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How can we ask someone to display "all the items that are fruits and only items that are fruits?"

If we ask someone to display "all the items that are fruits", then the display could reasonably display all the fruits and also some other random items like goats.

If we ask someone to display "only items that are fruits", then the display could reasonably display some of the items that are fruits and exclude many of them like oranges.

Does a simple phrase exist to express this?

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The standard way to express this is simply the reverse of your only and all:

Display all and only items that are fruits.

What about "all and only horses gallop?" This states that all horses gallop and only horses gallop... Nicholas Smith; Logic: The Laws of Truth (2012)

Consider, for example, some word that means DOG. Its meaning determines its extension—i.e.

x means DOG → x expresses a concept that is true of all and only dogs

or, in other words,

x means DOG → x is true of all and only dogs, where, by definition, a predicate is true (italicized) of a thing if and only if the concept it expresses is true of that thing. Paul Horwich; Meaning (1998)

We do want to say, however, that all and only bachelor-descriptions are unmarried-man—descriptions, and that all rabbit-descriptions are animal-descriptions. Edward Becker; The Themes of Quine's Philosophy (2012)

Human beings are fundamentally similar, from this point of view, when they are capable of acquiring and of manifesting all and only the same semiotic tendencies under the same causal conditions. J. Fetzer; Computers and Cognition (2001)

Property designators with more than one potential designatum of the relevant sort include general descriptions that fail to inform us much about the designatum, like 'the property that is instantiated by all and only items that are the color of Antarctica' or 'the entity that is instantiated by all and only quantities of the brand of soda endorsed by Ray Charles'. Joseph LaPorte; Rigid Designation and Theoretical Identities (2013)

... where Aristotle distinguishes 'definition' from 'unique property'. These two have the same extension–they pick out all and only items that fall under a term–but [']definition['] picks out the essence, while 'unique property' does not. J. Bryan et al; Authors and Authorities in Ancient Philosophy (2018)


In logic if and only if has the shorter form

iff (conjunction)

If and only if

Two figures are congruent iff one can be placed over the other so that they coincide.

—used in logic and mathematics m-w

However, I've never seen anything shorter than all and only.

Informally, we might say "List just the verbs in this passage," where one could reasonably assume that "just" means all the verbs in addition to only the verbs.

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  • @jsw29 You are right--corrected. Thank you.
    – DjinTonic
    Feb 25, 2022 at 16:42
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    Iff one is in a setting in which iff is a readily understood expression, one can always use it instead of all and only: for example, 'display all and only fruit' is logically equivalent to 'if and only if something is fruit, display it'.
    – jsw29
    Feb 25, 2022 at 22:00
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In the context of a given set of items and you want to request a subset that is only fruit (there are no non-fruit items, maybe not all the fruit items but no no-fruit ones) in the subset, -and- the subset that is all of the possible fruits items (there might be some non-fruit items, but the point is to have every one of the fruit items of the bigger set in this smaller set), then the most succinct way to refer to this subset is:

display exactly the items that are fruits.

'all' could be more items, 'only' could be fewer items, but exactly gets you the subset that is the overlap of these two, both all and only.

While this might be considered an inference from the overt definition of 'exactly', the same could be said for 'all' and 'only'. This usage is prevalent in more formal or technical situations.

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