Simulation-based Testing of Unmanned Aerial Vehicles with Aerialist
20150629 ``The Meaninglessness of Algebraic Semantics''
1. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
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
Rational Beings WITH-IN Logic and its Semantics
Satoru HANADA
shanada3007@eis.hokudai.ac.jp
Graduate School of Letters(M1), Hokkaido University
June 29, 2015
UNILOG2015 @Istanbul Univ.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
2. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
1 the Aim and the Method
the Aim
the Method
2 Prologue
3 A summarization and its presuppositions
A Summarization
its Presuppositions
4 Object- / Meta- Language and the Worlds
5 Summary and Further Investigations
Satoru HANAD The Meaninglessness of Algebraic-Semantics
3. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
the Aim
the Method
The Aim
any logical system and its semantics which are
object-languages do not contain any meanings.
e.g. Validity doesn’t come from formal logic, but from us.
e.g. John Woods(2015, p32)“(82) The value of ∼ A is
just when the value of ( )A( ) is F.”
Satoru HANAD The Meaninglessness of Algebraic-Semantics
4. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
the Aim
the Method
Method
Examine a possible summerization of
algebraic-semantics, and
Show its presupposition.
Introduce a distinction between object-language and
other things.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
5. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
‘WITH-IN’
Logic is not only inside the given system.
We can think from within inside the language.
(I would like to avoid demanding transcendental
elements.)
Satoru HANAD The Meaninglessness of Algebraic-Semantics
6. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
A Summarization
its Presuppositions
A possible summerization
A role of algebraic-semantics merely consists in
substituting algebraic equations and inequalities for
the axioms and rules of a given logical system.
(Algebraic-semantics is no more than a paraphrase
of LJ into algebra.)
Satoru HANAD The Meaninglessness of Algebraic-Semantics
7. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
A Summarization
its Presuppositions
→ - Right
α, β ⇒ γ
β ⇒ α → γ
(→ −Right)
The law of residuation
a ∧ b ≤ c ⇔ b ≤ (a → c)
No difference! ∴Algebraic-semantics does not explain the
meaning of logic?
Satoru HANAD The Meaninglessness of Algebraic-Semantics
8. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
A Summarization
its Presuppositions
McKinsey-Tarski’s Thm
LJ (/LDJ) is complete for Heyting Algebra composed of
the total of open sets (/Brouwer Algebra composed of
the total of closed sets).
Moreover,
finite model property
α is provable in LJ iff. α is tautology in finite arbitrary
Heyting algebra.
Then, we can get infinite number of models. And we do
not have any criteria to select which is the meaning.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
9. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
A Summarization
its Presuppositions
However, this criticism is based on naive
misunderstanding.
Presupposition
This semantics of the given system have to show
something about logical system, in addition to
completeness (and vice versa).
There is an order of values of systems and of their
semantics.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
10. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
(Look at a Figure)
distinction
Object-language is only a set of symbols and
operations.
Meta-language is language which we use and/or is
our linguistic activity.
There is outside of Meta-language, e.g. the ontic
world and the ontological world.
Remark
LJ and HA are seen as object-language.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
11. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
It is useful to compare the principle of bivalence with
Boolean Algebra with only 2 elements B(2).
Each of them is semantics of classical logic, so they are
of equal value as an object-language. But that criticism
might not attack the principle of bivalence.
Because the principle is not only inside object-language.
It connects language to the world.
the criticism mentioned aboved is category mistake.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
12. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
Conclusion
The meaning of logical system can be found in
meta-language and the world, which is outside of
object-language, by Rational Beings.
So every object-language has equal value.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
13. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
Start with a possible summerization.
Get some unacceptable conclusions.
Introduce a distinction between object-language and
other things.
Cancel the presupposition and get the conclusion.
Satoru HANAD The Meaninglessness of Algebraic-Semantics
14. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
Yet, it is not clear how to find meanings. How to get the
meaning is connected to next theme.
A Theme
In what way do knowledge and the world connect to each
of them.
After acquiring the view that there is no hierarchy and
meanings of logical systems, how do logics / the world /
knowledge look like?
Satoru HANAD The Meaninglessness of Algebraic-Semantics
15. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
Additional Refference
Komori, et Ono (2010) an Introduction to Modern
Mathematical Logic(“Gendai Suuri Ronnrigaku
Josetu”written in Japanese)
Aoyama, et al. (2007) Non-Classical Logics and
Algebraic-Models(“Hi-Koten Ronri to Daisuu
Moderu”written in Japanese)
Acknowledgements
Prof. Koji NAKATOGAWA(Hokkaido Univ.) and
Takuma IMAMURA(Toyama Univ. B4).
Satoru HANAD The Meaninglessness of Algebraic-Semantics
16. The
Meaninglessness
of Algebraic-
Semantics
Satoru HANAD
Outline
the Aim and the
Method
the Aim
the Method
Prologue
A summarization
and its
presuppositions
A Summarization
its Presuppositions
Object- / Meta-
Language and the
Worlds
Summary and
Further
Investigations
Outline
the Aim and the Method
Prologue
A summarization and its presuppositions
Object- / Meta- Language and the Worlds
Summary and Further Investigations
Thanks for your attention!
Satoru HANAD The Meaninglessness of Algebraic-Semantics