In what universe is directly quoting you making wild assumptions?you are making wild assumptions
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Oh, nevermind I know now.
The same universe in which inductive reasoning based on observable phenomena is considered blind faith.
Carry on.
In what universe is directly quoting you making wild assumptions?you are making wild assumptions
This is a definition problem. And that's okay. I say, when one accepts an axiom and builds on it without proof of the axiom, that's belief in the axiom. If we want to term that something different that's okay. But the initial axiom is unproven and we "accept" or "believe" or say "that's self-evident" and then build on it.Scientific theories are not beliefs. They are assumptions based on studies and observations; they're our best guess at what is happening but can't yet prove. Scientists don't look at things as self evident, they just say, "this is our best guess." When people study the possibility of that guess, and they all agree that it fits logically, they say, "Yeah we agree that's the most probable solution."
Doesn't make it a belief, just means that they can't come up with anything better yet.
I don't know how many times I need to state that inductive reasoning is not blind faith. I'll do it again thoughIn what universe is directly quoting you making wild assumptions?
added:
Oh, nevermind I know now.
The same universe in which inductive reasoning based on observable phenomena is considered blind faith.
Carry on.
What? The Axiom of Pairing most certainly has a proof. Take two sets, put them into a third set. Third set exists and its elements are the first two sets. Viola. Proven.Certainly! Any axiom that claims itself as self-evident must be something one believes before building upon the axiom. The axiom is then, the criterion of truth. These axioms are things we choose--and of course, can change any time we so desire, to our credit.
The Axiom of pairing is a good example. The axiom of pairing is uncontroversial, and is widely accepted. It however, has no proof and is taken to be self-evident.
I of course accept the axiom of pairing. It seems common sense to me.
To hearken back to Sextus though, this criterion of truthshouldrequire its own proof, of which it has none, and even were it to, it itself would rely on a criterion of truth, which must be proved, ad infinitum. At some point one must believe a criterion as self-evident.
Yes, the problem is that you've defined induction to mean something it isn't, which is exactly what I told you in the very first post I made in response to you.This is a definition problem.
To summarize, induction is moving from generalizations to specifics, while deduction is moving from broad generalizations to specific explanations.
Induction is something like Newton seeing the apple falling and inducing that the reason it falls is because some generally applicable universal (for the context of this discussion gravity doesn't hold absolutely universally but on planets it does for the most part) force is pulling the apple towards the ground. Deduction is noticing that everything touching the ground seems to be pulled back towards it, and determining that because of this fact, the apple falling from the tree will also move towards the ground. This is a very very fast example and probably isn't a perfect one, more a way to give you a picture.
Just as with terms like theory and hypothesis, these do not mean the same thing they might mean in the common every day use of the terms.
You say it now, and yet you've been arguing this entire time that inductive reasoning is the intellectual equivalent of a religious belief in God, which is blind faith and unprovable.I don't know how many times I need to state that inducting reasoning is not blind faith.
I still have not changed the definition of induction or defined it as something that it isn't. Remember the question? Does science employ induction? Yes. That's it.Yes, the problem is that you've defined induction to mean something it isn't, which is exactly what I told you in the very first post I made in response to you.
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See?
Actually, that's exactly what you've done when you openly state, as you just have, that induction in science requires and implies belief.I still have not changed the definition of induction or defined it as something that it isn't.
Induction is proven in science. Not pulled out of its ass like in religion.I still have not changed the definition of induction or defined it as something that it isn't. Remember the question? Does science employ induction? Yes. That's it.
Then you come in DON'T YOU DARE MAKE THIS ABOUT FAITH OR RELIGION
Okay man. We're not doing that. Thanks.
You're talking about theories. I'm not. I'm talking about axioms. You can't make a proof that begins with "The axiom of pairing is really a good guess," the proof would begin with "this is true because this is the application of the axiom of pairing, which is true" when the axiom has not been proven.Not really, but okay.
WHAT!? Induction isn't proven at all you colossal idiot. Induction is a method of reasoning that sometimes yields invalid results! And I STILL am not talking about religion.Induction is proven in science. Not pulled out of its ass like in religion.
