EXISTENT AND UNIVERSAL TROPOS
Finally, I can distinguish a particular Existent Tropos (𝛵𝑒) and Tropical Universal (𝛵𝑢). 𝛵𝑢 can be represented as a function from A to B, and 𝛵𝑒 is a specific case of application of that function.
In this sense, 𝛵𝑢 is essence of 𝛵𝑒. It is known, that essence is the common for all instances of its type. Hence, 𝛵𝑢 can be inherent for many individual 𝛵𝑒. This is the repeatable pattern of essence and its substantiation.
Heating of some substance can serve as an example. Heating itself is universal process, which can be applied in many situations. Let's define a function of heating by 100°C:
𝛵𝑢: C -> H.
You can think of C as anything cold, and H as the heated product.
The application of defined function will be 𝛵𝑒 or 𝛵𝑢(𝑒). If 𝑒 is water, then the result of 𝛵𝑒 will be boiling water. If 𝑒 is oil, then we will get heated non-boiling oil. As you can see, 𝛵𝑢 is applicable in many situation and is truly universal in this sense.
The importance of described distinction lies in the fact that categorical method works with tropical universals (𝛵𝑢) first, and only then is applied (𝛵𝑒) to specific situations. This fact again proves the validity of the Four Categories order: from Logos through Tropos to Substantiation.
To depict a universal nature of the categorical method, we can observe a simple isomorphism between two sets, which is described by two functions f: Bin -> Bool and g: Bool -> Bin, where Bin is a set of two objects {0, 1} and Bool is a set of two objects {true, false}.
If the table of correspondance is:
| Bin | Bool |
---------------------
| 0 | false |
| 1 | true |
Then f(0) = false and f(1) = true, and in the reverse order g(false) = 0 and g(true) = 1.
We can see, that our functions are defined for entire sets and are applicable for specific values producing isomorphism, which means that 1 becomes true and back. Definition of the function is universal and its specific application can be presented as mapping between two sets.
September, 2023
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