Logic 101

Thank you for posting an article to make us all get smarter...and more logical, Captain.
:)

And it is good for defeating androids who want to keep you prisoner on a rather drab planet with a guy named Mudd.

What I never understood with that one is that "People sometimes lie on Newsvine" would work perfectly, but no one ever seems to pick up on it.

I refuse to tolerate intolerance.

*poof* Joulesbeef explodes in a puff of logic.

they would always get so mad when I pointed out that their arguments weren't logical.

My deepest sympathies too, Celestina. I think there are three factors at play. One is that people tend to take criticism for presenting an illogical argument as if you are accusing them for being unintelligent. Intelligence is like a wielded sword. It's as alienating to some people as big muscles and a mean demeanor, or physical beauty for that matter. Which leads to the second important observation: Downplaying formal intelligence is an integral part of what we call social intelligence. Finally, topics with a high strong ideological connotations trigger the partisan response that blot out rational thinking.

A poisonous topic for any logical debate.

syllogism involving that proved the existence of God.

at least it didn't end in violence :)

I am not exactly sure what it is you are saying here. If you mean some of the premises in an
argument have hidden corollaries, then I agree. You need to find these hidden assumed premises, because the argument can be valid in form and still have a premise you don't agree with. If
that's what you mean, I'm with you!

I mean that logic assumes that a statement can be either TRUE or FALSE, but the real world doesn't work exactly that way. Statements have degrees of truth. One must be sure that premises are 100% TRUE, 100% of the time, or odd things can result. This means that definitions must be precise and TRUE/FALSE in nature. The Paradox of the Heap illustrates this nicely.

Yes, you must be absolutely sure that your premises are true, or your argument, while
valid, will not be worth anything. And yes, while few people would disagree that, by
definition, all men are mortal, there are universal premises that some folks assume to
be axiomatic that I would not agree with.

CRH is correct on this. The logic under consideration here is traditional Aristotelian logic. Nothing wrong with Aristotle. But the very notion of TRUTH vs FALSEHOOD is now open to question. Aristotle's Law of The Excluded middle whilst very useful in ordinary arguments, fails us in such arcane studies as quantum mechanics, cosmology, or, for that matter, journalism.

Many students of quantum gravity consider that topos theory trumps Aristotle. See Lee Smolin's Three Roads to Quantum Gravity. I'm hoping to prepare an article on the importance of cosmology in journalism and the social sciences, if only I can get my dim head around it ll.

Aristotle's Law of The Excluded middle whilst very useful in ordinary arguments, fails us in such arcane studies as quantum mechanics, cosmology, or, for that matter, journalism.

Strangeley, I find it very rarely usefull in any argument. Most things that I tend to argue about are not that cut and dry.

I believe Celestina made exactly the same point as your point about valid arguments. The truth
of the conclusion depends on the truth of the premises.

As far as your statement that "induction is not justified in the first place," I think you would find
that a lot of scientists disagree with you, as most scientific investigation is based on induction.
It is when they find a case that doesn't fit the model, that they through their premise out and
try again.

Induction is not nor has ever been "justified". Read David Hume or the "Problem Of Induction".

Also, many scientists do not really care about induction. Scientists are usually not as concerned with the philosophy, which is what this would fall under. Induction is dealt with in philosophy of science.

Even though induction is not logically sound in the same way deduction is doesn't mean it has never been justified. In his book "Fact, Fiction, and Forecast", Nelson Goodman points out that the justification of deduction is based on deductive reasoning and nothing else. He then asks why must induction, or any other form of inference, require a deductive basis? Why can't induction have an inductive justification? After all, the study of patterns of inference are based on how we actually do inference - deductive or inductive - in our everyday life.

An inductive inference takes the form "Past Xs have generally been Ys therefore future Xs should also be Ys" where Xs and Ys can be presidents, ages, mammals, lung, etc. As both scientists and your average man on the street will attest, this type of reasoning generally works well in practice. The inductive justification for induction argues that "past inductions have generally been successful therefore future inductions should be too". This is no more or less circular an argument than the one for deduction and so can be seen as a justification. However, there is no guarantee for induction's soundness (i.e. true premises lead to true conclusions) since inductive practice is not sound.

While the above argument attempts to give a pragmatic foundation to induction it does not address how we come up with hypothesis from observations in the first place. The process is what Hume thought of as nothing more than "custom" or "habit". Goodman calls this the "new riddle of induction": what makes one hypothesis that is consistent with our observations any better or worse than another? Popper (the author of the "Problem of Induction") doesn't really address this with his theory of falsifiability, he is only concerned with rejecting hypothesis once they are formed.

Anyway, I've rambled on a bit now. I guess the point I'm trying to make is that the philosophy of induction doesn't end with Hume and Popper. It's a rich subject that's still actively studied and one that has implications for the present day in the form of machine learning and data-mining.

Accordingtome, scientists may not CARE about induction or philosophy of science, but
they USE it. That was my point.

Accordingtome:

Scientists use induction A LOT. In fact, Godel proved mathematically that deduction is not sufficient. (Google "Godel's Incompleteness Theorem")

For example, induction is often used to generate a hypothesis.

Using the basis of past inductions to justify future ones is still circular, I think. YOU ARE STILL USING INDUCTION. Replace induction with experiences or the like and you will have the Uniformity Principle which I think you may have heard of. I am a huge fan of Popper, by the way.

