Infinite Regress & the perennial first cause
https://thephilosophyforum.com/discussi ... ent/804986
I find his dissatisfaction with infinite regression unsatisfactory for if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop, like that primordial snake ouroboros eating it’s own tail. — invicta
No. A closed loop does not answer Aristotle's quest for an explanation of Causation itself. Note that in the Ouroboros symbol, the snake that seems to be recreating itself, actually has a head and tail, a beginning and end. A true infinite loop would have no head or tail.
TPF : Infinite Regress vs First Cause
Re: TPF : Infinite Regress vs First Cause
No. A closed loop does not answer Aristotle's quest for an explanation of Causation itself — Gnomon
I don't think Aristotle would have described his work that way. He was surrounded by those who rejected the idea of an intelligible whole. He fought them tooth and nail. — Paine
I'm not an Aristotle scholar, so that comment was just my general impression. But here's a quote*1 that seems to have it both ways : Causal Monism (general causality) and Causal Pluralism (sequential causes). I suspect that Plato might be more inclined to view the First & Final Cause as a Holistic, Ultimate, Ideal entity or concept. In any case, only an Eternal (timeless) Cause would put an end to the infinite regress (space/time) of causation. Perhaps Einstein's Block Time*2 would qualify as Causal Monism, since there is no cyclic time for sequential causes to do their thing.
*1. Causality is at the heart of Aristotle’s scientific and philosophical enterprise.
. . . Aristotle is committed to a form of causal pluralism . . .
https://plato.stanford.edu/entries/aristotle-causality/
*2. Block Time? : "Everything everywhere all at once"
Those like Aristotle and Leibniz, who think that time is not independent of the events that occur in time, deny the existence of absolute time, ..
https://plato.stanford.edu/entries/time/
I don't think Aristotle would have described his work that way. He was surrounded by those who rejected the idea of an intelligible whole. He fought them tooth and nail. — Paine
I'm not an Aristotle scholar, so that comment was just my general impression. But here's a quote*1 that seems to have it both ways : Causal Monism (general causality) and Causal Pluralism (sequential causes). I suspect that Plato might be more inclined to view the First & Final Cause as a Holistic, Ultimate, Ideal entity or concept. In any case, only an Eternal (timeless) Cause would put an end to the infinite regress (space/time) of causation. Perhaps Einstein's Block Time*2 would qualify as Causal Monism, since there is no cyclic time for sequential causes to do their thing.
*1. Causality is at the heart of Aristotle’s scientific and philosophical enterprise.
. . . Aristotle is committed to a form of causal pluralism . . .
https://plato.stanford.edu/entries/aristotle-causality/
*2. Block Time? : "Everything everywhere all at once"
Those like Aristotle and Leibniz, who think that time is not independent of the events that occur in time, deny the existence of absolute time, ..
https://plato.stanford.edu/entries/time/
Re: TPF : Infinite Regress vs First Cause
Gnomon
A circle is a very close approximation of Pi which is infinity itself. — invicta
This is gobbledygook. But I would not be surprised were you unable to see that. — Banno
As usual, we have here a vocabulary conflict between people with opposing points of view. Such disagreements are not resolved by disparagement. The word "infinity" has several definitions, depending on context*1.
I suspect that ↪invicta is using the term "Infinity" to mean simply a never-ending series of numbers*2. Perhaps a better word would be "indefinite". His colloquial usage is different from your technical version, but not meaningless "gobbledygook"*3. My tongue-in-cheek "Pi is infinite" link may be somewhat "gobbledy", but it expressed a notion that may be closer to Invicta's usage regarding "infinite regress". The number PI is a never-ending series, but in practice it has a finite value*4. PI as a concept is irrational, and in a general sense unbounded or infinite*5.
*1. What is Infinity?
Infinity is an idea of something that has no end. In general, it is something without any bound. It is a state of endlessness or having no limits in terms of time, space, or other quantity.
In Mathematics, “infinity” is the concept describing something which is larger than the natural number.
*2. Infinity : a number greater than any assignable quantity or countable number (symbol ∞).
*3. Gobbledygook : language that is meaningless or is made unintelligible by excessive use of abstruse technical terms; nonsense.
*4. PI infinite :
How is pi infinite? It’s not infinite in value. It’s more than 3 and less than 4, so its numerical value is certainly finite. What’s infinite about it is the amount of time, or more precisely the amount of calculation, that it would take to express its exact value.
https://www.quora.com/How-is-%CF%80-inf ... inite-area
*5. PI is irrational :
Hence, pi is a real number, but since it is irrational, its decimal representation is endless, so we call it infinite.
https://www.scienceabc.com/pure-science ... inite.html
A circle is a very close approximation of Pi which is infinity itself. — invicta
This is gobbledygook. But I would not be surprised were you unable to see that. — Banno
As usual, we have here a vocabulary conflict between people with opposing points of view. Such disagreements are not resolved by disparagement. The word "infinity" has several definitions, depending on context*1.
