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Metafísica y Persona. Filosofía, conocimiento y vida
Año 16, Núm. 31, Enero-Junio, 2024, ISSN: 2007-9699
On Sommersian Concept Analysis
Sobre el análisis sommersiano de conceptos
UPAEP Universidad, México
josemartin.castro@upaep.mx
In this contribution we explore in what sense Sommers’ tree theory, a novel philoso-
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En esta contribución exploramos en qué sentido la teoría arborescente de Sommers,
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Introduction
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1
Metafísica y persona. Filosofía, conocimiento y vida
Año 16, Núm. 31, Enero-Junio, 2024, ISSN: 2007-9699
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decade of development, its connection with philosophy became clearer.
2
discipline with cultural import insofar as it is able to assist our rational com-
-
3
-
-
-
in The Concept of MindGedankenexperiment to
-
4
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In a seminal paper entitled The Ordinary Language Tree, Fred Sommers in-
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5
2
, Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies, pp.
, Formal Concept Analysis...
4
5
27
On Sommersian Concept Analysis
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1. Formal Concept Analysis
-
-
the superconcept. Formally, this can described with the aid of a formal con-
A formal context is a structure K = <G, M, I> where G and M are sets, and I
⊆ G x MG, and MGegenstände-
MerkmalegImg, m∈ I
gm
X ⊆ G and Y ⊆ M :
X →X
I
:= {m ∈ M |gIm for all g ∈ X}
Y →Y
I
:= {g ∈ G |gIm for all m ∈ Y }
A, B
such that A ⊆ G, B ⊆ M, A = B
I
, and B = A
I
A and B are called the extent and
A, B-
A
1
, B
1
≤ A
2
, B
2
⇐⇒ A
1
⊆ A
2
⇐⇒ B
1
⊇ B
2
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Metafísica y persona. Filosofía, conocimiento y vida
Año 16, Núm. 31, Enero-Junio, 2024, ISSN: 2007-9699
Aristotle x x x
x x x
Fred Sommers x x x
x x x
x x x
Edith Stein x x x
x x x
x x x
4. Smart
Aristotle, G. Ryle, F. Sommers, R. Wille, S. Weil, E. Stein, H. Arendt, S.
Kovalevskaya.
7. Male, Mathematician, Smart 9. Female, Mathematician, Smart
0. Male, Female, Mathematician, Philosopher, Smart
1. Male, Philosopher, Smart 6. Female, Philosopher, Smart
2. Male, Smart7. Mathematician, Smart
8. Female, Smart
5. Philosopher, Smart
R. Wille
S. Kovalevskaya Aristotle, G. Ryle, F. Sommers S. Weil, E. Stein, H. Arendt
Aristotle, G. Ryle, F. Sommers, R. WilleR. Wille, S. Kovalevskaya
S. Weil, E. Stein, H. Arendt,
S. Kovalevskaya
Aristotle, G. Ryle, F. Sommers, S. Weil,
E. Stein, H. Arendt
29
On Sommersian Concept Analysis
2. Sommers’ tree theory
6
in order to understand the structure of lan-
-
-
term is said to span such an individual.
For example, red spans Aristotle, a car or a wall, but it does not span num-
ber π
nonred spans
whatever red spans, and it fails to span whatever red fails to span: π can-
T| to
indicate the absolute value of a term T, as in mathematics, |red| would be
either rednonred
red-
-
-
6
, Robust Reality: An Essay in Formal Ontology
Metafísica y persona. Filosofía, conocimiento y vida
Año 16, Núm. 31, Enero-Junio, 2024, ISSN: 2007-9699
30
connected terms.
-
would be transitivity: any two terms U-related to a third must be U-related to
per-
son and prime, both of which are U-related to interesting but are not U-related
to each other.
then at least one of them must be included in the other. As an example, sup-
B| and |C|, and the third
term, to which they are both U-related, is |A
Now let |D
terms, say |B|, but N-related to |AE|, that
is U-related to |D| but not to |A|:
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31
On Sommersian Concept Analysis
red
the same type.
First, consider a bona de example:
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Metafísica y persona. Filosofía, conocimiento y vida
Año 16, Núm. 31, Enero-Junio, 2024, ISSN: 2007-9699
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3. Sommersian Concept Analysis
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Example 1:
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3. Interesting, Person, Theorem
2. Interesting
1. Interesting, Person
3. Interesting, Theorem
Sor Juana, Juan Orol,
Sor Juana, Juan Orol,
Binomial Theorem
33
On Sommersian Concept Analysis
Example 2:
to intension
Example 3:
2. Behavior, Person, Brain
3. Mass
0. Malice
1. Malice, Mass
Person, Brain
Behavior, Person
Person
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with respect to extension
Male| and |FemaleMale| and |Fe-
male|, and |Philosopher| and |Mathematician
Philosopher
1
| and |Philosopher
2
-
4. Smart
Aristotle, G. Ryle, F. Sommers, R. Wille, S. Weil, E. Stein, H. Arendt,
S. Kovalevskaya.
7. Male, Mathematician, Smart
9. Female, Mathematician, Smart
0. Male, Female, Mathematician, Philosopher, Smart
1. Male, Philosopher, Smart
6. Female, Philosopher, Smart
2. Male, Smart7. Mathematician, Smart 8. Female, Smart 5. Philosopher, Smart
R. Wille
S. Kovalevskaya
Aristotle, G. Ryle, F. Sommers
S. Weil, E. Stein, H. Arendt
Aristotle, G. Ryle, F. Sommers, R. Wille
R. Wille, S. Kovalevskaya
S. Weil, E. Stein, H. Arendt,
S. Kovalevskaya
Aristotle, G. Ryle, F. Sommers,
S. Weil, E. Stein, H. Arendt
35
On Sommersian Concept Analysis
Finally, consider another example:
Example 4:
-
ConjectureC
T(C)
be the concept tree associated to C, then if T(C)C
has an Eulerian path.
4. Interesting
2. Old, Interesting
3. Old, Interesting, Theory 1. Human, Old, Interesting 5. Interesting, Even, Prime
0. Human, Old, Interesting, Theory, Prime
Aristotle, Frege, Relativity, Darwinism, 2, 3
Aristotle, Frege, Relativity, Darwinism
Relativity, Darwinism Aristotle, Frege
2, 3
Metafísica y persona. Filosofía, conocimiento y vida
Año 16, Núm. 31, Enero-Junio, 2024, ISSN: 2007-9699
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desideratum
Concluding remarks
In this contribution we explored in what sense Sommers’ tree theory could
-
meantime, let us reconsider our intuitions about predicables and concepts.
References
, Medieval Logic: An Outline of Its Development from 1250 to c.
1400,
, On Metaphysics
, Bare Facts and Naked Truths: A New Correspondence Theory
of Truth
, Robust Reality: An Essay in Formal Ontology,
, Der Auau der realen Welt: Grundriß der allgemeinen Katego-
rienlehre
and , Substance Among Other Categories -
, Time and Modes of Being
, I., Ontological Investigations: An Inquiry into the Categories of Nature,
Man and Society
, E.J., The Four-Category Ontology: A Metaphysical Foundation for Natural
Science
, The Concept of Mind
Mind
, Formal Concept Analysis as Mathematical Theory of Concepts and Con-
cept Hierarchies
,
of concepts, in Ivan Rival, editor, Ordered Sets
