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A similar example would be of binary and decimal number where we are not sure about the number system or the person who proposed a number is not remotely available to disclose about number system.

e.g. 101. Is 101 decimal? [T/F] or Is 101 binary? [T/F]?

When context is not clear, it could be one hundred and one in decimal, or it could be a decimal representation of five in binary.

Is it even a fallacy, if so then which one?

It is like an argument without proper context.

10 Answers 10

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EDITED 9/11/2020

What is the name of this fallacy: Is 101 binary or decimal?

I prefer to call it the either-or fallacy, but it is also known as false dilemma among others. The idea is that a choice is given that constrains to two or perhaps a few options when a much broader reading of responses is both possible and warranted. In your example, 101 is a number in base-2 and base-10 and every base in between and beyond.

In regards to your picture, it highlights the likely cognitive source of the fallacy, and that is ambiguity. For instance, it is ambiguous when one writes 101 and does not explicitly explain which base it is.

What's the difference between ambiguity and a false dichotomy? Well, ambiguity is a lack of context to indicate the intention of the author, whereas a false dichotomy is an argument that exploits the lack of context. To be technically precise, an argument must have two or more premises and result in a conclusion, and many logicians accept that unstated premises can be reasonably understood by context. For instance, one could posit that an either-or fallacy is essentially understood as:

P1: 101 could be binary.
P2: 101 could be decimal.
Therefore, 101 is either binary or decimal.

So, technically the question alone independent of context might not be accepted as an argument and therefore fallacy, but ANY act of drawing a conclusion regarding 101 as binary or decimal and presuming those are the only two choices is clearly a fallacy.

Note, to resolve the ambiguity, mathematicians generally use brackets or subscripts or both to indicate base. For instance [101]_2, [101]_10, and [101]_16.

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  • 3
    Precisely. Who's to say it's not 2,117 encoded in base 46? or 15,130 in base 123? – Alexander Sep 10 at 11:56
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    Yes, I think it's even clearer if we say "is 101 a binary [representation of five] or a decimal [representation of hundred and one]". Actually it's a (valid) representation of both (and even more). A different question would be "is this the number hundred-and-one or five?" to which the answer would be "neither" since it isn't a number in the first place, but a representation of one. – ljrk Sep 10 at 13:50
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    @GregoryCurrie The question is according to the title 'what is the name of [the] fallacy?' I gave the name of the fallacy. There are more than two viable conclusions. Without indication, 101 is also hexadecimal. Your language demonstrates an equivocation between 'There are (only) two viable answers' and 'There are (at least) two viable answers'. – J D Sep 10 at 15:46
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    It's also possible to write the base in plain English ("two" or "sixteen"), because every number is written 10 in its own base. – Eric Duminil Sep 10 at 17:27
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    @GregoryCurrie, regardless of the number of options, the point is a lack of context. In both the cartoon and the OP's example we need to know more to know who is right. In the cartoon, someone painted a 6 or a 9 and for a reason. So one of the people is correct - the other lacks the information to determine the correct answer. In the OP's example, the typically assumed base is 10 so the answer is one hundred one. If someone was trying to be deceiving, they could say it was any other of an infinite number of bases. But that's just being intentionally disingenuous. – CramerTV Sep 10 at 18:39
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I add my answer there following comments where I think this is not a fallacy, but only an ambiguous statement or a lack of context.

The false dilemna would apply if in your context you would be forced to choose.

We could also dig towards the confirmation bias where one or many people only read what they goes towards their own opinion.

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I'd argue that the statement/question itself is perfectly fine, and in no way fallacious.
But it may be used as trick question to make a joke at the cost of the answerer.

The English question "A or B?" is somewhat ambiguous since it does not specifiy whether the or is inclusive or exclusive: or is by default inclusive, but questions of this pattern are usually meant with an exclusive or.

Since the statement evaluates to TRUE for inclusive or, but FALSE for exclusive or, this opens the possibility for the questioner to react to the answer by claiming it to be wrong whenever the answerer answers TRUE or FALSE (and of course, unanswerable is also wrong): for answer FALSE the exclusive reading they can claim that OR is inclusive since they did not say XOR, for the answer TRUE they can claim that TRUE XOR TRUE is FALSE and that "A or B?" is parsed as exclusive or in everyday English.

The unambiguously correct answer is thus: "both".

(This is like asking a child "Do you want cake or ice cream?")

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So, the question is confusing two different things.

