The Contradiction of All Conceptual Knowledge as False

There's too much semantics. I'd say the semantic overdose.

Conceptual structure comes from Kant's snooping. He was up to find what made us see things as we see them. Then were many those who tried to continue it. I could name the best but my own sympathy is to Quine. Let's say you see the world as abstractions, as recursions, and so on. Your objects have or have no size, they have their shape/form, etc. My worldview image can be different. I prefer the common sense along with logic. I don't believe any abstractions exist.

What is so important in your conceptual structure? – Your intentions. Some would say – your ontology, but that would be wrong. Why? We want see things as something we're seeing them, but this doesn't mean things are how we see them. We cannot imply it.

So when you're saying about contradictions inside the conceptual structure I wonder how can it be? This can be if your conceptual structure is the same as a formal system that is wrong. You're allowed to try to represent the CC, and at the same time it's not allowed to equate them.

Contradiction is a semantic category. It means you're saying more, than just p&~p. If I uttered something like a "round square", then I said two words which could considered as contradiction if we equated "round squares" with "p&~p" or the word "contradiction".

Any contradiction in your CC automatically leads to not being able to represent something of that.

You're talking to yourself?

I also find the example of Pythagoras's triangle to be the one – as a correspondence between thoughts and some models.

Usually conceptual contradiction put to some ontology problem as it was done by Alexius Meinong, who said that even round squares existed. But Aristotle much earlier tied contradictions with theoretical tasks:

1) according to Aristotle the truth is when a positive claim corresponds to what is, and a negative to what isn't. ("A is B" is true when A is indeed B, and "A isn't B" is false if A is B.)
2) if there are two implications from theories (considered that a theory tells us about general things or about all the things) such as one is "A" and another one is "not A", then a theory is wrong

At the same time I can find how a process of conceptualisation can be wrong, because conceptualising things we imagine or represent them, and their theoretisation is another lap. And this lap is just one of more further logical processes: we could consider that "A" would be false, and "not A" would be true, depending on what we would try to create, etc.

Besides, I think that our ability of conceptualisation is the inner rational process, and it helps us to put senses and some other forms of impressions to some places. As I presume Kant wanted to find these basic categories, so his interpretation was that we had time & space as our basic matrix, and on the matrix the things appear as things. Without it (that matrix) we would see no things. (However, maybe Kant was right, but Schopenhauer said that this Kant theory couldn't explain some extra cases, for instance, by what can we understand the proper order of things.)

jonbain

Just one thing: recently I tried to solve few tasks from a textbook of general logic (that includes the set theory). There were similar tasks on the relations. And what I noticed that there are different relations exist (however, I don't know about the math, since I'm not a mathematician).

Reflexive: for all x, xRx: "a human has the equal size of himself"
Non-reflexive: not for all x, xRx: "a sentence doesn't always correspond its grammar"
Irreflexive: there is no x such that, xRx "a mirror reflection doesn't show non-reversed image"

Symmetry: for all x and y, xRy: "x equal to y"
Non-symmetry: not for all x and y, xRy: "x is a brother of y" (some have sisters)
Assymetry: there's no x and y such that, xRy: "x is strictly greater, than y"

Transitive: for all x, y,and z, ((xRy)&(yRz))→(xRz): "x equals to y, y equals to z, then x equals to z"
Non-transitive" not for all x, y, and z, ((xRy)&(yRz))→(xRz): "x eats y, y eats z, but not always x eats z"
Intransitive: there's no x, y, and z such that ((xRy)&(yRz))→(xRz):

The last example I'll illustrate with the set theory:

If a, b, c, d... are some properties, and {a, b, c, ...}, {p, q, r, ...} are some sets, while "{a, b, c}Π{b, c, d}={b, c}" means Min function; "{a, b, c}U{b, c, d}={a, b, c, d}" means Max function; "~{b, c, d}={a, e, f, g...}" means Neg function; A, B, C,... – are sets (so, "A", for example, might be {a, b, c}), then:

