Ontology:Q35,29

1. M3–35,29 (pronounced 35,29. (M3)) [M3] (pronounced (M3):) Is 5 smaller than a breadbox? 1:(-)1:(-)1

Core characteristics

item type

M3 1:(-)1:(-)1

S2 (C (pronounced Category)) 1:(-)1:(-)1

[P] (pronounced P:) label [string] (L)

M3–35,29 (pronounced 35,29. (M3)) [M3] (pronounced (M3):) Is 5 smaller than a breadbox? 1:(-)1:(-)1

[MX] (pronounced MX; S2:) 5 is smaller than a breadbox 1:(-)1:(-)1

[P] (pronounced P:) alias (en) [string]

Is the number five smaller than a breadbox?

T/F?: (pronounced True or false?) 5 is smaller than a breadbox

QID references [Item] 1:(-)1:(-)1

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field, scope, or group [Item]

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case of [Item]

jamming proposition or question 1:(-)1:(-)1

statement with complicated truth value

sub-case of [Item]

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super-case of [Item]

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truth values

physically impossible

usually / most of the time

greater-than

map versus territory

Appearances

appears in work [Item]

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Wavebuilder combinations

[P] (pronounced P:) Wavebuilder (pronounced Wave-builder): forms result [Item]

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along with [Item]

M3–35,29 (pronounced 35,29. (M3)) [M3] (pronounced (M3):) Is 5 smaller than a breadbox? 1:(-)1:(-)1

forming from [Item]

M3–35,29 (pronounced 35,29. (M3)) [M3] (pronounced (M3):) Is 5 smaller than a breadbox? 1:(-)1:(-)1

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Wavebuilder characterizations

Wavebuilder (pronounced Wave-builder): route [Item]

M3–35,29 (pronounced 35,29. (M3)) [M3] (pronounced (M3):) Is 5 smaller than a breadbox? 1:(-)1:(-)1

along with [Item]

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forming from [Item]

--

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M3–35,29 (pronounced 35,29. (M3)) [M3] (pronounced (M3):) Is 5 smaller than a breadbox? 1:(-)1:(-)1

Prototype notes

3529. Is the number five smaller than a breadbox? -> demonstrates the need for non-binary truth values. the answer isn't yes or no. it isn't even "40% true". the only good answer is "not applicable", "category error", "this is not a physical object" as totally distinct from false.

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 "the 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 jamming propositions. 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 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 five times, and the breadbox is ultimately the same thing as five unless you want to treat models as fundamentally separate from the objects they model.