View source for Ontology:Q22,28

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== Core characteristics ==

<dl class="wikitable hue">
{{HueClaim |P=item type| {{Template:S1}} }}
{{HueRoster|EP=PPPA/L|lang=en| {{E:Q22,28}} | {{E:Q22,28/HZ}} | [[E:determinism (physics)]] }}  <!-- en: necessity (physics) -->
{{HueRoster|EP=PPPA|lang=en| [[E:lambda-calculus determinism|lambda-calculus determinism]] | mathematical function determinism | necessity (process of individual things being determined by laws of behavior and surrounding conditions) }}
{{HueRoster|EP=P42| -- }}
{{HueRoster|EP=P42/BB| -- }}  <!-- en: shares thematic block -->
{{HueRoster|EP=P34| -- }}
{{HueRoster|EP=P4| -- }}  <!-- en: case of -->
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== Wavebuilder combinations ==

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{{WaveBuildNone| {{E:Q22,28}} | -- | -- }}  <!-- en: Along With, Produces  ??  ?? -->
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=== Wavebuilder characterizations ===

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{{WaveRoute| -- | -- | {{E:Q22,28}} }}  <!-- en: From  ??  ?? -->
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== Background ==

Between philosophy and the sciences, the word "determinism" can refer to very different things. Philosophy typically assumes that determinism is a question which cannot be empirically characterized and things must be described as [[E:absolute determinism|determined]] or [[E:Free will|un-determined]] before there is any theory of how to know that. Mathematics and physics have more fine-grained ways of describing determinism. For any specific object, such as a [[E:twenty-sided die|twenty-sided die]], it is possible to use mathematics to enumerate {{em|how}} predictable or unpredictable the object is. For instance, one could roll a die to write down a sequence of numbers and term the sequence of numbers <dfn>pseudo-random</dfn>. The real die is <dfn>actually random</dfn>, but read the same set of die results over and over starting over at the beginning, and the term that would come to mind is that it is simply <dfn>uncorrelated</dfn> on a statistical plot or line graph of numbers in the same sense a pseudo-random number generator is. Another way to mathematically characterize the die would be to create a detailed physics model of an plastic icosahedron falling onto a table, such that it would be possible to render a die coming up randomly as a computer-generated image. This model would not tell you exactly what face {{em|your}} die will land on, but it would have a lot to say about the general process of {{em|any}} die landing on {{em|any}} face. This "[[E:Blender (3D modeling program)|Blender]] model" is the kind of determinism this entry is meant to describe. "Lambda-calculus determinism" is the concept of a mathematical function that specifies the overall process of how something happens and produces a result, randomized or not, but does not specify what result is going to happen to any specific, unique real-world object without knowing the initial conditions of that object.

Within [[E:lambda calculus|lambda calculus]], this mathematical-function-style determinism is the process used to define all mathematical functions and all operators, and effectively reconstruct {{em|all of math}}. To define "2 + 2", lambda calculus first defines what "2" is and then what "+" is: "2" remains "2" when it passes through an [[E:identity function|identity function]], the natural number "2" is a set of "{{TTS|tts=ones|1s}}" incremented from each other, "1" can be exclusively defined as as an identity function incremented into one, and "plus" can be trickily defined as incrementing a lot of ones repeatedly. Everything in lambda calculus conceptually comes from functions, including variables; a basic identity function gives the ability to add variables to all functions.

In this sense, it is possible to conceptualize all of math and all of physics through the lens of lambda calculus. Even the most complicated physics equation is ultimately one big pile of functions, and thus, without any requirement to be able to predict every die roll or the entire development of the whole universe, every physics equation is formed out of {{i|mathematical determinism}}.

Outside mathematics — for instance, within [[:Category:Marxism ontology|Marxist]] philosophy — this concept of limited determinism may be referred to as "necessity". <dfn>Necessity</dfn> refers to general observations that causal factors and processes within the material world lead to partially predictable results. Nonetheless, you may see traditional philosophers oppose "necessity" against "freedom" exactly the way they do with "determinism", partly due to the problem that philosophy does not understand the difference between [[E:absolute determinism|absolute]] and [[E:necessity (mathematics)|limited]] determinism. <del>This is nonsense.</del> This is not considered a problem in [[E:meta-Marxism|meta-Marxism]], where [[E:general-sense historical materialism|general-sense historical materialism]] makes use of [[E:relativistic determinism|relativistic determinism]] to bridge the gap between the observed physical world and localized seas of seemingly-deterministic objects. [[E:Quantum mechanics is secretly a science of ordinary stochastic processes|Seemingly]]-indeterministic quantum processes are the [[E:Determinism can form out of non-deterministic elements|substrate]] for predictable, traditionally-deterministic Newtonian processes. To some extent it can be argued that "determinism" and "indeterminism" [[E:superdeterminism|are actually the same indistinguishable thing]], and it is only the arbitrary labels that individual perceiving humans put onto physics that make any of this confusing. Lambda calculus and mathematical functions are helpful tools for making this concept clearer, because they show how a process can be predictable overall despite random elements going into it and altering the outcome.

== Usage notes ==

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* church numerals: https://pages.github.khoury.northeastern.edu/sholtzen/cs4400-fall24/lecture-notes/lecture-7/lecture-7.pdf
* plus: https://pages.cs.wisc.edu/~horwitz/CS704-NOTES/2.LAMBDA-CALCULUS-PART2.html
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