Difference between revisions of "Category"
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==Context== | ==Context== | ||
| + | * Whereas a [[Taxonomy]] tries to assign each entity to one and only one taxon, an [[Ontology]] or [[Category]] allows for any sort of overlap of entities into multiple categories. | ||
| + | * Categorization is a prerequisite of any debate. Most debates, however, wind up debating the meanings (or content) of the categories. | ||
| + | * Differing religions require a categorization to survive as described by Max<ref>S. Max ''Seeing Islam as Others Saw It- A Survey and Evaluation of Christian Jewish and Zoroastrian Writings on Early Islam'' https://www.academia.edu/31005715/Seeing_Islam_as_Others_Saw_It_A_Survey_and_Evaluation_of_Christian_Jewish_and_Zoroastrian_Writings_on_Early_Islam?email_work_card=view-paper</ref><blockquote>[In the late antiquity] period a considerable proportion of the apologetic writing seems to derive from real debate. This was particularly true in the early Abbasid era, when there were a number of propitious factors: the cosmopolitan nature of Baghdad and its province, the caliphs' patronage of scholarship, the emergence of Arabic as a ''lingua franca'' the universal deployment of '''dialectical reasoning based upon categorical definitions''', and the proliferation of converts and apostates, which meant that there were many with a genuine knowledge of two religions and with a real will to champion one over the other. But also, quite simply, there were matters that needed debating. Islam prompted questions that had not arisen before, such as "what were the attributes of a true prophet", and challenged long-cherished assumptions, such as that imperial ascendancy confirmed possession of truth. The latter point did put the non-Muslims on the defensive, especially the Christians and Zoroastrians, but for the Muslims too it was to be no easy contest. They were new at the game and entered the arena with only a weakly articulated confessional identity and an underdeveloped battery of doctrine, and it was thus particularly in the sectarian milieu of eighth and ninth-century Iraq that communal boundaries were staked out and dogmatic territories delineated.</blockquote> | ||
| − | + | ===Categorical Arguments=== | |
| − | + | [https://study.com/academy/lesson/categorical-arguments-definition-syllogisms-examples.html Categorical arguments] are logical arguments used to determine the category of an object or concept using a known classification of related or shared characteristics. They are constructed as a syllogism, a structured argument formed by two premises and a conclusion. Usually, the first presented statement is the major premise, while the second statement is the minor premise. The third statement is the conclusion. Consider this collection of '''Categorical Statements''' which taken together make a '''Categorical Argument'''. | |
| − | the | + | *Major Premise: All animals with fur are mammals. |
| − | + | *Minor Premise: All dogs have fur. | |
| − | + | *Conclusion: All dogs are mammals. | |
| − | + | Sometimes, a categorical argument can be a sentence, such as the following: ''If all animals with fur are mammals and all dogs have fur, then all dogs are mammals.'' The standard structure is an ''if-and-then'' statement. While we can apply logic to a simple if-then statement using a single premise and conclusion, it will not qualify as a categorical argument without two premises. | |
| − | + | ===Categorical Imperative=== | |
| − | the | + | A Categorical Statement that is taken as maxim that you would like all others to use as a basis for all of their actions, and perhaps even the basis for all of your actions as well. |
| − | + | ===Category Theory=== | |
| − | + | In Mathematics [[Category]] theory differs from graph theory in that it permits more than one edge from one vertex to another | |
| − | + | http://boole.stanford.edu/cs353/handouts/book4.pdf | |
| − | + | ||
| − | + | ==Problems== | |
| − | and the | + | * Categorization is often use by one group to exclude others who are not like themselves. |
| − | + | * Since there is no predetermined clear definition for most categories, the meaning of the category can morph over time to meet the goals any position what-so-ever. | |
| − | + | ||
| − | + | ===Quantum Theory=== | |
| − | + | The Category Problem <ref>Jacob Barandes, ''New Foundations for Quantum Theory'' 2024-03-04 https://www.youtube.com/watch?v=dB16TzHFvj0</ref> | |
| − | + | * The textbook axioms contain a profound problem. On the one hand, scientists talk about various phenomena physically happening, perhaps according to probabilistic laws | |
| − | + | ** Ornithologists talk about birds exhibiting foraging behavior | |
| − | + | ** Early-universe cosmologists talk about primordial gases mixing | |
