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Source: p 319, A Concise Introduction to Logic (12 Ed, 2014), by Patrick Hurley

in propositional logic it is usually simpler to equate “unless” with “or.”

In and using only ordinary English (and no Logic), how can 'unless' be interpreted to mean 'or'? Can semantic change explain how 'unless' = 'or'?

I wish to understand how 'unless' = 'or' directly and intuitively. So please do not refer to or use the alternative (Stipulative) definition that 'unless' = 'if not'.

unless = 1. prep.phr. On a less or lower condition, requirement, footing, etc., than (what is specified). With preceding negative, expressed or implied.

PS: I quoted the obsolete definition above, because I wish to understand 'unless' from first principles and because all the other definitions use some variant of 'if not'.

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    I will go to sleep unless she calls means either she will call or I will go to sleep. In formal logic, therefore, the first statement can be reduced to I will go to sleep, or she calls when you write out the formula. But you cannot simply swap out unless for or in ordinary English, because language is not about reducing statements to equations. Otherwise, we would never have had to invent propositional logic in the first place.
    – choster
    Commented Dec 29, 2015 at 22:28
  • Note to self: See ncbi.nlm.nih.gov/pubmed/22059303, brianbuccola.com/the-semantics-of-unless, journals.cambridge.org/action/….
    – user50720
    Commented Jan 20, 2016 at 21:25
  • unless is complemented by a clause that refers to a sufficient condition for something to occur (or not occur): I will get some sleep unless you need my help. If you need my help, I won't get some sleep but will remain awake, otherwise (i.e. if you don't need my help) I will go to bed.
    – TimR
    Commented Dec 18, 2023 at 16:04
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    I’m voting to close this question because "in propositional logic" is a specialist use - this would be better served by being on the mathematics SE
    – Greybeard
    Commented Dec 18, 2023 at 16:46

3 Answers 3

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Here's one situation where unless can mean or.

Take this book back to the library unless you renew it.

Either take this book back to the library or renew it.

There are lots of other situations where you cannot replace unless with or in everyday speech.

For example,

Take an umbrella unless it is sunny.

Because being sunny is a condition you have no control over, and it's your decision to take the umbrella or not, it doesn't work to rewrite this sentence with or. If you try to, you're stuck with something like:

Either take an umbrella or it is sunny,

which makes no sense at all.

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  • Ordinary propositional logic (the kind that is taught in introductory-logic courses) is not intended to handle imperatives (which are not propositions in the relevant sense). There are the forms of logic that do, but they are several layers of complexity away from the context in which this question was asked.
    – jsw29
    Commented Dec 18, 2023 at 22:03
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The word unless evolved from a prepositional phrase "on less than {something}" and expressed a threshold condition, as in this example from an imaginary conversation 600 years ago:

On less than fire, don't wake me up.

So in branching representation:

if there is no fire
  let me sleep
else
  wake me up

or

if there is a fire
  wake me up
else
  let me sleep

Nowadays we can say:

Don't wake me up unless there's a fire.

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"Unless" does not equal "or" 'directly and intuitively'.

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    Can you please transform this into a comment, and delete it as an answer? If the answer really is 'no', then I wish to leave this question unanswered lest some linguist in the future discovers the intuition.
    – user50720
    Commented Jan 2, 2016 at 16:21