When we know something, it is because of experience of the thing in a past situation.
1. First impressions and classifications of things. (word-sound-obeject association)
2. Recall of past impressions.
Idea is made to equal stimulus by first impressions. Number two, can be shown to be an equation of I=S, idea equals stimulus. This means that all qualities and things can equal the idea of them. The concept holds the attributes or the things essence, and the idea will either equal or not equal the stimulus. In order for positive correspondence to take place (valid cognition -- truth) idea must equal stimulus. When I doesn't equal S there is negative correspondence (invalid cognition -- lie).
From this it follows that all ideas exist as inequality relationships to stimulus. All ideas are concepts properties or concepts of things. When a stimulus triggers the concepts they must be equal to the idea in order for correspondence to exist. This means, that we can represent all qualities and things mathematically. When the stimulus has a number of qualities that equal the concept of the thing, than the thing is known (positive correspondence exists).
This proves that we might be able to formulate a mathematical system for correspondence of the properties of things. For this to be achieved, properties will be numerical, and the sum of properties will equal thing. Pn = T, properties equal thing.
The same applies to word association. W = S = I word equals stimulus, which equals idea. The word equals the stimulus or idea, because of the association of the word with the stimulus with them. Pn = T = Wn Total properties equal the thing, which equal the total definitions (words) of it.
According to my law of relative sound association, any sound can be used to trigger the idea. According to the law of non-ambiguity, a sound can not represent two different qualities or things without causing cognitive dissonance (W = I1, I2 =Cd). For example: If the sound "red" was equal to two different stimulus it would trigger two different ideas. For the sound-association to have a specific idea, the sound (word) that triggers that idea must not be triggered by a word associated with multiple ideas. For positive sound correspondence to exist Wn = I = S (words must equal stimulus by triggering the idea of it).
According to the law of Hebbian neuro-logical habit, the likelihood of a word triggering idea is equal to the number of times the word triggered the idea. Wn +nT (S=I) = SWa (word + ntimes associated with stimulus or idea equals strength of word association. There may be a certain level of strength to an associate where the word is associated with the idea or stimulus more fluidly.
As an example of this law (A. Hebbian word-association), when first meeting a person you are given their name. The less you see them the weaker the word-association, the more you see them the stronger the word-association. The strength of the association is also a law of the association between idea and stimulus. (B. Hebbian idea-stimulus-association) The more you think or have an idea of the stimulus the stronger the idea is associated with the stimulus. ƒI(S)= Sa (frequency of idea with an stimulus equals strength of association. ƒS(I) = Sa is also true.
We can make experiments that will exhibit how frequency of stimulus with an idea equals the ease of retrieval of the idea upon stimulus. We should be able to prove the greater the frequency the stronger the association.
Neurologically, this proves there is a cellular mechanism that operates according to the former mathematical laws of habit and cognition.
Other equations for cognition:
Similarity = Ip1 = Ip2 (Idea properties that equal idea properties) every positive correspondence is actually the similarity between S(It1) = S(It2)
Difference = Ip1 /=Ip2 (Idea properties that don't equal idea properties).
Consciousness is idea-stimulus similarity.
Stimulus-idea equals properties of thing (SI) = Pn(t)