#philmath — Public Fediverse posts

@tg9541 @bookstodon @philosophy

yes, agree in a way. but do not see a win in playing off those two against each other, as later (after their common work PM) their work developed rather independently in more or less complementary areas, sometimes overlapping in #PhilSci topics.

E.g., if one focusses in #philosophy first of all on questions of #ontology (of science), ANW's process ontology will be much more impressive than say the duplicating entities of logical constructs in 'logical atomism' (which imop is a late and needless sin of BR).

If, on the other hand, the main focus is #logic and logic related
#epistemology and/or #PhilMath, there is roughly anything deeper and more worth considering than the theory of incomplete symbols; and perhaps no more careful and penetrating study than the ramified theory of types as developed from the circulus vitiosus argument, even when this theory was abandoned in the sequel for independent reasons.

@tg9541 @bookstodon @philosophy

yes, agree in a way. but do not see a win in playing off those two against each other, as later (after their common work PM) their work developed rather independently in more or less complementary areas, sometimes overlapping in #PhilSci topics.

E.g., if one focusses in #philosophy first of all on questions of #ontology (of science), ANW's process ontology will be much more impressive than say the duplicating entities of logical constructs in 'logical atomism' (which imop is a late and needless sin of BR).

If, on the other hand, the main focus is #logic and logic related
#epistemology and/or #PhilMath, there is roughly anything deeper and more worth considering than the theory of incomplete symbols; and perhaps no more careful and penetrating study than the ramified theory of types as developed from the circulus vitiosus argument, even when this theory was abandoned in the sequel for independent reasons.

@tg9541 @bookstodon @philosophy

yes, agree in a way. but do not see a win in playing off those two against each other, as later (after their common work PM) their work developed rather independently in more or less complementary areas, sometimes overlapping in #PhilSci topics.

E.g., if one focusses in #philosophy first of all on questions of #ontology (of science), ANW's process ontology will be much more impressive than say the duplicating entities of logical constructs in 'logical atomism' (which imop is a late and needless sin of BR).

If, on the other hand, the main focus is #logic and logic related
#epistemology and/or #PhilMath, there is roughly anything deeper and more worth considering than the theory of incomplete symbols; and perhaps no more careful and penetrating study than the ramified theory of types as developed from the circulus vitiosus argument, even when this theory was abandoned in the sequel for independent reasons.

@tg9541 @bookstodon @philosophy

yes, agree in a way. but do not see a win in playing off those two against each other, as later (after their common work PM) their work developed rather independently in more or less complementary areas, sometimes overlapping in #PhilSci topics.

E.g., if one focusses in #philosophy first of all on questions of #ontology (of science), ANW's process ontology will be much more impressive than say the duplicating entities of logical constructs in 'logical atomism' (which imop is a late and needless sin of BR).

If, on the other hand, the main focus is #logic and logic related
#epistemology and/or #PhilMath, there is roughly anything deeper and more worth considering than the theory of incomplete symbols; and perhaps no more careful and penetrating study than the ramified theory of types as developed from the circulus vitiosus argument, even when this theory was abandoned in the sequel for independent reasons.

@tg9541 @bookstodon @philosophy

yes, agree in a way. but do not see a win in playing off those two against each other, as later (after their common work PM) their work developed rather independently in more or less complementary areas, sometimes overlapping in #PhilSci topics.

E.g., if one focusses in #philosophy first of all on questions of #ontology (of science), ANW's process ontology will be much more impressive than say the duplicating entities of logical constructs in 'logical atomism' (which imop is a late and needless sin of BR).

If, on the other hand, the main focus is #logic and logic related
#epistemology and/or #PhilMath, there is roughly anything deeper and more worth considering than the theory of incomplete symbols; and perhaps no more careful and penetrating study than the ramified theory of types as developed from the circulus vitiosus argument, even when this theory was abandoned in the sequel for independent reasons.

While I’m in the camp that “real” #CS is math, this short essay by Moshe Vardi may inspire interesting discussion. #philsci #philmath #sts cacm.acm.org/opinion/what...

What Is Theoretical Computer S...

#philsci
#philmath
#epistemology
#PhilosophyOfLogic

happy to have my most current research paper now approved as a fixed preprint at Cambridge Open Engage

https://www.cambridge.org/engage/coe/article-details/67063c69cec5d6c142aac4e0

#philsci
#philmath
#epistemology
#PhilosophyOfLogic

happy to have my most current research paper now approved as a fixed preprint at Cambridge Open Engage

https://www.cambridge.org/engage/coe/article-details/67063c69cec5d6c142aac4e0

#philsci
#philmath
#epistemology
#PhilosophyOfLogic

happy to have my most current research paper now approved as a fixed preprint at Cambridge Open Engage

