diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index 4670b91..a375f96 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -967,7 +967,7 @@ "_journal/2024-11/2024-11-20.md": "951b6034d60a40dbd8201c50abf0dbb9", "_journal/2024-11/2024-11-19.md": "d879f57154cb27cb168eb1f1f430e312", "set/cardinality.md": "270b48a3559c055cb15216f70101ecc2", - "geometry/area.md": "dc362cb5be314b2b9e4ecc53f2289af0", + "geometry/area.md": "7f947bb5ac782495a1fb4a63bb2463e7", "_journal/2024-11-23.md": "911f82ab8aede5ecdb96493aef64b0b9", "_journal/2024-11/2024-11-22.md": "51117030e2364dbce3a8d507dead86ae", "_journal/2024-11-24.md": "225661114ad1b605132873e83acdf777", diff --git a/notes/_journal/2024-07/2024-07-28.md b/notes/_journal/2024-07/2024-07-28.md index 4fa0fe3..c468b70 100644 --- a/notes/_journal/2024-07/2024-07-28.md +++ b/notes/_journal/2024-07/2024-07-28.md @@ -8,5 +8,5 @@ title: "2024-07-28" - [ ] Sheet Music (10 min.) - [ ] Korean (Read 1 Story) -* Initial notes on [[ontology/rdf/index|RDF]]. +* Initial notes on [[rdf|RDF]]. * Notes and flashcards on [[uri|URIs]]. \ No newline at end of file diff --git a/notes/_journal/2024-12-12.md b/notes/_journal/2024-12-12.md index 6e1ffa5..a4debcc 100644 --- a/notes/_journal/2024-12-12.md +++ b/notes/_journal/2024-12-12.md @@ -6,4 +6,7 @@ title: "2024-12-12" - [x] KoL - [x] OGS - [ ] Sheet Music (10 min.) -- [ ] Korean (Read 1 Story) \ No newline at end of file +- [ ] Korean (Read 1 Story) + +* Notes on monotone property of area. +* Initial proofs on some properties of integrals of step functions. \ No newline at end of file diff --git a/notes/ontology/rdf/images/triple-table-repr.png b/notes/encoding/images/triple-table-repr.png similarity index 100% rename from notes/ontology/rdf/images/triple-table-repr.png rename to notes/encoding/images/triple-table-repr.png diff --git a/notes/ontology/rdf/index.md b/notes/encoding/rdf.md similarity index 98% rename from notes/ontology/rdf/index.md rename to notes/encoding/rdf.md index 3fef104..f11f9f6 100644 --- a/notes/ontology/rdf/index.md +++ b/notes/encoding/rdf.md @@ -1,9 +1,8 @@ --- title: RDF TARGET DECK: Obsidian::STEM -FILE TAGS: ontology::rdf +FILE TAGS: rdf tags: - - ontology - rdf --- diff --git a/notes/ontology/rdf/uri.md b/notes/encoding/uri.md similarity index 99% rename from notes/ontology/rdf/uri.md rename to notes/encoding/uri.md index 60a5843..d80f0b3 100644 --- a/notes/ontology/rdf/uri.md +++ b/notes/encoding/uri.md @@ -3,7 +3,6 @@ title: Uniform Resource Identifiers TARGET DECK: Obsidian::STEM FILE TAGS: uri tags: - - rdf - uri --- diff --git a/notes/ontology/xml.md b/notes/encoding/xml.md similarity index 100% rename from notes/ontology/xml.md rename to notes/encoding/xml.md diff --git a/notes/geometry/area.md b/notes/geometry/area.md index 13b116f..c116472 100644 --- a/notes/geometry/area.md +++ b/notes/geometry/area.md @@ -189,6 +189,98 @@ Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Int END%% +This property lets us prove $\varnothing$ is measurable with the expected area: $$a(\varnothing) = a(T - T) = a(T) - a(T) = 0$$ + +%%ANKI +Basic +Is the empty set considered measurable? +Back: Yes. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Which axiom of area is used to prove $\varnothing$ is measurable? +Back: The difference property. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What does $a(\varnothing)$ evaluate to? +Back: $0$ +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What chain of equalities is used to prove that $a(\varnothing) = 0$? +Back: For any $T \in \mathscr{M}$, $a(\varnothing) = a(T - T) = a(T) - a(T) = 0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +This property also lets us state the **monotone property**: $$\forall S, T \in \mathscr{M}, S \subseteq T \Rightarrow a(S) \leq a(T)$$ + +%%ANKI +Basic +What does the monotone property of area state in FOL? +Back: $\forall S, T \in \mathscr{M}, S \subseteq T \Rightarrow a(S) \leq a(T)$ +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What name is given to the following property? $$\forall S, T \in \mathscr{M}, S \subseteq T \Rightarrow a(S) \leq a(T)$$ +Back: The monotone property. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Which axiom(s) of area are used to prove the monotone property? +Back: The nonnegative and difference properties. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Let $S, T \in \mathscr{M}$ such that $S \subseteq T$. Why is the difference property needed to show $a(T - S) \geq 0$? +Back: It states $T - S$ is measurable. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Let $S, T \in \mathscr{M}$ such that $S \subseteq T$. Why is the difference property needed to show $a(S - T) \geq 0$? +Back: N/A. The difference property says nothing about $S - T$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Let $S, T \in \mathscr{M}$ such that $T \subseteq S$. Why is the difference property needed to show $a(S - T) \geq 0$? +Back: It states $S - T$ is measurable. