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The theory goes: the simpler answer is more likely to be true because it is impossible for a series of events to be more likely.

The probability of A + B cannot be higher than A or B alone.

Of course that doesn't mean that A + B didn't occur, just that it is less likely.

> The theory goes: the simpler answer is more likely to be true because it is impossible for a series of events to be more likely.

If that were true then we would never have been able to do chemistry in the first place and get anything done by synthesis. The same applies to manufacturing. It's by careful planning and science that you overcome the probabilities and make it possible to conduct a series of events with perfection.

A more charitable interpretation of what I wrote would take it in the context we're discussing here.

A + B become increasingly more likely if you contrive circumstances for them to occur together. But even then the overall probability is increasingly small if you consider the number of events that have to have occurred over the previous 13 or billin years.

> It is important to remember that when we are dealing with scientific theories, we are not really all that concerned with truth.

Isn't truth the only thing science cares about?

Of course truth alone doesn't mean much and we usually conduct science not just for the sake of it, but those are downstream concerns.

> Are Newton's laws "true"? Well, they work reliably given certain constraints and they are definitely more simple than other theories, so it would be stupid not to use them.

Science doesn't necessitate any "reliability" on the theories/premises it uses. You set up your premise apply your theory to it and reach a conclusion.

It's up to others (i.e. engineers) to worry about how valid the premises are.

Deciding to use or not use some other theory as a premise isn't about being or not being "stupid" but rather about being able to prove something that others (be it scientists or engineers) will be interested in reading.

You can't get to the truth from science. You can only build a model of reality.

The degree with which that model corresponds with reality is a measure of truth, for some definitions of truth. But it's still always a map, a projection from reality according to some set of rules. It never actually is reality.

The thing that science cares about is building a better model of reality. Better models mean better predictions and better storytelling. The former is highly useful. The latter, I'm not so sure. Convincing storytelling can elevate a model higher than it's worth. There's a lot of storytelling in macroeconomics, and similarly in evolutionary biology's just-so stories.

I wonder if viewing science through the lens of "true" stories about reality, rather than as a ratchet for generating more precise predictive models, encourages overweighted stories too much.

> Isn't truth the only thing science cares about?

Not really. Truth is what math cares about. In science, there is no truth, there is just what is measurable, but that's just a proxy for reality, not the objective truth. Then you work with whatever measurements you have and try to predict more measurements.

In reference to your paragraph on scientific theory:

In actuality nothing in science or in reality can be proven to be true. In science it is only possible to disprove or falsify theories. You can actually extract this concept from a famous statement in science and statistics:

"Correlation does not imply causation"

This basically means nothing can be proven, we can only correlate things. If you negate that statement it turns into:

"No Correlation does imply non-causation"

Which means by establishing that two things do not correlate we've disproved or falsified causation.

If P is true, its negation is false.

>In actuality nothing in science or in reality can be proven to be true.

If this were the case, the word "true" would have no meaning. We prove things in science all the time. We proved that you can cross a river without getting wet, for instance. We proved that humans can travel to the moon.

The examples are endless, really.

>If P is true, its negation is false.

Not exactly sure what you're referring to here. Still let me give you some detail on how I negated that statement:

I'm essentially negating phrases within the sentence using the distributive property from algebra:

~(<Correlation> <does not imply> <causation>) = (<No Correlation> <does imply> <no causation>)

If the positive statement is valid the negated statement is also valid. Negating +2 into -2 doesn't make the -2 any less true then the +2, in fact it's not even applicable.

You should note that the negated statement (No Correlation does imply no causation) is a fundamental pillar in science experiments. It's part of the reason why researchers always convert their hypothesis to null hypothesis and then try to disprove it.

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>If this were the case, the word "true" would have no meaning. We prove things in science all the time. We proved that you can cross a river without getting wet, for instance. We proved that humans can travel to the moon. The examples are endless, really.

I want to emphasize that what I'm talking about isn't some theory I made up. This is established scientific philosophy within academia. It's actually one of the harder things to understand because it flies in the face of our natural intuition.

None of your examples have been "proven." What is happening is that you have formed a very reliable conclusion based on intuition, you haven't gathered proof. Lets take a look at your river example...

