Talk:Temperature paradox

State of article

@Botterweg14: If you're going to just remove it... surely, surely there is some "criticism" of the concept, or an accessible-to-normal-people explanation to be included in this article. This is the kind of paradox that only works on small children and academics. I get that it might be a problem in linguistics - how to formalize expressing such matters - but what is meant is blazingly obvious in conversation. It's not a "logical" paradox or a philosophical one if what is Really Being Said is clearly expressed, solely an issue with linguistics. If you dislike my additions, are there any sources that cover what I'm talking about? Because if there aren't such independent sources stating this fairly obvious bit, that's a bit of a warning sign... SnowFire (talk) 14:25, 25 October 2022 (UTC)

I've made some edits to try to address your concern about the previous text. But you're right that this is of much narrower interest than something like the Liar or the Barber. The natural language statement of the argument is indeed glaringly obviously invalid, and the puzzle comes simply from the attempts to formalize it which aren't going to be of much interest outside lingistics or philosophical logic. Hope that's clearer in the text now. Botterweg14 (talk) 15:54, 25 October 2022 (UTC)

Merely syntactic ambiguity?

The example given "works" because in English, the word "is" is used in a syntactically indistinguishable manner in two different grammatical constructs, namely as a copula and as an auxiliary verb for constructing the present continuous. Is there an instance of this paradox that can not be explained by mere syntactic ambiguity?

Otherwise, with the same reasoning, wouldn't the following argument also be an instance of the paradox?

1. The temperature is ninety.

2. The temperature is rising.

3. Therefore, rising is ninety.

Obviously, rising doesn't have an age ;-)

-- Placekeeper (talk) 09:38, 5 November 2022 (UTC)

This is probably a question for Quora or Reddit or some forum of that sort. But in a nutshell, no, the issue is the ambiguity of "temperature" not "is". With Partee's original formulation, the translation into extensional FOL would wrongly treat the argument as valid even though it takes "is" as "=" in the first premise and as a reflex of predication in the second. So it fails even though it takes into account the ambiguity of "is". Your alternate formulation wouldn't have this problem, since neither 90(R) nor R=90 would be well-formed in FOL on account of R being a predicate symbol and 90 being an individual constant. Botterweg14 (talk) 18:21, 5 November 2022 (UTC)

Yes, I also noticed that some time after asking the question, but you were faster than me :-) But I don't think this is for Quora because I am asking with the intention of improving the article.

What I am currently trying to resolve is that I can't fully reconstruct the connection of this paradox to the intension vs. extension distinction based on the solution suggested in the article text.

The article states: "... the first premise makes a claim about the temperature at a particular point in time, while the second makes an assertion about how it changes over time."

However, what does make "the temperature at a particular point in time" the extension and "how [temperature] changes over time" the intension of t?

From a mathematical point of view, I can consider $t$ to denote a function representing the temperature at a fixed place over time. My pattern matching compulsion then tempts me to consider $extension$ to be the higher-order function $\lambda t.t(T_{0})$, which evaluates $t$ at a fixed point in time $T_{0}$, and $intension$ to be $\lambda t.({\frac {dt(T)}{dT}}(T_{0}))$, i.e. a higher-order function that evaluates the value of the derivative of $t$ at $T_{0}$, and to define $R(x)\equiv x>0$. This also matches well with my above quotation from the article.

However, I can't see a general connection from extension to "evaluating a function at a fixed point in time" and from intension to "evaluating the derivative of a function at a fixed point in time" to intension. I am especially struggling with the latter because I don't see a general connection between intension and derivatives. The former appears to closer to the issue, but I am not convinced because in my current understanding, the two senses would be different intensions (evaluating $t$ at $T_{0}$ vs. evaluating ${\frac {dt(T)}{dT}}$ at $T_{0}$), and these two intensions may have different extensions in worlds where the premises hold (the number/temperature 90 vs. some number/rate of temperature change greater than zero) - if I am using the terminology correctly.

-- Placekeeper (talk) 10:10, 9 November 2022 (UTC)

I think the simple answer is that one person's intension is another person's extension-that-just-has-an-extra-unfilled-argument-slot. Potayto potahto. But if you're curious about this, there was some philosophical discussion in the 1980s about intensional logic versus two-sorted logic that you might find interesting. Botterweg14 (talk) 02:05, 10 November 2022 (UTC)