Philosophy Discussion Forums

Confirmation reasoning (at least in its most elementary form) goes like this:

(1) If h, then o.
(2) o
(3) Therefore, h.

(where h is some hypothesis and o is an observation that confirms h).

This type of reasoning is used in science all the time. For instance, we might say:

(a) If the general theory of relativity is true, then light rays passing near the sun will be bent.

And if we confirm that light rays passing near the sun do in fact bend, we would infer that the general theory of relativity is true.

Of course, this type of reasoning is formally invalid. You cannot say that the antecedent is true because the consequent is. This is known as the fallacy of affirming the consequent. Anyways, I bring this up because, it is often claimed that although this type of reasoning is formally invalid, if we had more than one confirmation instance, we could justifiably say that h is true. This brings up my question. Does two (or more than two) fallacious arguments make a sound one?

The issue is not merely one of confirmation, buit of a particular type of confirmation. The type is typically stated as "independent confirmation". But it is often misunderstood as merely meaning "someone else". But that isn't good enough.

Cross verification more spells out the right type of confirmation. Cross verification refers to, for example, multiplying 2 numbers and then comparing that answer to simply counting up from 1. The two methods of getting an answer cannot agree very easily unless the answer is correct. With a more precise and complex scheme, all possible errors can be discounted.

The result required to establish proof is merely, "the lack of alternatives". Thus in any serious proof, all alternative possibilities must be accounted by one means or another. Science often uses statistics for that very purpose.

Fhbradley:

You're talking about inductive reasoning. The idea that a pattern in past observations can be extended to predict future observations. Hypotheses are the patterns, proposed because of past observations.

It's not just used in science. It's the basis on which we get through pretty much every aspect of our lives. On a small everyday scale we constantly have to try to predict future experiences/observations. We do it on the basis of our past experiences. Is it justified? Yes. It is justified because it is has so far been useful. It seems, so far, to have worked. So we might as well keep doing it until it stops working. Utility is the justification.

Of course, this type of reasoning is formally invalid. You cannot say that the antecedent is true because the consequent is.

The antecedent is a hypothesis based on previous observations. It is never asserted to be true with absolute certainty. It is proposed to be probable because the consequent continues the pattern of past observations. That is why scientific theories can never be proved true.

The following link probably isn't intelligible if one hasn't been introduced to Bayesian reasoning, but it presents the "gold standard" approach that is continually gaining support in science.
http://plato.stanford.edu/entries/epist ... #BayConThe

Bayesian reasoning is merely saying, "it is more probable than not, therefore it is true."
Very many people have been murdered due to the probability of them being guilty.
I wouldn't suggest implementing such a standard for "truth".

I don't have much experience of the use of Baysian reasoning, but I would say that it is a mathematically formalised and quantified method for applying the principle of inductive reasoning. Inductive reasoning gives you the general qualitative idea that the reliability of a pattern of past observations is strengthened by future observations that fit the pattern and weakened or destroyed by those that don't fit the pattern. Baysian reasoning seems to allow you to actually quantify - to attach probabilities to - the strength of the pattern. But, as I say, my experience of Baysian reasoning is limited. so I may be wrong!

James:

Bayesian reasoning is merely saying, "it is more probable than not, therefore it is true."

This is not my understanding at all. If by "true" you mean "certain" then the incorrectness of your statement is obvious. Your statement would then amount to this: "If probability > 0.5 then probability = 1". Clearly the conclusion does not necessarily follow from the premise.

If you mean something else, you'll have to explain it.

In your example of people being "murdered", do you mean people being executed on flimsy evidence? If so, how does this relate to Baysian reasoning? In a legal setting, there is the concept of "proof beyond reasonable doubt" because the probability of guilt can never be shown to be 1.

James S Saint wrote:Bayesian reasoning is merely saying, "it is more probable than not, therefore it is true."
Very many people have been murdered due to the probability of them being guilty.
I wouldn't suggest implementing such a standard for "truth".

That's not at all what it's saying.

Steve3007 summarized it well. Bayesian reasoning makes maximal predictive use of all the information available. It determines how every piece of evidence should shift the strength of your belief (the probability you assign to it being right) in a hypothesis.

This is different from Popper's falsificationist approach in that it also allows the probability of a hypothesis to go up if evidence keeps supporting it all the time. However, Popper was right to notice that there's a big assymmetry, observations that go against your hypothesis have a much stronger (negative) impact on the degree of certainty one should attach to a hypothesis. Because most of the time the prior probability for a plausible hypothesis starts out relatively high already, so there's not much "surprise value" in observations that confirm it. Whereas, if your hypothesis predicts things wrongly, this should drastically change the certainty you assign to it.

Fhbradley wrote:Confirmation reasoning (at least in its most elementary form) goes like this:

(1) If h, then o.
(2) o
(3) Therefore, h.