One way in attempt to gather proof that crossing a river makes you wet is to observe 500 people crossing the river. If you observe that 500 people cross a river and all 500 got wet, what you have established is not a proof but a correlation that crossing the river is correlated to getting wet. Intuitively we assume that this is a proof, but from a rigorous and more philosophical standpoint not only have we not proven anything, it is actually fundamentally impossible to establish a "proof." Try to wrap your head around that.

Let me give you an example that's easier to understand and more inline with our intuitive understanding of the world. The following link is a research study on the correlation between birthrate and the population of storks: http://web.stanford.edu/class/hrp259/2007/regression/storke....

They arrive at the conclusion that baby's are delivered by storks because of the positive correlation. Our intuition tells us that this conclusion is improbable despite the correlation. Note that correlation, intuition and proof are completely separate things.

It is however possible to disprove things. If I establish that there is no correlation between cancer rates and heights then it is by logic impossible for height to cause higher cancer rates. What I have done is disproven height as a causative factor for cancer.

It is fundamentally impossible to prove anything. It is only possible to establish correlations. Correlations can only be used to falsify things or demonstrate the possibility of causation. This is not some weird thing I made up, this is established knowledge. I don't blame people for voting my OP down; Many researchers don't consider or even learn about the implications that the scientific method has on reality as we know it.

>This is established scientific philosophy within academia.

Well, I'm sure that is proof of its correctness?

>What is happening is that you have formed a very reliable conclusion based on intuition, you haven't gathered proof.

That's what proof is. Saying proof is not proof is not all that useful a conclusion to draw.

>it is actually fundamentally impossible to establish a "proof."

See? That's why it's a stupid conclusion.

>None of your examples have been "proven."

Did we go to the moon or didn't we? If going to the moon is not proof that we can go to the moon, then I don't see what business you have to say any of this.

>It is fundamentally impossible to prove anything. It is only possible to establish correlations.

Correlations are what the word "proof" refers to.

>This is not some weird thing I made up, this is established knowledge.

Well, congratulations. You've just established that God exists, too.

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"Proof" is that which is convincing to a 'fair and rational' mind. All you need are correlations that marginalize error. Things that are proven are true up to the invalidation of your assumptions. In science, those assumptions are experiences. In mathematics, they are axioms. There is no fundamental difference between the two, because mathematical axioms are also observed linguistic experiences.

>Correlations are what the word "proof" refers to. >That's what proof is. Saying proof is not proof is not all that useful a conclusion to draw.

No. Proof is a synonym for causation not correlation. Establishing correlation between stork population and baby population is not establishing proof that storks bring babies to mothers. Proof and correlation are entirely different things.

>See? That's why it's a stupid conclusion.

Sure applying the scientific method to daily life is stupid, but we're not talking about that. We're talking about the nature of logic itself. That is the context of this debate. You're attempting to deny the validity of my argument by shifting the context into some vague definition of the word proof.

I didn't say proof is a synonym for correlation, I said proof refers to correlation. Causation is itself a kind of correlation, but I wouldn't wouldn't call either of them synonyms. They are structural relations on experience.

Proof will compel rational systems into agreement. If I submit a proof to a computer, it will consume it and output that-which-was-proved. The correlation between the structure of the inputs and outputs are what the word 'proof' refers to. It's not that complicated.

>You're attempting to deny the validity of my argument by shifting the context into some vague definition of the word proof.

I'm not defining proof, I'm just telling you what it is. Words don't require definition to have meaning.

>Sure applying the scientific method to daily life is stupid

I don't know why you'd say this or why you think I'd agree with it.

You are starting from the assumption that science doesn't proof things (a statement that you no doubt have no proof of) and used it to conclude that proof is meaningless. What a fine conclusion -- it's utterly useless. But rather than imagine that your assumption was wrong, you want to dig in because "so many people" told you it was correct. Well? Give me a proof. Why should anyone believe these things? What rational advantage do you have by claiming proof is impossible?

Furthermore, why would you -- while saying proof is impossible -- ignore the fact that mathematics -- a discipline completely enamored with proof -- be a useful basis for science if science had no need of proof? Does that not strike you as completely absurd? Why would you believe such a thing?

>What rational advantage do you have by claiming proof is impossible?

