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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeJul 20th 2012

Created judgment.

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeJul 20th 2012
• (edited Jul 20th 2012)

Thanks! I put in some about judgements in first-order logic, in the hope that this will be clearer to less experienced readers.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJul 20th 2012

Thanks!

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeSep 17th 2012
• (edited Sep 17th 2012)

I have expanded the Idea-section at judgment a bit, trying to make the whole entry more useful to an actual newbie (check if I succeeded) and trying to connect it to the discussion that I am having with Toby in the other thread on hypothetical judgements/sequents.

As a result the Idea-section now overlaps quite a bit with the previous material that I sent to an Examples-section. But I think little harm is done for the moment.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeSep 28th 2012

In editing judgment to refer to deductive system, natural deduction, and logical framework correctly, I became unhappy with the overlaps mentioned above, so I moved the discussion of hypothetical and generic judgments down to its own section after the examples.

• CommentRowNumber6.
• CommentAuthorTobyBartels
• CommentTimeSep 29th 2012

I was going to complain, but it’s all right after all! So I’ll just complain about demoting the spelling ’judgement’ to parenthetical.

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeSep 30th 2012

Well, your version is not grammatical English in my idiolect — you need at least commas around ’or judgement’. I also think that the sentence (which is already a bit long with complicated structure) is more awkward to read without the parentheses, but I won’t insist beyond the commas.

• CommentRowNumber8.
• CommentAuthorTobyBartels
• CommentTimeSep 30th 2012

your version is not grammatical English in my idiolect

It is in mine (I suppose because it is a definition1) and is the only way to put the spellings on equal footing. But I will let it rest as you have it.

1. ‘A meta-proposition is called a judgement or judgment.’ would also work, but ‘Here we make a judgment or judgement.’ or ‘A judgement or judgment is made here.’ would not.

• CommentRowNumber9.
• CommentAuthorMike Shulman
• CommentTimeSep 30th 2012

Well, the spellings are already not on an equal footing, because the page is named ’judgment’ and not ’judgement’. And because one of them comes first, since English is written linearly. It doesn’t seem to me that adding some punctuation to make the sentence read more smoothly makes much of an additional difference. I’m not trying to give an advantage to the spelling I use either; I’d be just as happy with “judgement (or judgment)”. But I also don’t want to spend any more time discussing this! (-:

• CommentRowNumber10.
• CommentAuthorTobyBartels
• CommentTimeOct 1st 2012

the page is named ’judgment’ and not ’judgement’

That's one of our naming conventions.

one of them comes first

Are you one of those people who insists that the first spelling or pronunciation listed in a dictionary is the preferred one, no matter how much the dictionary stresses in its introduction that they are all equally good unless specifically labelled otherwise? (^_^)

• CommentRowNumber11.
• CommentAuthorMike Shulman
• CommentTimeOct 1st 2012

I’m not going to take the time to try to respond thoughtfully to that. (-:

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeDec 30th 2022

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeDec 30th 2022
• (edited Dec 30th 2022)

and to:

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeJan 23rd 2023
• (edited Jan 23rd 2023)

I have added (here) more and more original references (Frege, Russell & Whitehead, Hofmann).

Then I started a section on:

History of the notion and notation

Comments are most welcome. For instance:

So far I haven’t found anyone before Hofmann 1995 to use the modern notation

$hypothesis \;\;\vdash\;\; judgement$

in the generality of such hypothetical judgements: Notably Martin-Löf 1996, after promoting “$\vdash$” for absolute judgements, falls back to writing “$\vert$” when it finally comes to hypothetical judgements.

• CommentRowNumber15.
• CommentAuthorDavid_Corfield
• CommentTimeJan 23rd 2023

Rambling remarks, more for myself when I have time.

Crediting Frege with the introduction of the terminology “judgment” (Urtheil/Urteil) in formal logic implies we don’t take earlier authors who treat it as engaged in formal logic. Something’s certainly new with Frege, but is it formality as such?

Who else is there? From SEP: Brentano’s Theory of Judgement, some candidates

• Schmit, R., 1985, “Allgemeinheit und Existenz. Zur Analyse des kategorischen Urteils bei Herbart, Sigwart, Brentano und Frege”, Grazer Philosophische Studien 23, pp.58–78.

Did anyone earlier have a symbol for judgment? (At the very least, we should say a little more regarding the final reference that ’urteil’ had been a topic in German logic through the 19th C.)

Then what of Charles Peirce.?He speaks of judgment and assertion (the former more the internal act, the latter the public statement), and he has a formal treatment in terms of inscribing letter on the “sheet of assertion”.

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeJan 23rd 2023

Thanks, I have added (here) pointer to Brentano and then also to Kant and Hegel.

But I should say that I am just after the history of the notion in formal logic/type theory, otherwise it might be open-ended:

Martin-Löf suggested (here) that it was not to get sidetracked by psychology and philosophy that Russell & Whitehead switched Frege’s terminology from “judgement” to “assertion” – which makes some sense.

I have also added pointers to the origin of the doubled symbol “$\vDash$” (with hypothesis on the left): It looks like this is the fault of Kochen in 1961 not actively remembering what must have been a previous encounter with Frege’s notation (cf. Kochen (1971)). Ironic the large temporal difference between Kochen’s usage in 1961 and then Martin-Löf and finally Hofmann getting around to it in the 1990s…

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeJan 23rd 2023

which uses (introduces?) “$A \;\vdash\; B$” to mean “proof of $B$ assuming $A$”.

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeJan 23rd 2023

added further content to the history-section (here), such as a summary table (here)

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeJan 24th 2023

have considerably expanded the Idea-section (here) to provide more exposition of more of the idea of “judgements”.