# Is the condition '[a value] reduces to [number]' fulfilled when the value reduces to less than the number?

I am trying to deduce the nuances of the titular language for the purposes of a logic puzzle. To illustrate the specifics of the question, the following situation is provided.

Item A has a price of 40. Consider the following statement:

• When the price reduces to 30, I will buy the item.

The price of the item then reduces to 20. Interpreting the statement literally (and not trying to infer intent or implied meaning), according to the statement and situation provided, would the speaker buy the item?

As an alternative situation, consider the following: The temperature outside is 30. We then have the similar statement:

• When the temperature reduces to 15, I will go outside.

Due to some unrelated supernatural weather phenomenon, the temperature suddenly then reduces to −15. Would the speaker go outside? The purpose of this second example is to try to demonstrate the different uses of this (albeit unnatural) language: the answer to both questions must be the same, since otherwise the interpretation is not separate to the (presumed) intentions of the speaker.

Finally, to rephrase the question in the abstract, for a statement forming a condition on when a value 'reduces to' a number, is that condition fulfilled when the value reduces to a lesser number? In other words, is the condition "[X] reduces to [Y]" ([X] was a value greater than [Y], and now it is [less than] [Y]) linguistically distinct in those specifics from the imperative or descriptive statement "[X] reduces to [Y]" ([X] was a value greater than [Y], and it is now being reduced to [Y])? The parenthetical '[less than]' is the crux of the question: should it be present?

Please include explanations of the specifics of the semantics where relevant: this is a question of specific definition and correct usage, not a question of understanding common parlance.

• IMHO it is a bit ambiguous, but I would assume it means "30 or less". Probably something to take up with the puzzle setter. Mar 16 at 1:25
• The grammar is straightforward. You are asking about intention: there's no way anyone can determine intention. The puzzle setter may want you to interpret the statement literally, or he may want you to gauge human behaviour. "When the price reduces to 30, I will buy the item" may be interpreted as "The maximum I will pay is 30." I would observe that the item has reduced to 30; in fact it's gone even further. Mar 16 at 7:41
• 'When the price reduces to \$30' sounds unnatural to my ears, so I'd be predisposed against trying to read the mind of the setter anyway. 'When the price gets as low as \$30' would always be taken as 'When the price falls to \$30 or below'. Mar 16 at 19:15
• I’m voting to close this question because I feel the language is unnatural and that this frustrates second guessing of the setter's intentions. Mar 16 at 19:16
• I will pay 30. When the price drops below that, I'm still buying and insisting on paying 30. But I'm buying. You'd have to reword to force the buyer not to buy at 30 and below. Mar 22 at 22:00

Since you insist on a clinically "sterile" approach with no regard for inference from context, only the "letter of the law" meaning of these words... NO. The phrase "reduce to [a given measurement]" simply means "reach [a given measurement, after having been higher]." It makes no implication about what happens next. In particular, if you start the assertion with "when," then you would seem to be pointing to that exact moment in time.

When the temperature of water is reduced to 0 Celsius, ice crystals form.

In the strictest and most pedantic of interpretations, although of course we still get ice if we continue to lower the temperature, the phase change occurs at the exact moment of 0, not below.*

But meaning is not carried in individual words or phrases. Meaning is constructed, "at run time," by context. In your example, "I'll by when the price is reduced to 30," the most literal meaning is that you'll be standing with your money ready, and pounce the moment it ducks under \$30.01. But a reasonable hearer might also suppose that you might not be watching the price every second, and should you discover that you missed "the moment" of 30, would still buy at 20.

On the other hand, if Dr. Emmett Brown promises us that when his DeLorean accelerates to 88 mph we will, ahem, travel through time, then one might reasonably assume that 89 would also suffice—but as we see it in action, since the time-travel occurs at the exact moment of 88 mph, one is never able to reach 89 before disappearing.

* This is probably terrible science. Supercooling is a thing, and I'm sure the ice formation isn't instantaneous. (Except when it is.) Just an illustration.

• The second part of your answer seems to be treating the 'price' to be changing continuously, whereas in the example, the price was 40, and then, instantaneously, changed to 20 (such as if a 50% discount were to have been applied)—it never was 30. This is the crux of my question: would the specification 'drop to exactly 30' be necessary, or would it be redundant? ​ The first part of your answer seems to address this, though, and I'll accept it on that basis. Thank you for your answer!
– Fie
Mar 16 at 19:39
• @Fie Under that scenario, and using the strictest possible interpretation, then the conditional "When the price is reduced to 30" was never fulfilled. It was "reduced to 20." You said this is for a logic puzzle; perhaps the question is whether you want to be intentionally misleading? Because yes, a reasonable and casual hearer, who assumes the usual consumer motives of saving money etc., will infer a meaning of "I'll buy at 20," but you could call them wrong. Mar 16 at 19:43
• Part of why I included the specifications I did is because the question isn't intended to relate to this specific situation. The example could have instead (and perhaps should have) described a change in temperature (an arbitrary decrease in which isn't strictly desirable), an angle of firing, or some other quantity with which you might associate a number which can decrease in value.
– Fie
Mar 16 at 20:36
• @Fie Then I'll go with my overly-reductive definition: "reach [a given measurement, after having been higher]." And "when" means "at the moment that. By the way, I also forgot to mention, "X reduces to Y" is a bit of an awkward phrase in this scenario. It's not wrong, but many of these situations would more idiomatically use "X is reduced to Y." The non-reflexive version tends to be used more for conversions: "4/4 reduces to 1," "the broth reduces to a sauce." Mar 16 at 20:53