| − | there | + | ** Microbiologists talk about DNA replicating, etc. |
| − | + | ** Often one works with statistical averages over such phenomena happening as in classical physics. | |
| − | + | ** For example if you can assign exact trajectories of a particle undergoing Brownian motion in a fluid, then one can compute the statistical averages over the trajectory. | |
| − | + | * On the other hand, according to the textbook axioms, quantum theory is an instrumentalist recipe that narrowly predict only: | |
| − | a | + | ** measurement outcomes |
| − | + | ** measurement-outcome probabilities | |
| − | + | ** expectation values defined as statistical averages of measurement outcomes weighted by measurement outcome probabilities | |
| − | + | * So the only outputs are narrowly about measurement outcomes alone, NOT about general phenomena happening. | |
| − | with | + | * Unless one changes the axioms, there is a conceptual gap here between one category (phenomena happening, birds foraging, early-universe-cosmology gases mixing) and another (sub?)category of measurement outcomes. And its simply a category error to contuse these two things. |
| − | a | + | * This dilemma is the category problem. In particular, it would be a category error to confuse 'happening averages' with 'measurement-outcome averages' - i.e. quantum-theoretic expectation values. |
| − | + | ||
| − | + | *The Category Problem and Expectation Values | |
| − | the | + | ** In particular, it would be a category error to confuse 'happening averages' (X happening) with 'measurement-outcome averages' (X measurement) — i.e., quantum-theoretic expectation values |
| − | other | + | ** In other words, just because these two quantities are both in (brackets), and may sometimes have approximately the same numerical value for certain choices of the symbol X, that doesn't mean they're physically the same categorical kind of thing! |
| − | + | ** And yet this elision between (X happening) and (X measurement) is implicit and pervasive in textbooks and the research literature, from condensed-matter physics to quantum gravity. | |
| − | + | ||
| − | + | The Measurement Problem | |
| − | + | *Activating the theory's measurement-outcome predictions requires saying "poof" at some point and magically invoking a 'measurement,' which the textbook axioms don't define | |
| − | + | *On the one hand, if one doesn't invoke the measurement axioms, then there is no connection with physical reality | |
| − | + | ** Mathematical symbols written on paper are no more physically real than Magritte's famous "pipe" or Korzybski's '"maps"! | |
| − | + | * On the other hand, choosing to invoke the measurement axioms depends on making a subjective decision about when a 'measurement' has happened, meaning that one outcome is singled ;out for collapse, with in-principle empirical consequences | |
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| − | + | ==References== | |
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Latest revision as of 20:42, 7 December 2024
Contents
Full Title or Meme
A category is a group of ideas collected under a common heading.
Context
- Whereas a Taxonomy tries to assign each entity to one and only one taxon, an Ontology or Category allows for any sort of overlap of entities into multiple categories.
- Categorization is a prerequisite of any debate. Most debates, however, wind up debating the meanings (or content) of the categories.
- Differing religions require a categorization to survive as described by Max[1]
[In the late antiquity] period a considerable proportion of the apologetic writing seems to derive from real debate. This was particularly true in the early Abbasid era, when there were a number of propitious factors: the cosmopolitan nature of Baghdad and its province, the caliphs' patronage of scholarship, the emergence of Arabic as a lingua franca the universal deployment of dialectical reasoning based upon categorical definitions, and the proliferation of converts and apostates, which meant that there were many with a genuine knowledge of two religions and with a real will to champion one over the other. But also, quite simply, there were matters that needed debating. Islam prompted questions that had not arisen before, such as "what were the attributes of a true prophet", and challenged long-cherished assumptions, such as that imperial ascendancy confirmed possession of truth. The latter point did put the non-Muslims on the defensive, especially the Christians and Zoroastrians, but for the Muslims too it was to be no easy contest. They were new at the game and entered the arena with only a weakly articulated confessional identity and an underdeveloped battery of doctrine, and it was thus particularly in the sectarian milieu of eighth and ninth-century Iraq that communal boundaries were staked out and dogmatic territories delineated.
