me here, because I know how that can sound at first. Later you may "remember differently" or find a record of the logic that you put down. At that time, you will know that your original deduction was wrong. But that was what you still distinctively knew at the time. With new knowledge to revise the structure that you had, you now distinctively know that the square root of 25 is not 6.
The bigger question, and the part where you may be right that we can induce abstractly, is when you make the claim, "What I remember today is the same thing I remembered yesterday." What a head twister honestly! That by nature is always an induction. Or is it? Can't I simply decide yes or no? I can, but it is a belief, and therefore an induction, is the deduced conclusion to that then applicable knowledge?
If I have no outside evidence of the past, or record of the past, the answer is still what I ultimately decide. If I remember, "Yes, I do," then I've been given an answer, but from my own mind. If I remember that I do in fact, remember what I remembered yesterday, that's an answer that I distinctively know. But is it true? Is that really a deductive answer to an induction? It is, because its the distinctive knowledge that I have. Same as if I experienced that I did not remember the same thing I did yesterday (even if I'm incorrect objectively). Finally it is deductive if I conclude, "I can't trust my own memory anymore, so I don't know."
But, and here's the kicker, is the answer to this induction, a deduction or another induction? What's interesting about this case is it may not fit either. I'm not sure, so I'm going to break it down.
Is there a premise in the drawn conclusion to the original induction?
Case 1. I remember that what I remembered yesterday, is what I remember today.
As what we discretely experience is what we distinctively know, then I distinctively know this. Thus this conclusion is actually a deduction, even if there was some outside evidence, even if this was not true.
Case 2. I remember that what I remembered yesterday, is not what I remember today.
The outcome is the same as case one. This is distinctive knowledge.
Case 3. I conclude "I'm unsure if what I remembered today is what I remembered yesterday."
Lets call this the Descartes Doubt case. The answer to case 3 cannot be found by anything outside of our own deductions again. This is the "I doubt even my own thinking". What is the answer that we deduce in this case? "That I cannot remember if what I remembered yesterday, is what I remember today." This is not an induction, as we have concluded that this is the case with no alternatives. This is what I discretely experience.
In short, in what we conclude in a prior reference to our memory, an abstraction, is a deduction because it is whatever we experience.
But, lets compare this to another scenario in which I know I wrote down what I remembered yesterday, "The square root of 25 is 5" (according to my made up rules). If I remembered this existed, and this paper could prove that I correctly remembered what I knew yesterday, then I would deductively know that I could not ascertain an answer unless I found it. This is not the same as claiming, "I believe the paper says the square root of 25 is 6" This is an induction, and can only be denied or confirmed once the paper is discovered.
The entire point I want to note is that abstractions, which are entirely in our head, can never be inductions in themselves. We can use those abstractions as inductions, and when we do, we can gain applicable knowledge be deductively solving the conclusion. When we make abstractions in our head and apply them to abstractions in our head (that we have made up) there is no induction, because it is whatever we conclude.
That being said, we can classify deductions in two ways, and I believe these are important identities.
1. Deductions in which the premises are not changed.
2. Deductions in which the original premises are changed and amended.
Recall that when one applies an induction, they can amend their terms to fit the new conclusions. So for example, if I considered all cats green as an essential property, and I found a feline that matches all the essential properties of a cat except that it was red, I might decide to amend the essential property of color into an accidental property. I could also simply keep the color as an essential property, and conclude from the induction that I had found a new animal. That choice is mine. But perhaps noting when we change or amend our original distinctive knowledge versus when we do not change or amend our original distinctive knowledge is a key difference.
I don't think this is what you meant by (0, 0): I think you are arguing for the allowance of minimally ambiguous terminology. — Bob Ross
This was a reference to a mathematical concept. If you're not familiar with it, its not a good example, so lets not worry about it.
I would clarify that the applicable is not the attempt to verify inductions, it is the deductive result of an induction
If this is the case, then it is distinctive knowledge. — Bob Ross
Since distinctive knowledge is a particular knowledge that precludes the involvement or prior inductions in its conclusions, no. Recall that both forms of knowledge are deductions. Just like the hierarchy of inductions, it is the steps that we take to arrive at those deductions that create the essential difference.
I still think we are slowly converging in our views, it is just taking a while (: — Bob Ross
Ha ha! Yes, I honestly feel our views are off by only very small differences. I think this is one of the reasons the conversation has been so engaging and helpful (for me at least). You've been able to point out that slightly semantic/alternative view point that really tests what I'm proposing, and makes me think. It has helped me amend and leave out a few approaches that you have shown are unnecessary or simply confusing. As always, it is appreciated to find another person who is interested in the truth of the matter and the refinement of the discussion.
I think you are starting to explore recursively reason on itself and, thusly, realizing that "deductions" and "induction" are innate in us. — Bob Ross
One thing I want to clarify is that I agree that the capability to deduce and induce are innately within us. Distinctively knowing these words and these concepts is something which must be discovered. One can accidently deduce or induce, but not have any distinctive knowledge that they do. So what I meant by, "The logic of deduction and induction are reached by..." I mean the knowledge of the logic of deduction and induction are reached by..."
I think "discrete experience" is a convenient clumping of many aspects of the fundamentals of the mind, but to achieve your grounding of deductions, premises, conclusions, induction, predictions, etc, I think you are going to have to at least conceptually analyze the sub-categories. — Bob Ross
Full agreement with you. Another large write up from me! I hope I covered the points, please let me know if there is something that I missed or did not clarify. I fully expect a response on the claim that abstracts are essentially distinctive knowledge and cannot be inductively concluded.