# Formal Formulations

As s of Reasoning, and a dialectic for the Distinction of Objects.

With Reasoning by , the distinction between and is drawn as follows:

• is used to draw Distinctions; and,
• is used to erase Distinctions.

With Reasoning by , the distinction between and is confused as follows:

• is concerned with Distinctions; and,
• is concerned with Distinctions.

In the case of , the confusion may be constructive or destructive, depending on whether the is strong or weak, respectively.

For example, the above between and is quite weak and reveals very little knowledge with respect to the Forms of Reasoning.

On the other hand, the between mathematical s and physical s is quite strong and reveals a great deal of knowledge, with respect to the the behavior of Physical Objects.

Gramatically, the kind reader can easily recognize the use of by noting the use of the word "as", "like". "likewise", etc. That is to say, an assertion which is made with reasoning by typically has the :

```                ... X ... as ... Y ...
```
and asserts that X is analogous to Y.

Likewise, the kind reader can easily recognize the use of by noting the use of the word "is". That is to say, an assertion which is made with reasoning by typically has the :

```                ... X ... is ... Y ...
```
and asserts that X is identical to Y.

The kind reader is urged to observe this distinction and how it permeates the language.

noun
plural - analyses

1. The separation of an intellectual or substantial whole into its constituent parts for individual study.
2. Chemistry. a. The separation of a substance into its constituent elements to determine either their nature (qualitative analysis) or their proportions (quantitative analysis). b. The stated findings of such a separation or determination.
3. Mathematics. a. A branch of mathematics principally involving differential and integral calculus, sequences, and series and concerned with limits and convergence. b. The method of proof in which a known truth is sought as a consequence of a series of deductions from that which is the thing to be proved.
4. Linguistics. The use of function words such as prepositions, pronouns, or auxiliary verbs instead of inflectional endings to express a grammatical relationship; for example, the cover of the dictionary instead of the dictionary's cover.
5. Psychoanalysis.
6. Systems analysis.
[Medieval Latin, from Greek analusis, a dissolving, from analuein, to undo : ana-, throughout. See ana- + luein, to loosen.]