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We are trying to understand the English word "unless". Consider the following statement:

"I will not go to Best Buy unless I need a TV".

It appears that I can rephrase the sentence as:

"I will not go to Best Buy if I do not need a TV".

This in turn can be rephrased as” "If I do not need a TV then I will not go to Best Buy"

Clearly this is a conditional statement (of the type p → q), rather than a biconditional statement. This, of course, leaves open the possibility that I might still go to Best Buy to purchase a laptop.

If, on the other hand, I really wanted to say "I have no absolutely no reason to go to Best Buy unless I need a TV" then it appears to be a biconditional statement (of the type p ↔ q).

So which one of these is correct, or does "unless" have ambiguous semantics?

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  • There is no biconditional in the second example either, it just says:"If I do not need a TV then I have absolutely no reason to go to Best Buy". The converse, "if I have absolutely no reason to go to Best Buy then I do not need a TV", does not follow from this without extra information that Best Buy is the place to go buy TVs, so needing a TV gives one reason to go there. But that background information is extra-logical, and adding it goes beyond what was expressed by "unless".
    – Conifold
    Jan 26, 2022 at 7:34
  • "A unless B" is usually read in English as "A, if not B". In propositional logic "if not B, then A" is equivalent to "B or A". Jan 26, 2022 at 7:39
  • See also this post as well as this one. Jan 26, 2022 at 7:40
  • See also How does 'unless' mean 'or' intuitively? Jan 26, 2022 at 7:41
  • Conclusion: the statement above means ""If I need a TV, then I will go to Best Buy" Jan 26, 2022 at 9:02

1 Answer 1

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Let us consider the schema 'ϕ, unless ψ'.

The usual textbook translation of this statement into propositional calculus is

¬ψϕ,

equivalently,

ϕψ.

Sure, you may think up more elaborate propositional contexts to better express the 'unless' statement. See the handout by Michael O'Rourke for an illustrative discussion on the matter.

However, just by truth-functional manipulation, we do justice neither to the natural language conjunction 'unless' nor to propositional calculus (since that would fall beyond its purpose) if we intend to express the semantic peculiarity of 'unless'.

A good way to better assess the ingredients of meaning as in the present case is to take a glance at its translations into other natural languages, for different languages may express the same meaning grammatically marking different aspects. For example, in many cases, the natural translation of 'unless' into Turkish (my native language) is a temporal expression that can be equated to a phrase 'so long as ... not ...'. Hence, it is not a surprise to come across such as paper that tells

It is standard practice to interpret 'unless' as a truth-functional connective equivalent to 'if not', or, less frequently, to 'if and only if not'. I intend to challenge this practice by showing that when 'unless' connects sentences describing events, or states of affairs that occur, or hold, at different times, 'unless' is not truth-functional. I will do so by showing that 'unless' is sensitive to temporal orderings in ways that logicians inured to 'ignore tense' have failed to notice. Furthermore, I argue that this failure leads to translations of English which are not only misleading, but often obviously wrong. [Chandler, Marthe (1982): The Logic of 'Unless', Philosophical Studies 41, pp. 383-405]

Consequently, I'd recommend you to employ temporal logic. There are many systems of temporal/tense logic. In order to not get bogged down in formalisms, I present one that directly puts 'unless' as an operator W into logical vocabulary.

The following diagram from (p. 19 in An Introduction to Practical Formal Methods using Temporal Logic by Michael Fisher. Chichester: John Wiley & Sons Ltd, 2011) depicts two cases in which a property (situation, state, etc.) indicated by a proposition ϕ does not persist and persists indefinitely depending on the occurrence of the property indicated by ψ. Thus, ϕ is true while ψ is false until ψ is true, else ϕ is false.

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For a broader examination of 'unless', see also: von Fintel, Kai (1992), "Exceptive Conditionals: The Meaning of Unless," North East Linguistics Society 22, pp. 135-148.

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