Editing Ontology:Q35,29

{{ArticleTitle|[M3] Truth value: "The number five is smaller than a breadbox" - MX / Q35,29|NoContents=y}}
<includeonly><onlyinclude><dfn class="{{{class|field_mdem}}} manual" data-dimension="{{{dimension|M3}}}" data-qid="35,29"><data data-field="" data-series="" data-work="" data-chapter="" data-tale="" data-object="" data-note="" data-lexeme=""></data>{{Template:I{{{I|M3}}}|Q=35,29}}<!--
  --->{{#if: {{{1|}}} | [[E:Q35,29|{{{1}}}]] | [[E:Q35,29|Is 5 smaller than a breadbox?]] }}<ins class="field"></ins>{{WaveScore|sum=1|quilt=1|ply=1|enddfn=1}}</onlyinclude></includeonly>{{HueNumberPreview|E=Q35,29}}
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== Core characteristics ==

<dl class="wikitable hue">
{{HueClaim |P=item type| {{Template:M3}} | {{Template:S2}} }}
{{HueRoster|EP=PPPA/L|lang=en| {{E:Q35,29}} | {{E:Q35,29/DS}} }}
{{HueClaim |EP=PPPA|lang=en| Is the number five smaller than a breadbox? | {{TTS|tts=True or false?|T/F?:}} 5 is smaller than a breadbox }}
{{HueRoster|EP=P42| -- }}  <!-- en: QID references -->
{{HueRoster|EP=P34| -- }}  <!-- en: field, scope, or group -->
{{HueRoster|EP=P4| {{E:Q940}} | {{E:Q618/STM|statement with complicated truth value}} [[Category:Non-binary statements ontology]] }}
{{HueRoster|EP=P3| -- }}
{{HueRoster|EP=P5| -- }}
{{HueRoster|P=truth values| physically impossible | usually / most of the time | greater-than | map versus territory }}
</dl>

=== Appearances ===

<dl class="wikitable hue">
{{HueRoster|EP=P14| -- }}
</dl>

== Wavebuilder combinations ==

<dl class="wikitable hue data_wavebuild three">
{{WaveBuildNone| {{E:Q35,29}} | Integers are basically apples / Integers are basically bread loaves | greater-than }}  <!-- en: Along With, Produces  ??  ?? -->
</dl>

=== Wavebuilder characterizations ===

<dl class="wikitable hue data_wavebuild three">  
{{WaveRoute| -- | -- | {{E:Q35,29}} }}  <!-- en: From  ??  ?? -->
</dl>

== Background ==

When it comes to logic, there are multiple possible systems for formalizing propositions into simple mathematical structures which can be fed into operators. One is binary formal logic, in which all statements are categorized into the boolean values True or False. This system is sufficient for relatively simple statements like "3 is an odd number". Another is fuzzy logic, in which statements can be assigned a fractional value between 0 and 1. This system may be useful for statements such as "this population of cats is all orange" — if 20% of the cats are orange, then the statement is exactly 20% true. However, any overly simple mathematical system of logic will quickly falter at statements which do not neatly match the assumptions of the logical system. These statements can be termed {{TTS|html=dfn|jamming propositions|E=Q941}}. The alarming thing about jamming propositions is how easy it is to generate one. The field of mathematics is full of claims about particular numbers, such as "5 is ...". Everyday life is full of claims about physical objects, such as "... is smaller than two loaves of bread" (decades ago, these were commonly put in a bread box). If we toss these two genres of statements together, we get the claim "five is smaller than a bread box". How should this claim be evaluated? Superficially, the claim almost sounds normal. Mathematical objects certainly have relationships with the physical world of some kind. Speaking more literally, quantum physicists spend a lot of time writing about objects which are almost invisible except through very indirect methods that reveal them to the world as mere numbers spiking out of a graph of charges that are distinguished from other signal blips by other dimensions of numbers. Can a number be smaller than an apple? What are numbers and where do they exist?

One of the most intuitive answers is to say that 5 cannot be smaller than a breadbox because 5 cannot be physically smaller or larger than anything. This answer is potentially unsatisfying because it suggests that mathematics and the definition of numbers have nothing to do with reality, while every day mathematics is used in engineering and physics.

The second most intuitive group of answers is to say that 5 {{em|must}} be smaller than a breadbox because whenever we speak of the number five it is always written on some substrate such as a page, a brain, or a tiny group of transistors which is smaller than bread box size. Barring a special attempt to create a room-sized sculpture of a single numeral or find the single most inefficient way to encode "5" in binary, you can never fill up a breadbox with a single mention of the number five.

From here, the answers begin to get more esoteric. Is the integer five to be defined using set theory? If so, the breadbox is smaller than five when it is not five breadboxes, or not bigger than five loaves of bread. Is five to be interpreted as a lambda calculus function? If so, five is the act of repeatedly referring to a reference to anything in a chain five references deep, and the breadbox is ultimately the same thing as five unless you want to treat models as fundamentally separate from the objects they model. Is five the answer to an infinite sum? Is five the number of moves to end an impartial game? Is five the number of dimensions making up 3+1+1-dimensional space-possibility-time? Each of these possibilities presents a slightly different truth value. When the number 1 refers to something easily comparable in the physical world, the truth value will be a term of comparison such as "usually lighter than" or "greater-than". When the number 1 refers to something truly abstract, the truth value will be a kind of error state such as "physically impossible" or "map versus territory".

The real answer would seem to be this: we know what five is. Five is five times greater than one, but one has no default definition. So what exactly is the number 1?

== Answers ==

(put answering propositions here)

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