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Let $S, T \in \mathscr{M}$ such that $S \subseteq T$. Why is the nonnegative property needed to show $a(T - S) \geq 0$? +Back: It states the area of any measurable set is $\geq 0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + ### Invariance Under Congruence If $S \in \mathscr{M}$ and $T$ is congruent to $S$, then $T \in \mathscr{M}$ and $a(S) = a(T)$. diff --git a/notes/ontology/philosophy/dialetheism.md b/notes/ontology/dialetheism.md similarity index 100% rename from notes/ontology/philosophy/dialetheism.md rename to notes/ontology/dialetheism.md diff --git a/notes/ontology/index.md b/notes/ontology/index.md index 2d13cf3..381d2bb 100644 --- a/notes/ontology/index.md +++ b/notes/ontology/index.md @@ -1,3 +1,124 @@ --- title: Ontology +TARGET DECK: Obsidian::H&SS +FILE TAGS: ontology +tags: + - ontology --- + +## Overview + +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. + +%%ANKI +Basic +What did Quine declare as *the* ontological question? +Back: "What is there?" +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). + +END%% + +%%ANKI +Basic +Who is attributed *the* ontological question? +Back: Willard Van Orman Quine. +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). + +END%% + +%%ANKI +Cloze +{Ontology} is the {philosophical study of being}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +{Epistemology} is the {philosophical study of knowledge}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +{Taxonomy} is the {branch of science concerned with categorization}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +{Mereology} is the {philosophical study of part-whole relationships}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +What does Effingham mean when saying "concreta" and "abstracta" are terms of art? +Back: They are terms defined freely by a person to mean whatever one wants. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +In general, ontologists often categorize things as either {concreta} or {abstracta}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Generally speaking, what does someone *probably* mean by "concrete" things? +Back: Things that exists in space and/or time. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Generally speaking, what does someone *probably* mean by "abstract" things? +Back: Things that exist in neither space nor time. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is a material object considered concreta? +Back: Usually. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is an immaterial object considered concreta? +Back: Possibly. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is a material object considered abstracta? +Back: Not usually. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is an immaterial object considered abstracta? +Back: Possibly. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +## Bibliography + +* 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/). +* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). +* 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). \ No newline at end of file diff --git a/notes/ontology/philosophy/nominalism.md b/notes/ontology/nominalism.md similarity index 100% rename from notes/ontology/philosophy/nominalism.md rename to notes/ontology/nominalism.md diff --git a/notes/ontology/philosophy/permissivism.md b/notes/ontology/permissivism.md similarity index 100% rename from notes/ontology/philosophy/permissivism.md rename to notes/ontology/permissivism.md diff --git a/notes/ontology/philosophy/index.md b/notes/ontology/philosophy/index.md deleted file mode 100644 index b3d613d..0000000 --- a/notes/ontology/philosophy/index.md +++ /dev/null @@ -1,124 +0,0 @@ ---- -title: Ontology -TARGET DECK: Obsidian::H&SS -FILE TAGS: ontology::philosophy -tags: - - ontology ---- - -## Overview - -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. - -%%ANKI -Basic -What did Quine declare as *the* ontological question? -Back: "What is there?" -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). - -END%% - -%%ANKI -Basic -Who is attributed *the* ontological question? -Back: Willard Van Orman Quine. -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). - -END%% - -%%ANKI -Cloze -{Ontology} is the {philosophical study of being}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -{Epistemology} is the {philosophical study of knowledge}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -{Taxonomy} is the {branch of science concerned with categorization}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -{Mereology} is the {philosophical study of part-whole relationships}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -What does Effingham mean when saying "concreta" and "abstracta" are terms of art? -Back: They are terms defined freely by a person to mean whatever one wants. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -In general, ontologists often categorize things as either {concreta} or {abstracta}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Generally speaking, what does someone *probably* mean by "concrete" things? -Back: Things that exists in space and/or time. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Generally speaking, what does someone *probably* mean by "abstract" things? -Back: Things that exist in neither space nor time. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is a material object considered concreta? -Back: Usually. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is an immaterial object considered concreta? -Back: Possibly. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is a material object considered abstracta? -Back: Not usually. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is an immaterial object considered abstracta? -Back: Possibly. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -## Bibliography - -* 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/). -* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). -* 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). \ No newline at end of file diff --git a/notes/ontology/philosophy/properties.md b/notes/ontology/properties.md similarity index 98% rename from notes/ontology/philosophy/properties.md rename to notes/ontology/properties.md index 1de65bd..d23293f 100644 --- a/notes/ontology/philosophy/properties.md +++ b/notes/ontology/properties.md @@ -1,7 +1,7 @@ --- title: Properties TARGET DECK: Obsidian::H&SS -FILE TAGS: ontology::philosophy +FILE TAGS: ontology tags: - ontology ---