https://www.cambridge.org/engage/coe/article-details/67063c69cec5d6c142aac4e0

#philsci
#philmath
#epistemology
#PhilosophyOfLogic

happy to have my most current research paper now approved as a fixed preprint at Cambridge Open Engage

https://www.cambridge.org/engage/coe/article-details/67063c69cec5d6c142aac4e0

#philsci
#philmath
#epistemology
#PhilosophyOfLogic

happy to have my most current research paper now approved as a fixed preprint at Cambridge Open Engage

https://www.cambridge.org/engage/coe/article-details/67063c69cec5d6c142aac4e0

For an example in a #PhilMath paper, I'm looking into this sum:
Sum[(-1)^(l + 1) 2^2^l, {l, 0, k}] for odd k.
It diverges fast & I have values for k up to 9, but I'm wondering if there exists a closed form for it. I tried some techniques from Concrete Mathematics (to no avail) and Wolfram Alpha exceeded computation time. Probably I shouldn't expect a closed form due to the iterated exponent.

Suggestions? Or could someone check it for me in Mathematica, please? 💡➕ :boost_requested: #ICanHazSums

For an example in a #PhilMath paper, I'm looking into this sum:
Sum[(-1)^(l + 1) 2^2^l, {l, 0, k}] for odd k.
It diverges fast & I have values for k up to 9, but I'm wondering if there exists a closed form for it. I tried some techniques from Concrete Mathematics (to no avail) and Wolfram Alpha exceeded computation time. Probably I shouldn't expect a closed form due to the iterated exponent.

Suggestions? Or could someone check it for me in Mathematica, please? 💡➕ :boost_requested: #ICanHazSums

For an example in a #PhilMath paper, I'm looking into this sum:
Sum[(-1)^(l + 1) 2^2^l, {l, 0, k}] for odd k.
It diverges fast & I have values for k up to 9, but I'm wondering if there exists a closed form for it. I tried some techniques from Concrete Mathematics (to no avail) and Wolfram Alpha exceeded computation time. Probably I shouldn't expect a closed form due to the iterated exponent.

Suggestions? Or could someone check it for me in Mathematica, please? 💡➕ :boost_requested: #ICanHazSums

For an example in a #PhilMath paper, I'm looking into this sum:
Sum[(-1)^(l + 1) 2^2^l, {l, 0, k}] for odd k.
It diverges fast & I have values for k up to 9, but I'm wondering if there exists a closed form for it. I tried some techniques from Concrete Mathematics (to no avail) and Wolfram Alpha exceeded computation time. Probably I shouldn't expect a closed form due to the iterated exponent.

Suggestions? Or could someone check it for me in Mathematica, please? 💡➕ :boost_requested: #ICanHazSums

For an example in a #PhilMath paper, I'm looking into this sum:
Sum[(-1)^(l + 1) 2^2^l, {l, 0, k}] for odd k.
It diverges fast & I have values for k up to 9, but I'm wondering if there exists a closed form for it. I tried some techniques from Concrete Mathematics (to no avail) and Wolfram Alpha exceeded computation time. Probably I shouldn't expect a closed form due to the iterated exponent.

Suggestions? Or could someone check it for me in Mathematica, please? 💡➕ :boost_requested: #ICanHazSums

to whom it concerns

#PhilMath
#logic
#SetTheory
#PartialOrders

@philosophy
@Jose_A_Alonso

taken from the birdsite:
J D Hamkins today points to an imop philosophically interesting discussion about the role of Zorn's lemma at

https://mathoverflow.net/questions/436346/zorns-lemma-old-friend-or-historical-relic/

to whom it concerns

#PhilMath
#logic
#SetTheory
#PartialOrders

@philosophy
@Jose_A_Alonso

taken from the birdsite:
J D Hamkins today points to an imop philosophically interesting discussion about the role of Zorn's lemma at

https://mathoverflow.net/questions/436346/zorns-lemma-old-friend-or-historical-relic/

to whom it concerns

#PhilMath
#logic
#SetTheory
#PartialOrders

@philosophy
@Jose_A_Alonso

taken from the birdsite:
J D Hamkins today points to an imop philosophically interesting discussion about the role of Zorn's lemma at

https://mathoverflow.net/questions/436346/zorns-lemma-old-friend-or-historical-relic/

to whom it concerns

#PhilMath
#logic
#SetTheory
#PartialOrders

@philosophy
@Jose_A_Alonso

taken from the birdsite:
J D Hamkins today points to an imop philosophically interesting discussion about the role of Zorn's lemma at

https://mathoverflow.net/questions/436346/zorns-lemma-old-friend-or-historical-relic/

to whom it concerns

#PhilMath
#logic
#SetTheory
#PartialOrders

@philosophy
@Jose_A_Alonso

taken from the birdsite:
J D Hamkins today points to an imop philosophically interesting discussion about the role of Zorn's lemma at

https://mathoverflow.net/questions/436346/zorns-lemma-old-friend-or-historical-relic/