History Main / ProofByExamples

22nd Jun '15 4:15:56 AM ShorinBJ
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:: Hasty Generalisation

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:: Hasty GeneralisationGeneralization
8th Nov '13 6:09:12 PM RatherRandomRachel
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** A (simple) example of this might be: "A new plant found seems to fit into a particular category with several others. All of the plants within this category need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."

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** A (simple) example of this might be: "A new plant found seems to fit into a particular category with several others. All of the plants within this category seem to need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."
23rd Sep '13 3:20:52 AM RatherRandomRachel
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** A (simple) example of this might be: A new plant found seems to fit into a particular category with several others. All of the plants within this category need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory.

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** A (simple) example of this might be: A "A new plant found seems to fit into a particular category with several others. All of the plants within this category need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."
23rd Sep '13 3:13:04 AM RatherRandomRachel
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** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)
*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather, it is rigorous deductive reasoning.

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** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for A (simple) example of this might be: A new plant found seems to fit into a particular category with several others. All of the value of 1 or 0) plants within this category need three things to thrive - carbon dioxide, water and that if we assume the theory works at value k (k being any given number) we can prove that a light source. Therefore, it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)
*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather,
seems likely this plant will also need those three to survive. We should study it is rigorous deductive reasoning.to confirm or deny this theory.
11th Jun '13 2:19:17 PM DCC
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Added DiffLines:

In short, mistaking inductive reasoning for deductive reasoning
19th May '13 10:19:55 PM trumpetmarietta
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** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)

to:

** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...))
*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather, it is rigorous deductive reasoning.
6th Apr '13 7:22:17 PM SenseiLeRoof
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** To clarify. Induction - at it's most basic is proving it by proving two things. THe Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)

to:

** To clarify. Induction - at it's its most basic is proving it by proving two things. THe The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)
6th Nov '12 3:59:58 PM MasamiPhoenix
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* An attempt at real induction. Inductive logic admits that its conclusions are not ''necessarily'' true, but rather that they are ''probably'' true, and it tends to attempt to be as exhaustive as possible and to eliminate as many alternative explanations as possible, to reduce the possibility that the conclusion is wrong to as close to zero as possible. However, an honest scientist (i.e. practitioner of inductive logic) would freely admit that there is the possibility, however slim, that the entirety of his/her science is entirely wrong.

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* An attempt at real induction. Inductive logic admits that its conclusions are not ''necessarily'' true, but rather that they are ''probably'' true, and it tends to attempt to be as exhaustive as possible and to eliminate as many alternative explanations as possible, to reduce the possibility that the conclusion is wrong to as close to zero as possible. However, an honest scientist (i.e. practitioner of inductive logic) would freely admit that there is the possibility, however slim, that the entirety of his/her science is entirely wrong.wrong.
** To clarify. Induction - at it's most basic is proving it by proving two things. THe Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)
9th Jun '12 6:11:04 PM Goldfritha
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* When you are ''disproving'' by example.

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* When you are ''disproving'' by example.
example -- this is termed a "counter-example."
4th Nov '11 12:44:48 PM Muramasan13
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::A common version is to assume that anything can be extended off to infinity, or that since having a little of something is good, having more must be better. It's a line of thinking commonly used by those talking about future technology:

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::A common version is to assume that anything can be extended off to infinity, or that since having a little of something is good, having more must be better. It's a line of thinking commonly used by those talking about future technology:
technology.
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