I suspect that ↪invicta is using the term "Infinity" to mean simply a never-ending series of numbers*2. Perhaps a better word would be "indefinite". His colloquial usage is different from your technical version, but not meaningless "gobbledygook"*3. My tongue-in-cheek "Pi is infinite" link may be somewhat "gobbledy", but it expressed a notion that may be closer to Invicta's usage regarding "infinite regress". The number PI is a never-ending series, but in practice it has a finite value*4. PI as a concept is irrational, and in a general sense unbounded or infinite*5.
*1. What is Infinity?
Infinity is an idea of something that has no end. In general, it is something without any bound. It is a state of endlessness or having no limits in terms of time, space, or other quantity.
In Mathematics, “infinity” is the concept describing something which is larger than the natural number.
*2. Infinity : a number greater than any assignable quantity or countable number (symbol ∞).
*3. Gobbledygook : language that is meaningless or is made unintelligible by excessive use of abstruse technical terms; nonsense.
*4. PI infinite :
How is pi infinite? It’s not infinite in value. It’s more than 3 and less than 4, so its numerical value is certainly finite. What’s infinite about it is the amount of time, or more precisely the amount of calculation, that it would take to express its exact value.
https://www.quora.com/How-is-%CF%80-inf ... inite-area
*5. PI is irrational :
Hence, pi is a real number, but since it is irrational, its decimal representation is endless, so we call it infinite.
https://www.scienceabc.com/pure-science ... inite.html
Re: TPF : Infinite Regress vs First Cause
In Mathematics, “infinity” is the concept describing something which is larger than the natural number. — Gnomon
Huh? — jgill
Sorry, I forgot to provide a link. That quote came from a math website. I didn't make it up.
Infinity is not a real number, it is an idea. An idea of something without an end. . . .
{1, 2, 3, ...} The sequence of natural numbers never ends, and is infinite.
https://www.mathsisfun.com/numbers/infinity.html
Huh? — jgill
Sorry, I forgot to provide a link. That quote came from a math website. I didn't make it up.
Infinity is not a real number, it is an idea. An idea of something without an end. . . .
{1, 2, 3, ...} The sequence of natural numbers never ends, and is infinite.
https://www.mathsisfun.com/numbers/infinity.html
Re: TPF : Infinite Regress vs First Cause
A circle is a very close approximation of Pi which is infinity itself. — invicta
You would deny Invicta the privilege of meaning what he says? — Banno
No. As I pointed out above, the meaning of "infinite" varies depending on context and intent. So, I'm merely allowing ↪invicta to use the word in a way that suits his context. I don't necessarily agree with his conclusions, but I want to hear his argument -- in his own words -- not necessarily in my personal vocabulary.
Infinity is not a real number, it is an idea. An idea of something without an end. . . .
{1, 2, 3, ...} The sequence of natural numbers never ends, and is infinite.
https://www.mathsisfun.com/numbers/infinity.html
You would deny Invicta the privilege of meaning what he says? — Banno
No. As I pointed out above, the meaning of "infinite" varies depending on context and intent. So, I'm merely allowing ↪invicta to use the word in a way that suits his context. I don't necessarily agree with his conclusions, but I want to hear his argument -- in his own words -- not necessarily in my personal vocabulary.
Infinity is not a real number, it is an idea. An idea of something without an end. . . .
{1, 2, 3, ...} The sequence of natural numbers never ends, and is infinite.
https://www.mathsisfun.com/numbers/infinity.html
Re: TPF : Infinite Regress vs First Cause
Disagreements about terminology are unnecessary. Discussants can instead acknowledge the clear definitions in mathematics: — TonesInDeepFreeze
Math definitions will not resolve the terminology disputes in this thread because ↪invicta is not making a mathematical proposition. "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics : the abstract science of number, quantity, and space. That may be why such open-ended (infinite???) concepts are annoying to some posters, since it can't be ruled True or False by numerical authority. Satisfactory (not true or false) answers will depend as much on intuition as on logic.
As evidenced by never-ending dialogues on this forum, some philosophical questions, including definitions, are often as clear as mud. If metaphysical meanings were as "clear" as math, we wouldn't have forums for extended argumentation. Instead, we could just "shut up and calculate". For those who prefer the clarity of Math, here's a nice online discussion forum :
Wolfram Community :
https://community.wolfram.com/content?c ... athematics
The Metaphysics of Stephen Wolfram :
https://www.youtube.com/watch?v=-jNMh8uuqQY
Math definitions will not resolve the terminology disputes in this thread because ↪invicta is not making a mathematical proposition. "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics : the abstract science of number, quantity, and space. That may be why such open-ended (infinite???) concepts are annoying to some posters, since it can't be ruled True or False by numerical authority. Satisfactory (not true or false) answers will depend as much on intuition as on logic.
