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brendan.curran.paul

Joined: Jun 2025
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Lessons · Negating “Some” Statements

brendan.curran.paul

Edited Saturday, Jan 03

@Kevin Lin Thank you for clearing this up for me! Appreciate it a lot :)

Lessons · Negating “Some” Statements

brendan.curran.paul

Edited Sunday, Dec 28 2025

@Kevin Lin Thank you for this clarification. However could I trouble you for some additional insights into this, as your comment just sparked something in my brain as to whether it could be possible to understand the above to be in a parallel relationship with negating the "All" quantifier, namely:

[Negating "Some"]

1) Initial: Some A are B (A <-s-> B)

2) Negates to: No A are B (A -> /B)

[Negating "All"]

3) Initial: All A are B (A -> B)

4) Negates to: Some A are not B (A <-s-> /B)

But notice that the 1) and 4) above, don't they amount to saying the same thing? Namely, saying "some A are B" effectively the same thing as "some A are not B" (A <-s-> B = A <-s-> /B?)

IF it is the case that the above statements 1) and 4) mean the same thing, shouldn't their contrapositives 2) and 3) also effectively mean the same thing? Ah but here I realized I walked into a contradiction, as there's no way "No A are B" would mean the same as "All A are B"...!

Thanks for indulging me as I thought aloud here--but I guess my qualm with 1) and 4) above still stands, that whether defining "Some" to mean "at least one" rather than "less than all" would be considered more a matter of linguistic convention than it is a matter of strict logic.

The motive for asking this question also stems partly from the fact that I do not come from an English-speaking country, and could not help comparing the meaning of "some" in English to the meaning of "some" in certain other languages.

Hoping to hear back - Many thanks!

Lessons · Negating “Some” Statements

brendan.curran.paul

Friday, Dec 19 2025

Question:

If what we are doing is denying the "some" relationship, couldn't the negation work both in the negative and in the positive senses?

Namely:

['Negative' negation]

Initial: Some parrots are clever.

1st step: It's not the case that some parrots are clever.

Final: No parrots are clever.

['Positive' negation]

Initial: Some parrots are clever.

1st step: It's not the case that some parrots are clever.

Final: All parrots are clever.

If any error(s) in logic were made above, would appreciate corrections and explanations. Many thanks!