Timeline for Logical and alphabetological variant?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2014 at 16:13 | history | edited | Andrés E. Caicedo | CC BY-SA 3.0 |
deleted 34 characters in body; edited tags
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| Mar 15, 2014 at 10:17 | history | edited | Frode Alfson Bjørdal | CC BY-SA 3.0 |
added 21 characters in body
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| Mar 12, 2014 at 6:59 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
improved formatting
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| Oct 5, 2013 at 14:56 | comment | added | François G. Dorais |
Please use *italics* or **bold** instead of $math$ to emphasize text.
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| Oct 4, 2013 at 15:38 | review | Close votes | |||
| Oct 5, 2013 at 12:03 | |||||
| Oct 2, 2013 at 22:26 | comment | added | Frode Alfson Bjørdal | Noel: I can confirm that the notion of $\alpha$-equivalence is appropriate for what I was calling $alphabetical \ variant$. I would share your surprise if neither Frege nor Russell were on to this. But it would be interesting to know the details. Perhaps even earlier authors partly originated the language use? | |
| Oct 2, 2013 at 20:10 | comment | added | Frode Alfson Bjørdal | In fact, for the same reason as it was suggested a problem with my chosen terminology that $alphabetology$ was a taken term, it may be taken as an advantage. For the distinction I want to make is one which pertains to the science of alphabets, as it were - in logic and mathematics; i.e. the term $alphabetological \ variant$ so taken is an alphabetological term. | |
| Oct 2, 2013 at 18:35 | comment | added | Frode Alfson Bjørdal | I see. However, the context of my use of the term would not be likely to be confused with the science of alphabets. So I will consider whether I find a good replacement, and if not perhaps I use $alphabetological$ despite its somewhat esoteric prior use. | |
| Oct 2, 2013 at 18:27 | comment | added | Trevor Wilson | I don't think that "alphabetological variant" is a good term, because it would suggest the notion of a variant in the sense of alphabetology (which seems to be a real word for the study or science of alphabets.) | |
| Oct 2, 2013 at 18:26 | comment | added | Noel Vaillant | Can you confirm you are referring to the notion of $\alpha$-equivalence as per this? If so, I would be surprised if the idea did not originate from Russell or Frege. If not, I am not familiar with your notion. | |
| Oct 2, 2013 at 17:44 | comment | added | Frode Alfson Bjørdal | Thanks, Noel. That leaves only the alphabetological variant, it seems. | |
| Oct 2, 2013 at 15:52 | comment | added | Noel Vaillant | However, the formulas $\forall x((x\in z)\leftrightarrow(x = x))$ and $\forall y((y\in z)\leftrightarrow(y = y))$ are $\alpha$-equivalent for all $z\not\in\{x,y\}$, which is probably the notion you want to refer to (as Takeuti) under the label 'alphabetical variant'. As for 'logical variant', i have the feeling you are asking for the provenance of the so-called 'Lindenbaum-Tarski congruence' $\Gamma\vdash (\phi\leftrightarrow\psi)$ | |
| Oct 2, 2013 at 15:40 | comment | added | Noel Vaillant | For what it's worth, Takeuti's proof theory (2nd ed. 1987) refers to 'alphabetical variants' in p. 18 def 2.15 with reference to substitutions of bound variables only (so $x=x$ and $y=y$ are not alphabetical variants when $x\neq y$ according to this definition). | |
| Oct 2, 2013 at 14:55 | history | asked | Frode Alfson Bjørdal | CC BY-SA 3.0 |