(where h is some hypothesis and o is an observation that confirms h).

This type of reasoning is used in science all the time. For instance, we might say:

(a) If the general theory of relativity is true, then light rays passing near the sun will be bent.

And if we confirm that light rays passing near the sun do in fact bend, we would infer that the general theory of relativity is true.

Of course, this type of reasoning is formally invalid. You cannot say that the antecedent is true because the consequent is. This is known as the fallacy of affirming the consequent. Anyways, I bring this up because, it is often claimed that although this type of reasoning is formally invalid, if we had more than one confirmation instance, we could justifiably say that h is true. This brings up my question. Does two (or more than two) fallacious arguments make a sound one?

It is. Especially since the "if, then" means to denote a causal relationship and should not be read as a material implication. So really: H causes O. If not H, then probably not O. O. Probably H. That is kind of how the reasoning works. So it is not formally invalid, since we are not simply affirming the consequent, but reasoning in causal terms to the conclusion that we are justified in believing the antecedent on account of the consequent.

Basically we are presupposing some stuff, for instance that O is not caused by some other event than H. But when we go about testing hypothesises, we often try to deduce startling consequences. If these obtain under controlled circumstances, then we are justified in believing the antecedent, since it helped us predict the outcome, which would not be startling if the causal claim is in fact true.

Wowbagger wrote:Steve3007 summarized it well. Bayesian reasoning makes maximal predictive use of all the information available. It determines how every piece of evidence should shift the strength of your belief (the probability you assign to it being right) in a hypothesis.

That is exactly what calculating probability IS!

Wowbagger wrote:This is different from Popper's falsificationist approach in that it also allows the probability of a hypothesis to go up if evidence keeps supporting it all the time. However, Popper was right to notice that there's a big assymmetry, observations that go against your hypothesis have a much stronger (negative) impact on the degree of certainty one should attach to a hypothesis. Because most of the time the prior probability for a plausible hypothesis starts out relatively high already, so there's not much "surprise value" in observations that confirm it. Whereas, if your hypothesis predicts things wrongly, this should drastically change the certainty you assign to it.

That is not an issue of "surprise value" or even "asymmetry". The bottom line is that if only one effect takes place without the hypothesized cause, the hypothesis is false. If only once 2+2 actually does not equal 4, then 2+2 does not equal 4.

It only takes a single false incident for a hypothesis to be invalidated. That is why they have falsification.
Proof only comes when ALL alternatives are eliminated, not merely when the current information implies the probability of a truth.

Don't think in absolutes, think probabilistically.

James:

It only takes a single false incident for a hypothesis to be invalidated. That is why they have falsification.

That's true in principle. But in practical situations it's not generally possible to be 100% certain that what you have observed is a falsifying event. And the more previous supporting evidence there is for the hypothesis the more certain you have to be that you have indeed witnessed a falsification before abandoning the hypothesis.

The recent supposed measurement of neutrinos travelling slightly faster than light is a great example. They carefully checked their measurements and still seemed to have discovered faster-than-light travel. But Einstein's Relativity still wasn't ditched because it is such a well supported theory. Sure enough, it recently seems to have turned out that there were errors in the measurement process after all.

---

By the way, I did some reading about Bayesian reasoning and I think I know why you mentioned "murder" and the legal system. I didn't realize before now that in some court cases attempts have apparently been made to get the jury members to explicitly use Bayesian methods to work out the probability of the defendant being guilty. No matter how logically sound the methods might be, I can see how this could cause problems! Trials don't use juries because of the mathematical or analytical skills of the general public. They use them out of a democratic sense that we should be judged by our peers.

Steve3007 wrote:I didn't realize before now that in some court cases attempts have apparently been made to get the jury members to explicitly use Bayesian methods to work out the probability of the defendant being guilty.

Assuming juries were competent and trained in analytic thinking, this would be the best way to go about it. But since this often isn't the case, I fear that it would lead to big confusion!

Wowbagger said:

...Popper was right to notice that there's a big assymmetry, observations that go against your hypothesis have a much stronger (negative) impact on the degree of certainty one should attach to a hypothesis. Because most of the time the prior probability for a plausible hypothesis starts out relatively high already, so there's not much "surprise value" in observations that confirm it. Whereas, if your hypothesis predicts things wrongly, this should drastically change the certainty you assign to it.

I only just read this properly and wanted to make an observation about it.

It seems to me the assymmetry that Popper was concerned about is a natural consequence of the fact the hypothesis, in order to attain the status of hypothesis in the first place, has already been supported, directly or indirectly, by previous observations. So the fact that there is relatively little surprise value in confirming observations is a reflection of the fact that lots of such observations have already been made and packaged up into a prior probability.

Maybe not a particularly interesting or controversial observation, but I thought I'd make it anway!