Categorical Arguments
Categorical arguments are logical arguments used to determine the category of an object or concept using a known classification of related or shared characteristics. They are constructed as a syllogism, a structured argument formed by two premises and a conclusion. Usually, the first presented statement is the major premise, while the second statement is the minor premise. The third statement is the conclusion. Consider this collection of Categorical Statements which taken together make a Categorical Argument.
- Major Premise: All animals with fur are mammals.
- Minor Premise: All dogs have fur.
- Conclusion: All dogs are mammals.
Sometimes, a categorical argument can be a sentence, such as the following: If all animals with fur are mammals and all dogs have fur, then all dogs are mammals. The standard structure is an if-and-then statement. While we can apply logic to a simple if-then statement using a single premise and conclusion, it will not qualify as a categorical argument without two premises.
Categorical Imperative
A Categorical Statement that is taken as maxim that you would like all others to use as a basis for all of their actions, and perhaps even the basis for all of your actions as well.
Category Theory
In Mathematics Category theory differs from graph theory in that it permits more than one edge from one vertex to another http://boole.stanford.edu/cs353/handouts/book4.pdf
Problems
- Categorization is often use by one group to exclude others who are not like themselves.
- Since there is no predetermined clear definition for most categories, the meaning of the category can morph over time to meet the goals any position what-so-ever.
Quantum Theory
The Category Problem [2]
- The textbook axioms contain a profound problem. On the one hand, scientists talk about various phenomena physically happening, perhaps according to probabilistic laws
- Ornithologists talk about birds exhibiting foraging behavior
- Early-universe cosmologists talk about primordial gases mixing
- Microbiologists talk about DNA replicating, etc.
- Often one works with statistical averages over such phenomena happening as in classical physics.
- For example if you can assign exact trajectories of a particle undergoing Brownian motion in a fluid, then one can compute the statistical averages over the trajectory.
- On the other hand, according to the textbook axioms, quantum theory is an instrumentalist recipe that narrowly predict only:
- measurement outcomes
- measurement-outcome probabilities
- expectation values defined as statistical averages of measurement outcomes weighted by measurement outcome probabilities
- So the only outputs are narrowly about measurement outcomes alone, NOT about general phenomena happening.
- Unless one changes the axioms, there is a conceptual gap here between one category (phenomena happening, birds foraging, early-universe-cosmology gases mixing) and another (sub?)category of measurement outcomes. And its simply a category error to contuse these two things.
- This dilemma is the category problem. In particular, it would be a category error to confuse 'happening averages' with 'measurement-outcome averages' - i.e. quantum-theoretic expectation values.
- The Category Problem and Expectation Values
- In particular, it would be a category error to confuse 'happening averages' (X happening) with 'measurement-outcome averages' (X measurement) — i.e., quantum-theoretic expectation values
- In other words, just because these two quantities are both in (brackets), and may sometimes have approximately the same numerical value for certain choices of the symbol X, that doesn't mean they're physically the same categorical kind of thing!
- And yet this elision between (X happening) and (X measurement) is implicit and pervasive in textbooks and the research literature, from condensed-matter physics to quantum gravity.
The Measurement Problem
- Activating the theory's measurement-outcome predictions requires saying "poof" at some point and magically invoking a 'measurement,' which the textbook axioms don't define
- On the one hand, if one doesn't invoke the measurement axioms, then there is no connection with physical reality
- Mathematical symbols written on paper are no more physically real than Magritte's famous "pipe" or Korzybski's '"maps"!
- On the other hand, choosing to invoke the measurement axioms depends on making a subjective decision about when a 'measurement' has happened, meaning that one outcome is singled ;out for collapse, with in-principle empirical consequences
References
- ↑ S. Max Seeing Islam as Others Saw It- A Survey and Evaluation of Christian Jewish and Zoroastrian Writings on Early Islam https://www.academia.edu/31005715/Seeing_Islam_as_Others_Saw_It_A_Survey_and_Evaluation_of_Christian_Jewish_and_Zoroastrian_Writings_on_Early_Islam?email_work_card=view-paper
- ↑ Jacob Barandes, New Foundations for Quantum Theory 2024-03-04 https://www.youtube.com/watch?v=dB16TzHFvj0