As evidenced by never-ending dialogues on this forum, some philosophical questions, including definitions, are often as clear as mud. If metaphysical meanings were as "clear" as math, we wouldn't have forums for extended argumentation. Instead, we could just "shut up and calculate". For those who prefer the clarity of Math, here's a nice online discussion forum :
Wolfram Community :
https://community.wolfram.com/content?c ... athematics
The Metaphysics of Stephen Wolfram :
https://www.youtube.com/watch?v=-jNMh8uuqQY
Re: TPF : Infinite Regress vs First Cause
↪Gnomon
"Pi is infinity" is not a mathematical proposition?
Or will you claim anything in order to defend your account? — Banno
As previously noted, I interpret his use of "infinity" as a philosophical postulation, not a mathematical proposition. Apparently, your more restrictive*1 vocabulary (your account) does not allow that distinction.
*1. Two-Valued Logic is Not Sufficient to Model Human Reasoning
https://ceur-ws.org/Vol-1651/12340059.pdf
↪TonesInDeepFreeze
"Pi is infinity" is not a mathematical proposition?
Or will you claim anything in order to defend your account? — Banno
As previously noted, I interpret his use of "infinity" as a philosophical postulation, not a mathematical proposition. Apparently, your more restrictive*1 vocabulary (your account) does not allow that distinction.
*1. Two-Valued Logic is Not Sufficient to Model Human Reasoning
https://ceur-ws.org/Vol-1651/12340059.pdf
↪TonesInDeepFreeze
Re: TPF : Infinite Regress vs First Cause
Wrong. I and others have studied infinite regress in detail, as infinite compositions or iterations. — jgill
Irrelevant ! I didn't intend to defend ↪invicta's conclusions, but just to defend his right to use a colloquial meaning of "infinite" in a philosophical proposition, without being challenged to present a mathematical or scientific justification. The OP presents metaphors of snake-circles, not mathematical proofs. Is "self-caused" a mathematical concept?
Obviously, what has incensed some posters in this thread is the supernatural implications of the OP. Which they hope to demolish by turning a broad philosophical question into a narrow technical definition. Even though the universe is now known to have a finite beginning in spacetime, some thinkers like to think of it as infinite/eternal, so they don't have to deal with open-ended questions such as the OP.
PS___I usually find you to be more open-minded than the True/False debunkers. In a different thread, one poster asserted that "the opposite of science is pseudoscience". Which is indicative of either/or ; two-value reasoning. In that case, Philosophy must either present empirical evidence, or be rejected as Pseudoscience. Personally, I view Philosophy as complementary to Science, using different methods.
Colloquial : (of language) used in ordinary or familiar conversation; not formal or literary. ___Oxford
STUDENTS’ COLLOQUIAL AND MATHEMATICAL DISCOURSES ON INFINITY AND LIMIT
https://files.eric.ed.gov/fulltext/ED496910.pdf
What is "the natural number" ? — jgill
I'm not a mathematician, so I don't discriminate between Natural and Super-natural numbers. Is Infinity literally supernatural?
In mathematics, the natural numbers are the numbers 1, 2, 3, etc., possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to ... ___Wikipedia
↪Banno
Irrelevant ! I didn't intend to defend ↪invicta's conclusions, but just to defend his right to use a colloquial meaning of "infinite" in a philosophical proposition, without being challenged to present a mathematical or scientific justification. The OP presents metaphors of snake-circles, not mathematical proofs. Is "self-caused" a mathematical concept?
Obviously, what has incensed some posters in this thread is the supernatural implications of the OP. Which they hope to demolish by turning a broad philosophical question into a narrow technical definition. Even though the universe is now known to have a finite beginning in spacetime, some thinkers like to think of it as infinite/eternal, so they don't have to deal with open-ended questions such as the OP.
PS___I usually find you to be more open-minded than the True/False debunkers. In a different thread, one poster asserted that "the opposite of science is pseudoscience". Which is indicative of either/or ; two-value reasoning. In that case, Philosophy must either present empirical evidence, or be rejected as Pseudoscience. Personally, I view Philosophy as complementary to Science, using different methods.
Colloquial : (of language) used in ordinary or familiar conversation; not formal or literary. ___Oxford
STUDENTS’ COLLOQUIAL AND MATHEMATICAL DISCOURSES ON INFINITY AND LIMIT
https://files.eric.ed.gov/fulltext/ED496910.pdf
What is "the natural number" ? — jgill
I'm not a mathematician, so I don't discriminate between Natural and Super-natural numbers. Is Infinity literally supernatural?
