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1年以上前 (2015/06/29)にアップロードin政治・経済

This is the slide which I used at my presentation ``The Meaninglessness of Algebraic-Semantics’’ ...

This is the slide which I used at my presentation ``The Meaninglessness of Algebraic-Semantics’’ at UNILOG2015.

Don’t hesitate to ask.

- Outline

the Aim and the Method

Prologue

A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

The Meaninglessness of

Satoru HANAD

Algebraic-Semantics

Outline

Rational Beings WITH-IN Logic and its Semantics

the Aim and the

Method

the Aim

the Method

Prologue

Satoru HANADA

A summarization

shanada3007@eis.hokudai.ac.jp

and its

presuppositions

A Summarization

its Presuppositions

Graduate School of Letters(M1), Hokkaido University

Object- / Meta-

Language and the

Worlds

June 29, 2015

Summary and

Further

UNILOG2015 @Istanbul Univ.

Investigations

Satoru HANAD

The Meaninglessness of Algebraic-Semantics - 6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

1 the Aim and the Method

Semantics

the Aim

Satoru HANAD

the Method

Outline

the Aim and the

2 Prologue

Method

the Aim

the Method

3 A summarization and its presuppositions

Prologue

A Summarization

A summarization

and its

presuppositions

its Presuppositions

A Summarization

its Presuppositions

4 Object- / Meta- Language and the Worlds

Object- / Meta-

Language and the

Worlds

5 Summary and Further Investigations

Summary and

Further

Investigations

Satoru HANAD

3">the Aim

A summarization and its presuppositions

the Method

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

The Aim

Outline

the Aim and the

any logical system and its semantics which are

Method

the Aim

object-languages do not contain any meanings.

the Method

Prologue

A summarization

e.g. Validity doesn’t come from formal logic, but from us.

and its

presuppositions

e.g. John Woods(2015, p32)“(82) The value of ∼ A is

A Summarization

its Presuppositions

just when the value of ( )A( ) is F.”

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

3">the Aim

A summarization and its presuppositions

the Method

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

Method

Outline

the Aim and the

Examine a possible summerization of

Method

the Aim

algebraic-semantics, and

the Method

Prologue

Show its presupposition.

A summarization

and its

Introduce a distinction between object-language and

presuppositions

other things.

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

‘WITH-IN’

Outline

the Aim and the

Method

Logic is not only inside the given system.

the Aim

the Method

We can think from within inside the language.

Prologue

(I would like to avoid demanding transcendental

A summarization

and its

elements.)

presuppositions

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A Summarization

A summarization and its presuppositions

its Presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

A possible summerization

Outline

the Aim and the

A role of algebraic-semantics merely consists in

Method

the Aim

substituting algebraic equations and inequalities for

the Method

Prologue

the axioms and rules of a given logical system.

A summarization

(Algebraic-semantics is no more than a paraphrase

and its

presuppositions

of LJ into algebra.)

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A Summarization

A summarization and its presuppositions

its Presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

→ - Right

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

α, β ⇒ γ

Outline

(→ −Right)

β ⇒ α → γ

the Aim and the

Method

the Aim

the Method

Prologue

The law of residuation

A summarization

and its

presuppositions

A Summarization

its Presuppositions

a ∧ b ≤ c ⇔ b ≤ (a → c)

Object- / Meta-

Language and the

Worlds

Summary and

Further

No difference! ∴Algebraic-semantics does not explain the

Investigations

meaning of logic?

Satoru HANAD

6">A Summarization

A summarization and its presuppositions

its Presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

McKinsey-Tarski’s Thm

Semantics

Satoru HANAD

LJ (/LDJ) is complete for Heyting Algebra composed of

the total of open sets (/Brouwer Algebra composed of

Outline

the Aim and the

the total of closed sets).

Method

the Aim

the Method

Moreover,

Prologue

A summarization

finite model property

and its

presuppositions

α is provable in LJ iff. α is tautology in finite arbitrary

A Summarization

its Presuppositions

Heyting algebra.

