2011-04-15, 03:09 AM
(This post was last modified: 2011-04-15, 10:21 PM by CautionSin.)
The manner in which scientific hypotheses are arrived at is illogical. Wrote this a few weeks ago on facebook, not sure how well written it is, and I'm going to refuse to read back through it. Its all pretty basic stuff. ~Hume's Riddle of Induction
Let H represent the hypothesis, and let I represent the test implications. The testing of an hypothesis looks something like this:
H->I (If "H" were true and the situation was like this, then "I" would be true)
I or ~I ("I" either happens or it doesn't, not "I")
In the case that "I" is false, and what you thought would be the result didn't happen, then the conclusion that deductively follows is ~H (not "H" or your hypothesis was wrong). This structure of argument is valid and also called Modus Tollens argument form.
In the case that "I" is true, the commonly arrived at conclusion is that H is true (or that your hypothesis is correct). Unfortunately that leaves us with the deductive fallacy of affirming the consequent, and an invalid argument.
Though in reality it isn't necessarily that simple, "H" is accompanied with numerous other auxiliary hypotheses which you also assume (we'll represent them as "A1&A2&...&An"). Also, the "I" is really representing another conditional "if my circumstances hold, then this event will occur" (we'll represent this as "C->E").
The new arguments structure looks something like this:
(H & (A1 & A2 & ... & An)) -> (C -> E) for simplistic sake i'll simplify this now...
(H & ((A1 & A2 & ... & An) & C)) -> E
E or ~E
In the case of not E, then any one more more of the hypothesis, the auxiliary, and the circumstances (H, An, C) were not the case. And in the case of E, commonly you would accept your hypothesis, affirming the consequent once again.
To explain why affirming the consequent is bad logic: If it rains, i'll get wet. I got wet. It rained. (well it rained, or you just took a shower, etc.)
Back to the subject, why in the case of science is this also bad logic? If you attempt to understand the positive results inductively, affirming that the positive conclusion follows, you have to assume the PUN (Principle of Uniformity in Nature, that is that "the future will be like the past"). The problem with the PUN is that the logic be it, cannot be understood deductively nor even inductively. It follows:
"In my experience, past instances of the future have turned out to be like the past instances of their pasts"
assume the PUN "the future will be like the past"
conclude the PUN "..."
This is completely ridiculous and makes the entire claim ridiculous because its just begging the question also called circular reasoning. So, the logic for justifying an already skeptical inductive maneuver is circular reasoning. The PUN is the logical equivalent of a PNN (Principle of Non-uniformity in Nature). The only difference is, people who believe in the PNN are termed crazy (saying the world will end tomorrow, etc.), but really they have as much logical basis for that statement as anyone else saying something like "all copper conducts electricity, gravity, the sun will rise, even that the next step I take an abyss won't open up under me that i'll fall in, etc."
Let H represent the hypothesis, and let I represent the test implications. The testing of an hypothesis looks something like this:
H->I (If "H" were true and the situation was like this, then "I" would be true)
I or ~I ("I" either happens or it doesn't, not "I")
In the case that "I" is false, and what you thought would be the result didn't happen, then the conclusion that deductively follows is ~H (not "H" or your hypothesis was wrong). This structure of argument is valid and also called Modus Tollens argument form.
In the case that "I" is true, the commonly arrived at conclusion is that H is true (or that your hypothesis is correct). Unfortunately that leaves us with the deductive fallacy of affirming the consequent, and an invalid argument.
Though in reality it isn't necessarily that simple, "H" is accompanied with numerous other auxiliary hypotheses which you also assume (we'll represent them as "A1&A2&...&An"). Also, the "I" is really representing another conditional "if my circumstances hold, then this event will occur" (we'll represent this as "C->E").
The new arguments structure looks something like this:
(H & (A1 & A2 & ... & An)) -> (C -> E) for simplistic sake i'll simplify this now...
(H & ((A1 & A2 & ... & An) & C)) -> E
E or ~E
In the case of not E, then any one more more of the hypothesis, the auxiliary, and the circumstances (H, An, C) were not the case. And in the case of E, commonly you would accept your hypothesis, affirming the consequent once again.
To explain why affirming the consequent is bad logic: If it rains, i'll get wet. I got wet. It rained. (well it rained, or you just took a shower, etc.)
Back to the subject, why in the case of science is this also bad logic? If you attempt to understand the positive results inductively, affirming that the positive conclusion follows, you have to assume the PUN (Principle of Uniformity in Nature, that is that "the future will be like the past"). The problem with the PUN is that the logic be it, cannot be understood deductively nor even inductively. It follows:
"In my experience, past instances of the future have turned out to be like the past instances of their pasts"
assume the PUN "the future will be like the past"
conclude the PUN "..."
This is completely ridiculous and makes the entire claim ridiculous because its just begging the question also called circular reasoning. So, the logic for justifying an already skeptical inductive maneuver is circular reasoning. The PUN is the logical equivalent of a PNN (Principle of Non-uniformity in Nature). The only difference is, people who believe in the PNN are termed crazy (saying the world will end tomorrow, etc.), but really they have as much logical basis for that statement as anyone else saying something like "all copper conducts electricity, gravity, the sun will rise, even that the next step I take an abyss won't open up under me that i'll fall in, etc."