This page needs a lot more work, it was thrown together from various scribbles to just touch on the topic of logic so that I could hurriedly pass on to the definition of knowledge and how it uses logic. I hope to someday develop this page further and make it consistent and define some passed over concepts.
Multifarious particular phenomena are presented to me. If I see red, it is a particular trope of red that I see. Again, reflecting on this I recognize that I cannot see that particular trope of red while at the same time not seeing it. This is also a particular reflective observation, which is observed but not not observed.
If I see a square, it is a particular individual square, and I don't both see it and not see it at the same time. This is a different reflective observation, which is observed while not not observed.
All of these phenomena are all particulars. But I notice similarites and differences between them. I notice that the red is different from the square. I notice that my observation that I don't both see red and not see it at the same time is similar to my observation that I don't both see the square and not see it at the same time.
The more phenomena that are present or have been present, the more similarities and differences I notice. It is at this point that my mind begins to generalize a number of similar phenomena into a single abstract idea. My mind begins to see and abstract a common form to the variety of particulars. It takes what is the same from them and leaves out what is different. This creates my idea of a type.
Reflection shows me that I can't help but do this abstract generalization. Reflection notices that when I think about how the present relates to the past I seldom recall particulars from my past but instead I recall abstract generalizations, i.e. types.
Reflection looks at my thoughts and notices that some particular thoughts are followed in time by other particular thoughts, whereas other particular thoughts don't follow in time other particular thoughts. Reflection also recognizes that there isn't a thought being both positive and negative at the same time in the same way.
From the aforementioned phenomena noticed by reflection of a phenomena being present but not at the same time as its not being present I made an abstract generalization. I will call this the "principle of either/or" meaning any phenomena can be either present or absent but not both. What about positive and negative but not both? It seems I must reflect on a phenomena to be able to assert the law of identity, or to recognize the law of noncontradiction. I don't make any assertions of laws, I merely suggest guiding principles of reflection only to be noticed in each instance.
Traditional logic deals with: 1) Identity/nonidendity 2) Groups of individuals with a particular predicate 3) If, then 4) If and only if, then 5) necessary condition/sufficient condition
Mathematical logic is different from what we are looking for. The manipulation of signs according to already established rules already makes use of a logical understanding, for the signs are empty and so don't convey the logical relationships and forms I am looking for.
Logic is the moving from one thought to another thought in a way that holds mutliple thoughts in a coherent relation to one another without creating a contradiction, which would not allow a system of a thoughts in coherent relation to other thoughts.
In its use in the Western tradition, logic seems to me to be reducible to two types: 1)logic of entailment, and 2) logic of association.
Logic of entailment is when one thought cannot be separated from the other thought without destroying the system of thoughts.
Logic of association is when one thought can be separated from the other thought and the system of thoughts isn't destroyed (conditional statements and so forth), i.e. their connection is not necessary. In this type there would not be a problem with the thoughts themselves if they had been connected to different thoughts, it might change the whole world from our perspective, but in considering the thoughts themselves they would be indistinguishable from other associated thoughts or if switched around with other thoughts, etc.
1) It can't be a sequence of concatenate thoughts. I can think of Socrates, and then after think of Mickey Mouse, that doesn't make me think there is a logical connection between the two thoughts. 2) It is not an association brought about by constant conjunction of one thought following another thought. 3) It is not a compunction to think one thought after another thought. I can think that all men are mortal, and then after think that the man in front of me is immortal.
There is a an illuminating parallel between logic and space. An object can be in one room and not in any other room. That room can represent a type. That room can be in a building, which is a larger, more inclusive type. I can draw as many overlapping spatial areas as I want over the object. It can be in many rooms at once, or many counties at once etc. When there is a contradiction or a logical deduction depends on when a volume of space is clearly defined in relation to everything else as X and not-X.
One can believe one thing in isolation. One can have many beliefs that are isolated from each other. One can have beliefs that contradict one another. One can have a system of harmonious beliefs. And one can have a mix of all of these. What logic from phenomena will do, in one sense, is to maximize the number of data input, maximize the relevancy of that data, and maximize the consistency of that relative data into a system.
If a particular necessarily belongs to a type, and there is a second type not identical with the first type, the particular does not necessarily belong to the second type.
If something has happened in the past it will continue to happen
Something must be the case because it is more beautiful
Something must be the case because it is more just or good
Something must be the case because it is more simple or complex
Something must have a telos
If somethings are similar in certain ways they must have a deeper connection
Something must be the case because it is intelligible
Something must be the case because it makes sense or fits in context
Authority or tradition
provides a method