Properties as Numbers and Feelings

I presume properties Pφ can be described as numbers Nφ and feelings Fφ.

Let's look at the tablet below:

x, y, and z - are variables; 
N^1-4 - are function of numbers of objects;
F^1-4 - are function of feelings of objects;
a, b, c - are objects;
1, 2, 3 - number of objects;
e, d - equality or differences (whether or not objects equal or difference).

To make it shorter, there may be some feelings (Fφ), not maybe specifically, and using them you can say whether objects are different (d). If objects are not different, then they are equal (e). A function of number (Nφ) represents how many objects are there. 

So, as you can see from the talbet, the function of number N¹ demonstrates objects a and b are the same (the 4^th column, rows 1-3), while the object c is different two the rest (the 4^th column, the 4^th row). Our expactations of the number may be quite different by the columnt five of N², in which somehow each row contains two object. But it must be that among three variables (x,y,z) we can find two a`s, not one or three (the 6<sup>th</sup> column, 1,2, and 4 rows), and at the same time a=b that is being demonstrated by this column of N<sup>3</sup> (the 6<sup>th</sup> column, the 3<sup>rd</sup> row). The last column of number function demonstrates that fact that a`s may be taken as three different (e.g. as some kind of a criteria), while b=c or a=b (the 7^th column).

The system of feelings can present that type of relations we may have. What does it mean? If objects a, b, and c are different through feelings (or a feeling), it doesn't mean this can't be that a=b or b=c; this is being demonstrated by F¹ in the 8^th column. Might be that in the series of aa or bb we can or cannot be certain whether those objects are the same. So that point is reflected in both of columns (F² and F³: the 9^th and the 10^th), and from that point of view, only appearing of c can sure us among those objects there are differences. The last column of F⁴ demonstrates us that it doesn't really matter about the objects, because even between apparently similar ones there are differences (the 10^th column).

Generally speaking, we may have more completed tablets, but it's okay to have a quite smaller. One can size properties at the different level, but behind this process a certain logic is required. The logic of feelings (no matter which) and the number is seemed to be pretty easy to comprehend. Only what is left behind and this gotta be known is that how to unite those number and feeling function together.

Let's write the general formulas to find P's. Okay, here are they:


And here's another tablet:


And finally we can see that there are sixteen properties for these feelings and numbers of objects. Of course it also might be (but for that no tablets we're gonna draw) that some of these properties are the same (or maybe all of them are the same), but this is another assumption that should be checked due to the significations of theirs. Besides, we can be certain about some relevances between groups of these notions, like P³¹⊃ F¹ or (P⁴¹&P⁴⁴) ⊃ N⁴.

An important things appear here that may be used to doubt in the Leibniz's indiscernibility of identicals law, but how? We cannot be certain about whether or not two identical things are identical in all of their properties, or - even more serious - if objects are defined with their properties, then we never know are any two objects are identical. An example: for the properties P³³, P³⁴, P⁴³, P⁴⁴ there are no rigorous answer about their objects, so as we can see: 


By this it's seen those a's are not equal due to the 5^th row the 9^th column. And sometimes the differences cannot be seen as like in that example of P¹¹: