Reorganize ontology/RDF/XML.
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@ -967,7 +967,7 @@
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"_journal/2024-11/2024-11-20.md": "951b6034d60a40dbd8201c50abf0dbb9",
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"_journal/2024-11/2024-11-19.md": "d879f57154cb27cb168eb1f1f430e312",
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"set/cardinality.md": "270b48a3559c055cb15216f70101ecc2",
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"geometry/area.md": "dc362cb5be314b2b9e4ecc53f2289af0",
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"geometry/area.md": "7f947bb5ac782495a1fb4a63bb2463e7",
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"_journal/2024-11-23.md": "911f82ab8aede5ecdb96493aef64b0b9",
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"_journal/2024-11/2024-11-22.md": "51117030e2364dbce3a8d507dead86ae",
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"_journal/2024-11-24.md": "225661114ad1b605132873e83acdf777",
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@ -8,5 +8,5 @@ title: "2024-07-28"
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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* Initial notes on [[ontology/rdf/index|RDF]].
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* Initial notes on [[rdf|RDF]].
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* Notes and flashcards on [[uri|URIs]].
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@ -7,3 +7,6 @@ title: "2024-12-12"
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- [x] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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* Notes on monotone property of area.
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* Initial proofs on some properties of integrals of step functions.
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Before Width: | Height: | Size: 18 KiB After Width: | Height: | Size: 18 KiB |
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@ -1,9 +1,8 @@
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---
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title: RDF
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TARGET DECK: Obsidian::STEM
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FILE TAGS: ontology::rdf
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FILE TAGS: rdf
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tags:
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- ontology
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- rdf
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---
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@ -3,7 +3,6 @@ title: Uniform Resource Identifiers
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TARGET DECK: Obsidian::STEM
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FILE TAGS: uri
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tags:
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- rdf
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- uri
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---
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@ -189,6 +189,98 @@ Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Int
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<!--ID: 1732381333365-->
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END%%
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This property lets us prove $\varnothing$ is measurable with the expected area: $$a(\varnothing) = a(T - T) = a(T) - a(T) = 0$$
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%%ANKI
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Basic
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Is the empty set considered measurable?
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Back: Yes.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716384-->
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END%%
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%%ANKI
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Basic
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Which axiom of area is used to prove $\varnothing$ is measurable?
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Back: The difference property.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716403-->
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END%%
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%%ANKI
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Basic
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What does $a(\varnothing)$ evaluate to?
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Back: $0$
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716406-->
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END%%
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%%ANKI
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Basic
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What chain of equalities is used to prove that $a(\varnothing) = 0$?
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Back: For any $T \in \mathscr{M}$, $a(\varnothing) = a(T - T) = a(T) - a(T) = 0$.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716410-->
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END%%
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This property also lets us state the **monotone property**: $$\forall S, T \in \mathscr{M}, S \subseteq T \Rightarrow a(S) \leq a(T)$$
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%%ANKI
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Basic
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What does the monotone property of area state in FOL?
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Back: $\forall S, T \in \mathscr{M}, S \subseteq T \Rightarrow a(S) \leq a(T)$
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716414-->
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END%%
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%%ANKI
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Basic
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What name is given to the following property? $$\forall S, T \in \mathscr{M}, S \subseteq T \Rightarrow a(S) \leq a(T)$$
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Back: The monotone property.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013767208-->
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END%%
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%%ANKI
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Basic
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Which axiom(s) of area are used to prove the monotone property?
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Back: The nonnegative and difference properties.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716417-->
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END%%
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%%ANKI
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Basic
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Let $S, T \in \mathscr{M}$ such that $S \subseteq T$. Why is the difference property needed to show $a(T - S) \geq 0$?
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Back: It states $T - S$ is measurable.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716421-->
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END%%
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%%ANKI
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Basic
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Let $S, T \in \mathscr{M}$ such that $S \subseteq T$. Why is the difference property needed to show $a(S - T) \geq 0$?
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Back: N/A. The difference property says nothing about $S - T$.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716426-->
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END%%
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%%ANKI
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Basic
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Let $S, T \in \mathscr{M}$ such that $T \subseteq S$. Why is the difference property needed to show $a(S - T) \geq 0$?
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Back: It states $S - T$ is measurable.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716430-->
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END%%
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%%ANKI
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Basic
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Let $S, T \in \mathscr{M}$ such that $S \subseteq T$. Why is the nonnegative property needed to show $a(T - S) \geq 0$?
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Back: It states the area of any measurable set is $\geq 0$.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1734013716434-->
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END%%
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### Invariance Under Congruence
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If $S \in \mathscr{M}$ and $T$ is congruent to $S$, then $T \in \mathscr{M}$ and $a(S) = a(T)$.
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@ -1,3 +1,124 @@
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---
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title: Ontology
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TARGET DECK: Obsidian::H&SS
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FILE TAGS: ontology
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tags:
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- ontology
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---
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## Overview
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Ontology is the philosophical study of being. Generally *things* are split into two broad categories: **abstract** and **concrete** things. These words are "terms of art" and their definition is not standardized in any way.
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%%ANKI
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Basic
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What did Quine declare as *the* ontological question?
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Back: "What is there?"
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Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009).
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<!--ID: 1720912238054-->
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END%%
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%%ANKI
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Basic
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Who is attributed *the* ontological question?
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Back: Willard Van Orman Quine.
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Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009).
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<!--ID: 1720912259767-->
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END%%
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%%ANKI
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Cloze
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{Ontology} is the {philosophical study of being}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720912238058-->
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END%%
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%%ANKI
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Cloze
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{Epistemology} is the {philosophical study of knowledge}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720912238062-->
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END%%
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%%ANKI
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Cloze
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{Taxonomy} is the {branch of science concerned with categorization}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720912238066-->
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END%%
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%%ANKI
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Cloze
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{Mereology} is the {philosophical study of part-whole relationships}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720998380912-->
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END%%
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%%ANKI
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Basic
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What does Effingham mean when saying "concreta" and "abstracta" are terms of art?
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Back: They are terms defined freely by a person to mean whatever one wants.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782942-->
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END%%
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%%ANKI
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Cloze
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In general, ontologists often categorize things as either {concreta} or {abstracta}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782951-->
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END%%
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%%ANKI
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Basic
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Generally speaking, what does someone *probably* mean by "concrete" things?
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Back: Things that exists in space and/or time.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782957-->
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END%%
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%%ANKI
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Basic
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Generally speaking, what does someone *probably* mean by "abstract" things?
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Back: Things that exist in neither space nor time.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782965-->
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END%%
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%%ANKI
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Basic
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Is a material object considered concreta?
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Back: Usually.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782971-->
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END%%
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%%ANKI
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Basic
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Is an immaterial object considered concreta?
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Back: Possibly.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782978-->
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END%%
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%%ANKI
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Basic
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Is a material object considered abstracta?
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Back: Not usually.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782984-->
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END%%
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%%ANKI
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Basic
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Is an immaterial object considered abstracta?
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Back: Possibly.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782989-->
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END%%
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## Bibliography
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* Francesco Orilia and Michele Paolini Paoletti, “Properties,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/properties/](https://plato.stanford.edu/archives/spr2022/entries/properties/).
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* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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* Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009).
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@ -1,124 +0,0 @@
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---
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title: Ontology
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TARGET DECK: Obsidian::H&SS
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FILE TAGS: ontology::philosophy
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tags:
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- ontology
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---
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## Overview
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Ontology is the philosophical study of being. Generally *things* are split into two broad categories: **abstract** and **concrete** things. These words are "terms of art" and their definition is not standardized in any way.
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%%ANKI
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Basic
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What did Quine declare as *the* ontological question?
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Back: "What is there?"
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Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009).
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<!--ID: 1720912238054-->
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END%%
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%%ANKI
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Basic
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Who is attributed *the* ontological question?
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Back: Willard Van Orman Quine.
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Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009).
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<!--ID: 1720912259767-->
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END%%
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%%ANKI
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Cloze
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{Ontology} is the {philosophical study of being}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720912238058-->
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END%%
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%%ANKI
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Cloze
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{Epistemology} is the {philosophical study of knowledge}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720912238062-->
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END%%
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%%ANKI
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Cloze
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{Taxonomy} is the {branch of science concerned with categorization}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720912238066-->
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END%%
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%%ANKI
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Cloze
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{Mereology} is the {philosophical study of part-whole relationships}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720998380912-->
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END%%
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%%ANKI
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Basic
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What does Effingham mean when saying "concreta" and "abstracta" are terms of art?
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Back: They are terms defined freely by a person to mean whatever one wants.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782942-->
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END%%
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%%ANKI
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Cloze
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In general, ontologists often categorize things as either {concreta} or {abstracta}.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782951-->
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END%%
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%%ANKI
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Basic
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Generally speaking, what does someone *probably* mean by "concrete" things?
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Back: Things that exists in space and/or time.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782957-->
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END%%
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%%ANKI
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Basic
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Generally speaking, what does someone *probably* mean by "abstract" things?
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Back: Things that exist in neither space nor time.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782965-->
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END%%
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%%ANKI
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Basic
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Is a material object considered concreta?
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Back: Usually.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782971-->
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END%%
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%%ANKI
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Basic
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Is an immaterial object considered concreta?
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Back: Possibly.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782978-->
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END%%
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%%ANKI
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Basic
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Is a material object considered abstracta?
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Back: Not usually.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782984-->
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END%%
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%%ANKI
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Basic
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Is an immaterial object considered abstracta?
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Back: Possibly.
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Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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<!--ID: 1720894782989-->
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END%%
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## Bibliography
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* Francesco Orilia and Michele Paolini Paoletti, “Properties,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/properties/](https://plato.stanford.edu/archives/spr2022/entries/properties/).
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* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).
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* Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009).
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---
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title: Properties
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TARGET DECK: Obsidian::H&SS
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FILE TAGS: ontology::philosophy
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FILE TAGS: ontology
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tags:
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- ontology
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---
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