Rational advantage? You think I'm just stating bullshit for some kind of advantage? Look it up yourself. When did I say "so many people" told me so. Nobody told me shit, You can look this stuff up, it's established academic knowledge. Here's a link to start off with:

http://en.wikipedia.org/wiki/Falsifiability

>Furthermore, why would you -- while saying proof is impossible -- ignore the fact that mathematics -- a discipline completely enamored with proof -- be a useful basis for science if science had no need of proof? Does that not strike you as completely absurd? Why would you believe such a thing?

Look up the mathematics section on that wikipedia page I just linked. first line: "Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science"

Now the question you should ask yourself is not why I would believe such a thing but why it strikes you as completely absurd when it's common knowledge in science.

>You are starting from the assumption that science doesn't proof things (a statement that you no doubt have no proof of) and used it to conclude that proof is meaningless. What a fine conclusion -- it's utterly useless. But rather than imagine that your assumption was wrong, you want to dig in because "so many people" told you it was correct. Well? Give me a proof. Why should anyone believe these things?

Have you ever done science? You know the first thing they do after they come up with a hypothesis? I can tell you they don't immediately try to prove the hypothesis. The first thing they do is convert the hypothesis to a NULL hypothesis and then they try to DISPROVE it. It is the central tenant and quest of science to disprove the NULL hypothesis. Why do you think they do this? Does this not strike you as odd?

If you STILL don't believe me then take a look at the following page:

http://en.wikipedia.org/wiki/Scientific_evidence#Concept_of_...

I found this page on wikipedia searching for "scientific proof." Anyway, to "prove" what I say has legitimacy please read the following:

Under the section "Utility of Scientific Evidence": "Philosophers, such as Karl R. Popper, have provided influential theories of the scientific method within which scientific evidence plays a central role.[6] In summary, Popper provides that a scientist creatively develops a theory which may be falsified by testing the theory against evidence or known facts. Popper's theory presents an asymmetry in that evidence can prove a theory wrong, by establishing facts that are inconsistent with the theory. In contrast, evidence cannot prove a theory correct because other evidence, yet to be discovered, may exist that is inconsistent with the theory.[7]"

Did you get that? He says "Science cannot prove a theory correct." Read that and understand it. I guarantee your perspective of the world will widen as a result. I know we're a little hostile right now but if you put that aside and try to internalize and understand what he says then this knowledge you gain will represent a paradigm shift in your understanding of the world. It did for me.

Now go to the end of that page and read the last paragraph: "While the phrase "scientific proof" is often used in the popular media,[13] many scientists have argued that there is really no such thing. For example, Karl Popper once wrote that "In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof' an argument which establishes once and for ever the truth of a theory,"[14] and Satoshi Kanazawa has argued that "Proofs exist only in mathematics and logic, not in science."[15]"

If you understood what you just read then not only should you know why proving things is impossible, you should also know that the nonexistence of proof in reality is established scientific knowledge.

First off, I'm not uninformed on these matters. I've read all this before, and I don't need a lecture. I was in your shoes at one time.

>he first thing they do is convert the hypothesis to a NULL hypothesis and then they try to DISPROVE it.

Yes, you do a straightforward bijective transformation using no new information, and apparently everything is different. That's not important. You're just highlighting a duality between proof and disproof. You're proving invalidity rather than validity. It's still proof.

As for the rest of your post: Appeal to authority is not an argument. Appeal to popularity is not an argument. These people are wrong. That's essentially what I'm arguing.

I'm not claiming that everyone agrees with me. So why would I debate that? Why are you debating that?

> If P is true, its negation is false.

Where's your proof?

> "No Correlation does imply non-causation"

You're wrong. Random variables can be uncorrelated but not independent [1].

In general, you can't apply "algebra" to logic as you attempted above and explained below. Logic is very precise. To "prove" that `A => B` is equivalent `~B => ~A`, you use truth tables:

    | A | B | A => B | ~B => ~A |
    +---+---+--------+----------+
    | 0 | 0 |    1   |     1    |
    | 0 | 1 |    1   |     1    |
    | 1 | 0 |    0   |     0    |
    | 1 | 1 |    1   |     1    |

Your statements above aren't equivalent; the first is a tautology (it's always true), whereas the second is standard implication, which can be false.

[1] http://en.wikipedia.org/wiki/Normally_distributed_and_uncorr...