Semiotic Elucidation of the Emptiness View

2. by applying symbolic logic, it is shown that there are cases in which the logic of the middle-of-the-road school, traditionally considered illogical, is actually logically consistent.

3. by re-presenting arguments such as Tatsuki's "Middle Theory" in the form of symbolic logic formulas, we clarify the logical structure of these arguments.

6. this study is a pioneering attempt to link Buddhist thought and modern logic, and suggests the possibility of a dialogue between the two.

The paper is an ambitious study that offers a new perspective on the comparative study of Buddhist and Western logic and attempts to shed light on the logical aspects of Buddhist thought.

Describing Buddhist logic in terms of symbolic logic rather than formal logic

From the standpoint of traditional logic, Indian logic appears to be asymmetric, but from the standpoint of symbolic logic, it is not asymmetric but rather traditional logic's adherence to useless rules.

Concepts are always genitive

This mountain has fire in it

There is fire here!

Fire is "here."

Indian logic

Here" is the subject.

traditional logic

Fire, here and there Inclusion Decision

There is fire here. Existence judgment

$ -a+b=1

$ a < b

The meaning of the former expression is that "everything is either a or b.

$ a-b=0

There can be nothing that is "a" and not "b".

$ ab = a

a and what is b is a

These have no principalities.

Understood! I added it.

I'm not sure whether to write it in a set style or logical formula style for a modern writing style.

https://gyazo.com/93828a1999d0cf14c0862c8bfa48e9e0

[$ A \subset B; A \cap B = A; A\cap\overline B=\emptyset.

So this is the same thing expressed in three different ways.

Opinion that AI is also a typo

[$ A \subset \overline B; A \cap \overline B = A; A\cap B=\emptyset.

[$ A \cap \overline B \neq A; A\cap B \neq \emptyset.

[$ A \cap B \neq A; A\cap \overline B \neq \emptyset.

(formal) proposition

$ (x).\phi x.\subset (\exist x).\phi x

$ \phi a.\phi b.\phi c. \cdots\cdots: \subset \phi a \vee \phi b \vee \phi c \cdots\cdots.

Meaning: if φ(x) is true for all x, then φ(x) is true for at least one x.

$ \phi(a) \wedge \phi(b) \wedge \phi(c) \wedge \cdots \implies \phi(a) \vee \phi(b) \vee \phi(c) \vee \cdots

Meaning: φ(a), φ(b), φ(c), ... are all true, then φ(a) or φ(b) or φ(c) or ... is true.

Explanation: This shows a logical implication relation. It represents an inference from a conjunction (AND) to an election (OR). If all propositions are true, it means that at least one (in fact all) of them is true.

$ A \cap B = \emptyset, \quad B \cap C \neq \emptyset, \quad A \cap \overline C \neq \emptyset

E: Full-symbol negation (No A is B)

I: Singular Affirmative (Some A is B)

O: Special-person negation (Some A is not B)

This formula expresses these three propositional forms in set-theoretic terms:

These formulas are a set-theoretic interpretation of the propositional forms of traditional logic, expressed in modern symbolic logic.

It is not illogical that the idiosyncratic judgment takes the form of an existence judgment.

https://gyazo.com/e5589df72fe9b322a79806aebff4700e

That is, that people in languages that do not omit the subject are limited to certain thoughts by the constraints of the language and therefore cannot understand some of the conversations of people in languages that do omit the subject.

$ (\exist x).\phi(x).\equiv.\sim (x) . \sim \phi x

x for "people" and phi for "going to see cherry blossoms".

The one like sim is negative, equiv means equivalence as it is.

Meaning: "some x exists and φ(x) is true" is equivalent to the negation of "φ(x) is false for all x".

Commentary:.

By negating its entirety, it means "φ(x) is not false for all x".

This expression is one of the key theorems for quantifier duality. It expresses the relationship between existential and omnisymmetric quantifiers and shows that one can be defined by the other.

claude.icon

[Existence judgment: "A exists which is B."

They logically express the same content.

What has smoke is what has fire

Where there is smoke, there is fire.

In traditional logic, which was perfected in the Western Middle Ages following Aristotle, only the former was treated. The latter had to be rewritten in the form of a Priestly Affirmative Inclusion (A) like the former, or else in the form of a hypothetical inclusion.

Traditional logic since Aristotle dealt primarily with forms of the whole-person affirmative judgment (A). Existence judgments and judgments expressing special relations were often rewritten as either whole-person affirmative judgments or hypothetical judgments.

For example, the existence judgment "some S is P" could traditionally be rewritten as

As a full name positive judgment:

$ (\forall x)((Sx \wedge (\exists y)(Sy \wedge Py)) \rightarrow Px)

"For every x such that there exists an S which is S and which is P, x is P."

As a hypothetical judgment:

$ (\forall x)(Sx \rightarrow (\exists y)(Sy \wedge Py))

"If x is S, then there exists S such that P"

These rewrites were a way to get around the limitations of traditional logic, which cannot deal directly with existence judgments.

https://gyazo.com/4578efb5d5dfa563667e5a74b05fbfa1

$ \psi\alpha

$ \phi\alpha

$ (x)\phi x . \supset \psi x .

$ \phi \alpha . \supset \psi \alpha.

$ (x).\phi x.\supset \psi x : \phi \alpha.\supset \psi \alpha

(Ratzel's theory of apparent variables)

Claude said it was.

However, in India, from these five items, instead of a three-stage argument, we proceeded to Russell's THEORY OF APPARENT VARIABLES

In the first place, is the whole nominal quantifier itself a relatively new concept around 1900?

https://gyazo.com/7bb8a086fff5645c8a3d8f6744f92a16

This is a concept in logic proposed by Bertrand Russell, a theory that deals with variables bounded by quantifiers (∀ and ∃). The term "apparent variable" refers to a variable bounded by quantifiers.

claude.icon

Yes, we will gladly provide an explanation. I will explain the notation of symbolic logic used in this paper, along with the modern TeX notation and its meaning.

Meaning: All S is M. All M is P. Therefore, all S is P. (Trinitarianism)

$ (\forall x)(\phi(x) \rightarrow \psi(x)) : \phi(\alpha) \rightarrow \psi(\alpha)

This expression can be interpreted as follows

In other words, this entire equation represents

There is a general rule that says that if φ(x) for all x, then ψ(x) holds, and if φ(α) holds for a particular α, then ψ(α) also holds for that α."

This formula expresses the application of a general rule (a totally symmetrically quantified proposition) to a specific case, and is an application of Russell's Theory of Apparent Variables. It shows the relationship between a totally symmetrically quantified x and a particular α. It illustrates the use of variables (x) and free variables (α) bounded by quantifiers.

Chapter 2

"Nothing can be x and non-x.

According to Schröder's Logical Algebra, if a is a and nothing, then a is nothing.

$ a\times 0 = 0

Apart from what has already gone and what is yet to go, we do not recognize any other third kind of world path, namely, "what is now passing away.

$ a + -a = 1

I'm talking about how from this point on, the Dragon Tree Empty Argument is an Aristotelian method of reasoning that is NG, but from logical algebra, it's OK.

https://gyazo.com/c80f80f3ead929130881b59e81e34cb8

While the Saṅghya school adheres to the principle of the law of contradiction or the law of exhaustion, Buddhism tolerates a different kind of thought.

After criticizing you for equating sky with 0 in logical algebra because the original word for sky means zero, which is groundless, I give my reasons why I think sky is a good place to start.

But even then, not all of the empty arguments can be expressed by logic algebra, so I'm done talking about how logic may need to be extended - I'm not sure.

---