The question "Is 101 decimal or binary?" is a false dichotomy or false dilemma as 101 could be a representation in any number base > 1 since 1 and 0 are valid symbols.

However, the cartoon of two people with conflicting perspectives is not a false dichotomy. If anything, it's potentially an appeal to authority, since each person is staking their claim based on their position and asserting the correctness of it based solely on their point of view.

All said and done, what we've really got in the cartoon is failure to communicate.

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This is an example of:

False Premise

Technically, false premises are not fallacies (not even informal ones), but rather errors in observation or in the interpretation/translation of observations into logical premises (i.e., statements of fact). In this case the facts being claimed are clearly not justified by the actual observations.

It is possible to claim a variety of different fallacies being present in this translation/interpretation process (over-generalization, false dilemma, etc.) but these are specious as there's no logical reasoning apparent here, you have to infer it (speciously).

Consider this modified example, what if in the OP's picture, the 9/6 were replaced with a 3 and the observers still said "six" and "nine"? It's just a more obvious example of the same error, an observational failure/false premise.

If some insist on inferring reasoning from the observational process depicted, then what has happened is that each has assumed (without apparent justification) from what direction the symbol should be read, which is also a false premise. Less obvious is that both are assuming that it is a number/digit and not say a lower-case g, or a glyph/symbol from a writing system unfamiliar to them (in this way, most people reading this cartoon are also making a false premise). This too is a false premise.

Likewise any attempt to definitively say whether "101" is binary or decimal (or not a number at all, but just some ones and zeros next to each other) without any other context or applicable convention is another false premise.

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    This is an excellent answer, and the most correct. I feel like many answers are trying to over-read into the scenarios, when what the OP is actually asking about is quite clear. – Gregory Currie Sep 11 at 16:40
  • I'm also a bit interested to know if this is actually an observational error here? Presumably both actors in the cartoon are aware of how the shapes of 6 and 9 are related, but are forgetting to logically apply to their reasoning. (I suppose this is the basis for my answer). – Gregory Currie Sep 11 at 16:47
  • @GregoryCurrie I believe that that is covered in my answer (fourth paragraph) as another form of false premise: assuming how the glyph is to be interpreted without sufficient context. That's an implicit false presumption (as is the assumption that it is even a digit). – RBarryYoung Sep 12 at 14:43
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False dilemma is indeed a good term for this example. However because only two options are presented the term false dichotomy could also be used in this case.

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I am going to attempt to answer the intention of the question, which was around a seemly subjective assessment of fact with TWO viable conclusions.

I don't believe the OP is posing a false dilemma scenario.

This is a case of Affirming the Consequent

Decimal 101 looks like "101".

It looks like "101".

Therefore it is decimal 101. (?!)

However, there is another reason why it could look like "101": For instance, binary "101".

The fact that there are two people in the cartoon using flawed logic to arrive at two outcomes does not make this a false dilemma.

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I can see at least two interpretations for this question:

  1. Someone might assume "101" is necessarily either binary or decimal.
  2. Someone might assert "101 is a binary number" without considering the alternatives.

So in both cases the fallacy consists in "forgetting" about some of the logical possibilities. As pointed out before, case 1 might be termed a false dilemma and case 2 a false premise.

But I think they are really two examples of the same pervasive human thinking error:

the availability bias, which is the tendency to give excessive weight to the most obvious (familiar, recent, etc.) elements while disregarding other relevant ones: https://en.wikipedia.org/wiki/Availability_heuristic.

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The name for this is Paradox.

No-No Paradox

And the only way to solve this paradox is when all the players recognize that they are in a paradox and need to understand that both are talking about the same thing in different perspectives.

If one player cannot agree, he is trapped in the Dogma (in-the-box mindset)

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  • Do you have some reference for your claim? I don't see a paradox anywhere in the above example. – Eric Duminil Sep 10 at 17:25
  • There are a lot of different types of paradoxes, linked in the answer the one that applies for that – Roger Barreto Sep 11 at 8:58
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Frame challenge

Is 101 decimal? [T/F] or Is 101 binary? [T/F]?

A question cannot be True or False. Only a statement can be True or False. A question can be answered with Yes or No.

Example

101 is decimal. True or False?

The first part of the above is a statement and the second part is a question about the statement. We don't need to answer the statement - we need to answer the question part.


Let us make the statement and then ask the question.

101 is decimal. True or False?

The answer is of course Yes, because the statement is True or False. We just don't know which because the question is insufficiently defined.

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