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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.”

I seek only intuition; please do not answer with formal proofs or Truth Tables.

How can I understand 'unless' = 'or' directly and intuitively, without relying on the secondary definition that 'unless' = 'if not'?

My problem is my overcomplicated present understanding of 'unless': first I must remember 'unless' = 'if not', and then remember 'if not' = 'or' (which can be proven by comparing the Truth Tables for ~A => B and A ˅ B).

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  • Can you indicate why this feels indirect to you? It feels like a relationship that's capable of being motivated through natural language: do this, or (if you can't then) do that => do that unless you do this
    – Joseph Weissman
    Dec 29, 2015 at 21:21
  • @JosephWeissman Thank you for your comment, which already clarifies somewhat. 'unless' = 'or' feels indirect to me because I do not see any relationship between them in ordinary English, but then again my English is imperfect. I understand 'unless' to mean "NOT on a less compelling condition than".
    – user8572
    Dec 29, 2015 at 21:28

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One can find some plausible examples in natural language where 'or' and 'unless' are intuitively the same. For example, "hand over your wallet or I'll shoot you" is the same as "unless you hand over your wallet, I'll shoot you". But there are differences too: for example, 'or' is commutative: A or B is the same as B or A, but 'unless' is not generally so in natural language. One can hardly say that the two examples given earlier are equivalent to "unless I shoot you, you'll hand over your wallet".

The reason seems to be that 'unless' is a kind of conditional, i.e. it is one of many words, including if, should, provided, barring, when, had, would, else, otherwise, suppose, assume, allow, imagine, etc. that are used to express conditional thoughts. Conditionals in natural language don't behave the way the logic textbooks tell you. They are not truth functions but pragmatic devices with various purposes including stating a rule, a hypothesis, an inference, an evidential claim, a proviso, a precondition, a supposition, an assumption, a disposition, an explanation, a negotiation, a promise, a threat, a plan, a restriction, a requirement, an offer, etc.

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It seems to me that there is no such intuition.

"A unless B" is usually read in English as "A, if not B".

It is only trough the truth-functional equivalence between "if B, then A" and "not B or A" (and we all know how much debatable is the truth-functional definition of "if-then") that :

"A unless B" is equated to "B or A".

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"Unless" conveys much more meaning than a logical "or" as natural language conjunctions generally do. Even "or" in natural language is often not strictly a logical "or". The best way to understand logical operators is through truth tables. Trying to equate natural language "unless" with natural language "or" would be misleading: all they share is their truth table when "translated" into first order logic. Your use yourself truth tables, not natural language intuitions, to show that "if not" and "or" have the same logical structure. The best I can do for you is draw on an example: "I'll miss my train unless I run" and "either I run, or I'll miss my train" have similar meanings.

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