Object- / Meta-

Language and the

Worlds

Then, we can get infinite number of models. And we do

Summary and

Further

not have any criteria to select which is the meaning.

Investigations

Satoru HANAD

6">A Summarization

A summarization and its presuppositions

its Presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

However, this criticism is based on naive

Satoru HANAD

misunderstanding.

Outline

Presupposition

the Aim and the

Method

the Aim

the Method

This semantics of the given system have to show

Prologue

something about logical system, in addition to

A summarization

and its

completeness (and vice versa).

presuppositions

A Summarization

There is an order of values of systems and of their

its Presuppositions

Object- / Meta-

semantics.

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

(Look at a Figure)

Meaninglessness

of Algebraic-

Semantics

distinction

Satoru HANAD

Outline

Object-language is only a set of symbols and

the Aim and the

operations.

Method

the Aim

Meta-language is language which we use and/or is

the Method

Prologue

our linguistic activity.

A summarization

and its

There is outside of Meta-language, e.g. the ontic

presuppositions

world and the ontological world.

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Remark

Summary and

Further

LJ and HA are seen as object-language.

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

It is useful to compare the principle of bivalence with

Outline

Boolean Algebra with only 2 elements B(2).

the Aim and the

Each of them is semantics of classical logic, so they are

Method

the Aim

of equal value as an object-language. But that criticism

the Method

might not attack the principle of bivalence.

Prologue

A summarization

Because the principle is not only inside object-language.

and its

presuppositions

It connects language to the world.

A Summarization

its Presuppositions

the criticism mentioned aboved is category mistake.

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

Conclusion

Outline

the Aim and the

Method

The meaning of logical system can be found in

the Aim

the Method

meta-language and the world, which is outside of

Prologue

object-language, by Rational Beings.

A summarization

and its

So every object-language has equal value.

presuppositions

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

Outline

Start with a possible summerization.

the Aim and the

Method

Get some unacceptable conclusions.

the Aim

the Method

Introduce a distinction between object-language and

Prologue

other things.

A summarization

and its

Cancel the presupposition and get the conclusion.

presuppositions

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Yet, it is not clear how to find meanings. How to get the

Satoru HANAD

meaning is connected to next theme.

Outline

the Aim and the

A Theme

Method

the Aim

the Method

In what way do knowledge and the world connect to each

Prologue

of them.

A summarization

and its

After acquiring the view that there is no hierarchy and

presuppositions

A Summarization

meanings of logical systems, how do logics / the world /

its Presuppositions

Object- / Meta-

knowledge look like?

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

Additional Refference

of Algebraic-

Semantics

Satoru HANAD

Komori, et Ono (2010) an Introduction to Modern

Mathematical Logic(“Gendai Suuri Ronnrigaku

Outline

the Aim and the

Josetu”written in Japanese)

Method

the Aim

Aoyama, et al. (2007) Non-Classical Logics and

the Method

Prologue

Algebraic-Models(“Hi-Koten Ronri to Daisuu

A summarization

Moderu”written in Japanese)

and its

presuppositions

A Summarization

its Presuppositions

Acknowledgements

Object- / Meta-

Language and the

Worlds

Prof. Koji NAKATOGAWA(Hokkaido Univ.) and

Summary and

Takuma IMAMURA(Toyama Univ. B4).

Further

Investigations

Satoru HANAD

6">A summarization and its presuppositions

Object- / Meta- Language and the Worlds

Summary and Further Investigations

The

Meaninglessness

of Algebraic-

Semantics

Satoru HANAD

Outline

the Aim and the

Method

the Aim

Thanks for your attention!

the Method

Prologue

A summarization

and its

presuppositions

A Summarization

its Presuppositions

Object- / Meta-

Language and the

Worlds

Summary and

Further

Investigations

Satoru HANAD