Intransitive: there's no x, y, and z such that ((xRy)&(yRz))→(xRz) can be written as:

there's no A, B, C s.t. ((AΠB&(BΠC))→(AΠC), or

(({a, b}Π{b, c})&({b, c}Π{c, d}))→({a, b}Π{c, d})

I don't know whether all of such relations can exist in math or not, but for me the power of formal semantics bases on an ability that we can imagine every possible things, properties, or relations, and take part of them to work. So, it's like there's a tablet that has all the possible things, properties, and relations, and to pick certain things, properties, or relations – is the same as to claim some rows and columns to be true (i.e. to claim them as a function for certain sets).

Such an idea is always in math that each new dot y on the abscissa X that lays next to a dot x (on the same axis) has a greater value.

Being honestly, I can't say that I understand that conceptualization, however, there is a tip Kant's given us: 
about each of that impressions, feelings, and so on we have - we can ask a question - do they have a form or not? If they are - what is that? And if it has a form, it is true that this form is such that logic uses it? I mean can we maintain that material (of feelings, impressions, etc) as a relevant forms for logic? 

So, to answer this question is to make a theory about how impressions, feelings, and all kinds of phenomena find their forms, and to answer what logic is and what kind of material it uses? 

If to look at this question through a video you've recently posted - about the phenomenology.

Well, I can say that is also a problem - to find the basic elements of logic.

There are many attempts, and the primary one is that people usually use notions and they understand each other, despite the fact not everyone can defiene them. For instance, many of us can use notions 'science', 'life', 'logic', 'the whole', etc, but not everyone can difene them correctly. So, perhaps, the source of concepts is almost the same as the source of rationality.

Our perceptions can be taken, but how can they correspond with each other, by which mechanisms? Are our feelings and perceptions united to some system? 

Somebody says that the concepts are names, while it doesn't seem to be possible as soon as we start dealing with semantical problems (i.e. synonyms, omonyms, and the other ones, inclusing the paradoxes of naming). Besides, there are two types of arguments: when we're taking about the names as names, and when we're talking about things using names. Since there's no way to avoid using names, we may confuse them interchangeably. 

Well, perhaps, that's all I can say. I don't really know this subject, it doesn't seem to be easy.

Thank you a lot for such inspiring words!

Unfortunately I have come to this understanding - of how coding is important - too late.

But I tried to repatriate to it, by luring into this with logic. It is possible. 

Maybe you or someone else time to time would help me with it. I won't be sad if none would agree. 

But the central idea is to rewrite the main aspect of algorithms to logical forms. 

For me the logical forms is comprehensive. And, I hope, in many cases I could translate from the usual language to a logical one (or vice versa). An algorithm is almost the same, except that any algorithms is an extension of logic. So, it has some extra tips, that a typical logic doesn't have them. For instance, it has circles or iterations. 

Anyway, I've already started trying to formalize some of such procedures to logic. My first example is with cycles:

Let's say that we have to find which elements of a certain set has a value T, so that's how I see it:

Step 1. Input the elements of the set into the computer's memory
Step 2. If an element satisfies the form 2n+1 (let's suppose we've already had a procedure to solve it), then this element has a T value; else, it has V value.
Step 3. Load the first element of the list, and load the rest elements to the memory
Step 4. If a current element satisfies...

and so on. But that's not all what I wanted to write:

The "steps" are variables, and also "x", "y", and so on. "If", "then", "else" - are logical or functional constants, "=" - equality, and "T", "V" - are paramentrical constants. And there is an calculation operation. Therefore, if to write down it with three logical functions "if;then;else", "=", and calculations we can write this using just one logical operator:

step i: if x_i = y, then "step (x_i+1)+1"; else, "step x_i+1"
step j: if x_j = y, then "step (x_j+1)+1"; else, "step x_j+1"
step k: write "x_(k-2) = y"

Or the similar procedure. I don't know how to interact with the programs since I never coded anything (except for somthing simple in school). I think I have to read some books about it.