A small error in the beginning (or in principles) leads to a big error in the end (or in conclusions).See St. Thomas Aquinas (https://www.encyclopedia.com/people/philosophy-and-religion/philosophy-biographies/saint-thomas-aquinas#1G22830900131) De Ente et Essentia (https://isidore.co/aquinas/DeEnte%26Essentia.htm), proemium, which references Aristotle De Cœlo bk. 1 (https://isidore.co/aquinas/DeCoelo.htm#1-9), specifically 271b (https://isidore.co/aquinas/DeCoelo.htm#1-9):
…the least initial deviation from the truth is multiplied later a thousandfold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the end.Upon which St. Thomas commentates (In De caelo lib. 1 l. 9 n. 4 [97.] (https://isidore.co/aquinas/DeCoelo.htm#1-9)):
…one who makes a slight departure from the truth in his principles gets 10,000 [i.e,. many] times farther from the truth as he goes on. This is so because all things that follow depend on their principles. This is especially clear in an error at the crossroads: for one who at the beginning is only a slight distance from the right road gets very far away from it later on.* And he gives, as an example of what he is talking about, the case of those who posited a smallest magnitude, as Democritus posited indivisible bodies. By thus introducing a least quantity, he overthrew the most important propositions of mathematics — for example, that any given line can be cut into two halves. The reason for this effect is that a principle, though small in stature, is nevertheless great in power, just as from a small seed a mammoth tree is produced. Hence it is that what is small in the beginning becomes multiplied in the end, because it reaches unto all that to which the power of the principle extends, whether this be true or false.*St. Thomas's example here is exactly that of Chaos: A Mathematical Adventure (http://www.chaos-math.org), ch. 2 "Vector Fields" (http://www.chaos-math.org/en/chaos-ii-vector-fields), 9:10ff. (https://www.youtube.com/watch?v=9Ninjc2sDFQ%26index=2%26list=PLw2BeOjATqruoac7tS6Clnn-mpxlRkXfV%26t=9m10s); see also ibid. ch. 7 "Strange Attractors & the Buttery Effect" (http://www.chaos-math.org/en/chaos-vii-strange-attractors).
.The butterfly effect would be the same as a ripple effect when a stone is tossed into a perfectly calm body of water. The concentric circles of the ripple keep growing. Basic physics 101.
You have quotes around "butterfly effect" but you haven't said what that is.
.
The butterfly effect would be the same as a ripple effect when a stone is tossed into a perfectly calm body of water. The concentric circles of the ripple keep growing. Basic physics 101..
The "butterfly effect" appears to be a modern variant of the ancient philosophical axiom (http://www.catholicapologetics.info/catholicteaching/philosophy/axiomata.htm) "Parvus error in principiis, magnus in conclusionibus" or "Parvus error in principio, magnus est in fine":See St. Thomas Aquinas (https://www.encyclopedia.com/people/philosophy-and-religion/philosophy-biographies/saint-thomas-aquinas#1G22830900131) De Ente et Essentia (https://isidore.co/aquinas/DeEnte%26Essentia.htm), proemium, which references Aristotle De Cœlo bk. 1 (https://isidore.co/aquinas/DeCoelo.htm#1-9), specifically 271b (https://isidore.co/aquinas/DeCoelo.htm#1-9):Upon which St. Thomas commentates (In De caelo lib. 1 l. 9 n. 4 [97.] (https://isidore.co/aquinas/DeCoelo.htm#1-9)):*St. Thomas's example here is exactly that of Chaos: A Mathematical Adventure (http://www.chaos-math.org), ch. 2 "Vector Fields" (http://www.chaos-math.org/en/chaos-ii-vector-fields), 9:10ff. (https://www.youtube.com/watch?v=9Ninjc2sDFQ%26index=2%26list=PLw2BeOjATqruoac7tS6Clnn-mpxlRkXfV%26t=9m10s); see also ibid. ch. 7 "Strange Attractors & the Buttery Effect" (http://www.chaos-math.org/en/chaos-vii-strange-attractors).I think that makes sense.
philosophical axioms (http://www.catholicapologetics.info/catholicteaching/philosophy/axiomata.htm)I'm not sure. Email the webmaster and let him know: Lawrence Myers <cath_apolo@yahoo.com> (cath_apolo@yahoo.com). He's the one who compiled the list from scratch.
Where is the Latin for 7.7 (under First Principles of Reason)? My page cuts it off at the bottom.
7.7 The same causes in the same circuмstances produce always the same effects.
That's a nice list. Thank you, Geremia, I've asked several priests for such a list and they've told me there isn't one.He has another: A Scholastic List of Definitions for Philosophical Terms (http://www.catholicapologetics.info/catholicteaching/philosophy/definitions.htm)
this thread is very interesting.Interesting, seeing as St. Thomas believed in the globe earth.
This is exactly what happens when you start to believe the lie of the globe earth.
Therefore his entire work snowballed into massive error.If it was in error, where did it's predictive power come from, then?
If it was in error, where didit'sits predictive power come from, then?
.Yes, time travel is fantasy. But it's a fun fantasy to think about.
butterfly effect (https://www.urbandictionary.com/define.php?term=butterfly%20effect)
The scientific theory that a single occurence, no matter how small (https://www.urbandictionary.com/define.php?term=small), can change (https://www.urbandictionary.com/define.php?term=change) the course of the universe forever (https://www.urbandictionary.com/define.php?term=forever).
1. A man travelled back in time to prehistoric ages and stepped on a butterfly, and the universe was entirely different when he got back.
.
As soon as they say someone traveled back in time, you know they're talking about fantasy -- like "flat" earth fantasy. ::)
Yes, time travel is fantasy. But it's a fun fantasy to think about..
I know where that sample sentence came from -- a classic Sci-fi short story called "A Sound of Thunder"
A thrill seeking hunter went back to prehistoric times to hunt dinosaurs, and accidentally stepped on a butterfly. He irrevocably changed history when he got back. In fact, now I want to re-read it.
Here's the story in PDF:
..
Interesting, seeing as St. Thomas believed in the globe earth.
Interesting, seeing as St. Thomas believed in the globe earth.have you read the relevant quotes by St thomas? I dont think you have.
have you read the relevant quotes by St thomas? I dont think you have.I have and it is clear that he accepts that the earth is a sphere.
have you read the relevant quotes by St thomas? I dont think you have.He was a geocentrist who remarked that the model might be replaced in future. He never even mentioned the flat earth.
He was a geocentrist who remarked that the model might be replaced in future. He never even mentioned the flat earth.He did mention the fact that the earth is a sphere in passing. There is a flat earth site which purports to debunk this by claiming that his comments on spherical earth are a quote from Aristotle.
He did mention the fact that the earth is a sphere in passing. There is a flat earth site which purports to debunk this by claiming that his comments on spherical earth are a quote from Aristotle..
However, if one checks the relevant passage in Aristotle, one an see that St. Thomas is alluding to it but not quoting it. Also, in Latin, there is no ambiguity on whether St. Thomas agrees with what he is writing about spherical earth. In Latin, when quoting or alluding to the beliefs of others which one thinks are untrue, one uses the subjunctive mood of the verb. The St. Thomas passage referring to spherical earth, however, has the verbs in indicative, which means he thinks the statements are true.