Scientific hypothesis and theory is exactly what has given birth to theassumptionsthat you're labeling axioms. They're not self-evident truths, they're conclusions reached after vast testing throughout multiple fields.You're talking about theories. I'm not. I'm talking about axioms. You can't make a proof that begins with "The axiom of pairing is really a good guess," the proof would begin with "this is true because this is the application of the axiom of pairing, which is true" when the axiom has not been proven.
Induction, again, takes the specific, and expands it to the general. It is in every way "proven" in that it is based on objective observation of phenomena through testing.WHAT!? Induction isn't proven at all you colossal idiot. Induction is a method of reasoning that sometimes yields invalid results! And I STILL am not talking about religion.
They are self evident truths. Here's the definition: "An axiom, or postulate, is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy." The scientific theroies themselves mustbegin somewhereself-evident. And also "As used in modern logic, an axiom is simply a premise or starting point for reasoning. Axioms define and delimit the realm of analysis; the relative truth of an axiom is taken for granted within the particular domain of analysis, and serves as a starting point for deducing and inferring other relative truths. "Scientific hypothesis and theory is exactly what has given birth to theassumptionsthat you're labeling axioms. They're not self-evident truths, they're conclusions reached after vast testing throughout multiple fields.
This is not justification for your argument that induction requires belief.And here's one for induction: "There is always a possibility, though, that the premises may be true while the conclusion is false, since there is not necessarily a logical relationship between premises and conclusion."
The parallel line postulate is believed to be self-evident and that no other possibility could exist: "It is true that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles."Please explain one scientific belief that is self-evident. Something that we believe where no other possibility could ever exist.
Only applicable when employing specifically Euclidean geometry. You're confusing a convention in mathematics with inductive reasoning in science.In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate.A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or, in other places known as neutral geometry).
AndProbably the best known equivalent of Euclid's parallel postulate is Playfair's axiom, named after the Scottish mathematician John Playfair, which states:
At most one line can be drawn through any point not on a given line parallel to the given line in a plane.[1]
This axiom is not logically equivalent to the Euclidean parallel postulate since there are geometries in which one is true and the other is not. However, in the presence of the remaining axioms which give Euclidean geometry, each of these can be used to prove the other, so they are equivalent in the context of absolute geometry.[2]
Parallel postulate is NOT self evident.For two thousand years, many attempts were made to prove the parallel postulate using Euclid's first four postulates. The main reason that such a proof was so highly sought after was that, unlike the first four postulates, the parallel postulate isn't self-evident.
And boom goes the dynamite. Highlighted portion. It has been proven. Nothing self evident about it.Where Khayy?m and Saccheri had attempted to prove Euclid's fifth by disproving the only possible alternatives, the nineteenth century finally saw mathematicians exploring those alternatives and discovering the logically consistent geometries which result. In 1829, Nikolai Ivanovich Lobachevsky published an account of acute geometry in an obscure Russian journal (later re-published in 1840 in German). In 1831, J?nos Bolyai included, in a book by his father, an appendix describing acute geometry, which, doubtlessly, he had developed independently of Lobachevsky. Carl Friedrich Gauss had also studied the problem, but he did not publish any of his results. Upon hearing of Bolyai's results in a letter from Bolyai's father, Farkas Bolyai, Gauss stated:
"If I commenced by saying that I am unable to praise this work, you would certainly be surprised for a moment. But I cannot say otherwise. To praise it would be to praise myself. Indeed the whole contents of the work, the path taken by your son, the results to which he is led, coincide almost entirely with my meditations, which have occupied my mind partly for the last thirty or thirty-five years."[18]
The resulting geometries were later developed by Lobachevsky, Riemann and Poincar? into hyperbolic geometry (the acute case) and elliptic geometry (the obtuse case).The independence of the parallel postulate from Euclid's other axioms was finally demonstrated by Eugenio Beltrami in 1868.
No I am not confusing anything. Geometry is a branch of science and the question was posed, TO ME, to point out a single scientific belief that is self-evident. I did so.http://en.wikipedia.org/wiki/Parallel_postulate
Only applicable when employing specifically Euclidean geometry. You're confusing a convention in mathematics with inductive reasoning in science.
Not the same.