In mathematics, the natural numbers are the numbers 1, 2, 3, etc., possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to ... ___Wikipedia
↪Banno
Re: TPF : Infinite Regress vs First Cause
Usually when someone posts a link, it is taken as a suggestion to visit that link. So, without you saying what specifically you wanted me to take from the article, I would have detoured to read and study an article of which all you mean to say is what you posted anyway. — TonesInDeepFreeze
That is not my intention for using links. Instead, I try to say what I have to say in the post, and then add the links "for further reading"--- if someone is interested in more detail. In contentious threads like this though, where my limited knowledge will be challenged & dismissed, another function of links is to let the experts speak on the same topic, with the kind of authority I lack.
That is not my intention for using links. Instead, I try to say what I have to say in the post, and then add the links "for further reading"--- if someone is interested in more detail. In contentious threads like this though, where my limited knowledge will be challenged & dismissed, another function of links is to let the experts speak on the same topic, with the kind of authority I lack.
Re: TPF : Infinite Regress vs First Cause
His response is quite relevant to your claim that infinite regress is not addressed in mathematics. — TonesInDeepFreeze
Tones, apparently you didn't read the OP, and responded only to some abbreviated second & third replies to assertions about Pi & circles & infinity. I would have to be an idiot to make the "claim" you pin on me above. Perhaps that prejudicial misunderstanding is why some posters are treating ↪invicta as an idiot, or worse a woo-monger. I am not arguing with your mathematical acumen, just with your mis-interpretation of what is being said.
What I actually said was that his OP was not a scientific or mathematical assertion, but a philosophical "theory" for discussion. He was disagreeing with Aristotle's use of "infinite regression" as a reason for proposing a First Cause. Then, he offered an alternative metaphor of a snake eating its tail, raising the issue of whether a circle is an example of infinite regress, due to its association with the irrational never-ending number PI. He even asked if "anyone wanna trash this theory?". Would anyone in his right mind ask that of a mathematical fact?
I actually disagreed with his use of the Ouroboros metaphor. But when others began to make an issue of the PI/infinity concept, I simply pointed out that it was used in a metaphorical context, not as mathematical fact. So, get off his back. If you want to get technical, PI is indeed an infinite series of numbers*1, and a circle -- no beginning or end -- is sometimes used symbolically as a metaphor for infinity*2. Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate.
*1. The approximate value of pi is calculated to be 3.14159265…. and is an infinite decimal number. Therefore, it can be concluded from the above explanation that pi is an irrational number.
https://unacademy.com/content/question- ... al-number/
*2. Why is infinity not represented by a circle?
Why is the infinity symbol not a circle? Because it was already being used by the number zero, the letter 'O,' the composition operation for functions, and the degree symbol, among other things.
https://www.quora.com/Why-is-the-infini ... e-a-circle
Pi, spiral, symbol, math, infinity, irrational number :
golden-number-pi-hundred-digits-of-the-constant-forming-an-orange-HTA2H9.jpg
↪invicta
↪Banno
↪jgill
Tones, apparently you didn't read the OP, and responded only to some abbreviated second & third replies to assertions about Pi & circles & infinity. I would have to be an idiot to make the "claim" you pin on me above. Perhaps that prejudicial misunderstanding is why some posters are treating ↪invicta as an idiot, or worse a woo-monger. I am not arguing with your mathematical acumen, just with your mis-interpretation of what is being said.
What I actually said was that his OP was not a scientific or mathematical assertion, but a philosophical "theory" for discussion. He was disagreeing with Aristotle's use of "infinite regression" as a reason for proposing a First Cause. Then, he offered an alternative metaphor of a snake eating its tail, raising the issue of whether a circle is an example of infinite regress, due to its association with the irrational never-ending number PI. He even asked if "anyone wanna trash this theory?". Would anyone in his right mind ask that of a mathematical fact?
I actually disagreed with his use of the Ouroboros metaphor. But when others began to make an issue of the PI/infinity concept, I simply pointed out that it was used in a metaphorical context, not as mathematical fact. So, get off his back. If you want to get technical, PI is indeed an infinite series of numbers*1, and a circle -- no beginning or end -- is sometimes used symbolically as a metaphor for infinity*2. Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate.
*1. The approximate value of pi is calculated to be 3.14159265…. and is an infinite decimal number. Therefore, it can be concluded from the above explanation that pi is an irrational number.
https://unacademy.com/content/question- ... al-number/
*2. Why is infinity not represented by a circle?
Why is the infinity symbol not a circle? Because it was already being used by the number zero, the letter 'O,' the composition operation for functions, and the degree symbol, among other things.
https://www.quora.com/Why-is-the-infini ... e-a-circle
Pi, spiral, symbol, math, infinity, irrational number :
golden-number-pi-hundred-digits-of-the-constant-forming-an-orange-HTA2H9.jpg
↪invicta
↪Banno
↪jgill
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