WALLS:
I never said scientists don't use induction. Read it again.

As I side-note I am studying physics and philosophy at a university. Not that this makes me an authority, make no mistake, I do have a lot of exposure to science and philosophy is the point I guess.

Sorry guys, forgot to mention something else. Popper doesn't address these cause Popper is an 'anti-inductivist'. Also, I am uncertain about what you mean as far as the new riddle of induction. If you could clarify a little more I would appreciate it. I assume you are referring to the grue paradox.

Cassandra:
"As far as your statement that "induction is not justified in the first place," I think you would find
that a lot of scientists disagree with you"

This seems to be a claim that induction is justified in some way. If you have a way free of circularity, then please enlighten us. That seems to be your original point but I might me mistaken.

What I was trying to say was that scientists use induction, whether they call it that or not, to
arrive at an hypothesis, which they then proceed to test. And yes, Celestina, theoretically, if
they find a counter case, they should abandon or modify their hypothesis.

Ah, thanks for clarifying. If they are using induction, then wouldn't that mean testing has taken place followed by an extrapolation of the results? So this is such that they do not "test" anymore but look for some sort of "confirmation"? I take the Popperian viewpoint so I am just trying to be nuisance :)

@accordingtome: I thought my earlier post made it clear that the inductive justification for induction is circular, just like the deductive justification for deduction. If circularity is so bad, why rely on it to justify deduction?

Goodman's "new riddle of induction" is the question of how to choose between two hypotheses that are both generalisations of, and consistent with, the same observations. To take Celestina's Presidents example, what make "all Presidents are over 50 when they are elected" and more reasonable (given the observations) than, say, "all Presidents have the letter 'a', 'b', or 'c' in their surname", or "all Presidents are men". The first and third of these hypotheses are more reasonable than the second. Goodman's questions asks why this is so. This is something Popper's take on induction side-steps completely. Just because you can give Popper the label "anti-inductivist" doesn't make his arguments and better or worse.

The "grue paradox" you are referring to was proposed as an example by Goodman to make clear his attempt at an answer to his new riddle. It goes like this: define "grue" to be the property that something is green before the year 2046 and blue afterwards and define "bleen" to be blue before 2046 and green afterwards. Now suppose you have looked at many emeralds and you notice that they are all green. By definition, it is equally valid to say that they are all "grue" since it is not yet 2046. Which of the statements "all emeralds are green" and "all emeralds are grue" is the correct induction to make? They cannot both be true since after 2046 they contradict one another.

Most people respond that "all emeralds are green" is obviously the correct induction since "grue" is defined in terms of green and blue and you should always choose the simpler hypothesis. However, the situation is more subtle than first thought since it is equally valid to define "green" as "grue before 2046 and bleen afterwards". Goodman's solution to his new riddle is that the selection criteria we use to make inductions is our past experiences. "Green" and "blue" are better terms to use than "grue" or "bleen" as they have worked well as predictors in the past. Similarly, "being over 50" and "men" have worked better in hypotheses in the past than "contains 'a', 'b', or 'c' in their surname". Goodman calls this "entrenchment". It is an attempt to make clear what Hume called "custom" or "habit".

I also used to be a fan of Popper but I think he takes too strong a stand on induction and leaves a lot of questions answered. For example, Popper's requirement of falsification completely disallows probabilistic statements such as "there is a 1/6 chance of the die showing 5" since any number of rolls of 3 doesn't falsify the statement. Science uses statements like this all the time and there are well-known ways of testing. If you're interested in a solid, logical foundation for science that goes beyond Popper I would heartily recommend E. T. Jaynes "Probability Theory: The Logic of Science".

The "Principle of Uniformity" actually goes back to Hume. He suggests that "the future will resemble the past" be a principle from which induction can be logically justified. However, he then argues that we cannot justify this principle with anything other than induction.

I don't know what it is but something about probability, I don't like. I dislike the degrees of confirmation and so on. I don't like thinking that science would rest on induction when its only justification is circular.

I probably could help you understand this logic, but I probably wouldn't make much sense to most readers, although some would probably pretend they certainly understood it.

Urrrgh! Probability is a whole 'nother kind of logic, and it's way too messy to deal with here!

It seems to be an Aweful waste of money for somthing that

"they probably certainly know that you probably wouldn't, they don't certainly know that, although you probably wouldn't, there is no probability that you certainly would."

And yes Celestina that is what government is for " To prevent Anarchy :)

Absolutely not. Deconstructing logical fallacies such as the juxtaposition of terrorism and Islam and a number of other commonly used psy ops techniques is a service to society, and the only ones who benefit from people who ignore the rules of logic are populists.

If someone is trying to justify a point he or she has arrived at emotionally, and the best justification
the person can come up with is totally fallacious, then pointing that out just might make him or her think again. Either they come up with a better reason, or they at least realize
they believe something without any justification, which might in some cases turn out to be progress.
So I respectfully disagree with your point.

If only... one of the things that seems to have a bit too much relevance on the Vine is the DATE that things are posted. It seems like, after 24 hours, if a piece never made it to the front page in that time, it won't matter how many comments or votes it gets, it's not going to hit the front page later on... even if it takes folks a while to discover items.

I'd like to see a little less weight on the posted date, myself.