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According to Humes's argument, induction by its nature assumes a uniformity that is not justified. This is a very deep and interesting observation, and a point often used by the religious to justify that any observation reached using scientific method uses induction, and therefore is purely speculative, and likely irrational.

Is a conclusion based on induction rational or irrational? Does it always work?

Is deduction rational or irrational? Does it always work? ( assuming something can be rational always works, which may or may not be the case)

Can the conclusion that there is a creator of the universe be rational?

Also please watch this. Is the logical proof for god valid? Hamza (person in the video) makes the argument that we can make a logical conclusion that a person is likely to have a great great great great grandparent. But isn't that assumption purely based on the evidence of his own existence, and thus induction?

  • Related/background: plato.stanford.edu/entries/induction-problem – user3164 May 16 '13 at 17:03
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    It seems there are two different questions here (rationality of inductive reasoning; proof of the existence of god). Could you split them into two posts? – DBK May 17 '13 at 15:30
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The guy in the video is wrong. He says: we can know things without the sensible world, for example: you know your great(...)grandma has lived because you're here, yet you cannot sense her. However, the fact your great(...)grandma has lived relies on physical evidence that you exist. Therefore, this isn't an example of knowledge without information from the senses.

Induction

You cannot get to absolute knowledge with only induction. This is commonly explained with swans: if you have seen 1, 2, 3, ..., n white swans, that doesn't make it arguable there are no black swans (unless you've seen all swans, of course). Someone who does something like that, isn't working rationally. Here's how induction works, you can easily see this isn't a valid reasoning:

  1. P1 has property X

  2. P2 has property X

    ...

  3. Pn has property X


Therefore, all P have property X

This is not true because you didn't prove it for Pn+1.

Deduction

Deduction is rational though. It works like this:

  1. If P is true, then Q is true

  2. Q is false


Therefore, P is false

This is a valid reasoning in normal logic. If P would have been true, Q would have been true. However, Q is false, so P cannot be true, therefore must be false.

Quinque viae

The argument Hamza uses to try to proof God's existence is one of the Quinque viae: "five ways" to God, by Thomas Aquinas. It's the argument of the Unmoved Mover:

  • Some things are in motion.
  • A thing cannot, in the same respect and in the same way, move itself: it requires a mover.
  • An infinite regress of movers is impossible.
  • Therefore, there is an unmoved mover from whom all motion proceeds.
  • This mover is what we call God.

Note that point 3 and 5 are easily questionable.

For point 3: Why wouldn't an infinite regress of movers be possible?

For point 5: this proof only proves the existence of an unmoved mover, however, God (whether that's the Christian or another God) is more than only an unmoved mover. Therefore, this doesn't prove Gods existence, but merely the existence of an unmoved mover.

In Thomas' defense: he didn't intend this as a proof, but as a way to God (remember "quinque viae"). This is a way to get to the idea of God, not to prove God.

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    I understand its not a path to absolute knowledge, but it is rational to use induction to arrive at a conclusion. Going back to the swan example, if you have observed a million swans, all of which are white. The assumption that all swans are white is false, but what about the assumption that most swans are white, and likely hood of having a different colored swan is unlikely. That previous assumption is based on prior knowledge, and with an assumption of uniformity, the next swan observed will most likely be white.The question is, is this assumption rational? – Anonymous May 16 '13 at 13:22
  • And also what issues do most religious people have with this? – Anonymous May 16 '13 at 13:23
  • @Anonymous it's rational to make an educated guess based on induction with a large n, however, that doesn't make it rational to prove something with induction. An assumption isn't really correct or incorrect. It's your assumption, from that moment it's true, in your system. Some people use other assumptions. – Keelan May 16 '13 at 13:24
  • @Keelan : '(unless you've seen all swans, of course)' - hmmm - how will I know when I've seen them all...? :-) – Vector May 17 '13 at 1:37
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    @Anonymous - no religious person can have a substantial objection to any of this, because, as Keelan explained, such exercises are not designed to be conclusive proofs, but simply a way of making the concept of God more approachable to the human intellect. If 'Hamza', or anyone else, believes such proofs to be conclusive, they are in error, and if their religous convictions are built on such proofs, they are very questionable: Debunk the proof and their convinction will of necessity disintegrate. Religion is based on FAITH, not REASON. – Vector May 17 '13 at 1:43
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It's important to clarify what we mean here by 'rational'. If 'rational' means logically provable, than induction is not rational. The form of an inductive argument doesn't guarantee its correctness:

All hitherto As have X property

Therefore

All As have X property

Is not necessarily true. Imagine if I introduced you to two of my siblings, and they both happen to be boys. Does that mean that all of my siblings are necessarily boys? This is unlike deductive logic, which can be deemed rational in this way.

Given:

  1. If P is true, then Q is true

  2. P is true


Therefore, Q is true

Note that this form of argument is valid no matter what the premises may be. (The above example is one of the most simplest in logic, modes ponens)

However, if by rational you mean 'reasonable', than the answer is often (but not always, as the example above) yes. For example, if there was a certain liquid, and you've seen 100 people drink this liquid and die soon afterwords, it would be very reasonable to avoid drinking this liquid (we might give it a name, like "poison", in order to indicate to others to behave similarly). In the example used in the video that you've linked to, every human (and mammal) that I'm aware of was begot by a mother, therefore, it's reasonable to assume that all mammals were begot by a mother, unless I have reason to believe otherwise.

You may wonder, why does it seem like induction is reasonable sometimes, but not all the time? After all, what's different between the example of the brothers and the example of the mothers? This question has been asked in many different forms and fits under the heading of The Problem of Induction. I believe that the intuitive answer is the use of probability, or Bayesian inference: if there's a large enough sample size of observations, than the likelihood of those observation being coincidental are lower. In reality , there are a few other factors at play as well, and (what humans generally consider to be) reasonable actions are based on both heuristics about the sample size and probability of the similarities observed being coincidence, as well as intuitive beliefs about the way in which the universe behaves.

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According to Humes's argument, induction by its nature assumes a uniformity that is not justified.

Uniformity isn't necessarily assumed, but it is inferred if the data coming in is consistent enough. The 'white swan' example only works because all swans from 1 to n are white. What colour is a tulip? The data will indicate whether an assumption of uniformity is rational or not.

It's the same with the uniformity of laws of physics - to the best of our ability to observe, the fundamental rules that we've discovered seem to apply universally and with an amazing degree of accuracy. Models where the laws of physics are mutable, while interesting, don't describe the universe we find ourselves in nearly as well. We didn't take uniformity as a starting assumption (indeed the opposite - 'celestial' and 'terrestrial' physics were once believed to be categorically different), rather a conclusion from repeated observation.

This is a very deep and interesting observation...

To paraphrase said observation: "Things that seem consistent/uniform may not in fact be consistent/uniform"

Indeed! It's been the relentless search for abnormalities and investigations into such that drives most of our scientific endeavours! See the discovery of the atomic nucleus for a dramatic disproof of the uniformity of goddamn solid matter itself!

However, I have a feeling this is a prelude to some religions apologetics, and religious apologists aren't thinking about things like that, right? Sure enough:

... and a point often used by the religious to justify that any observation reached using scientific method uses induction, and therefore is purely speculative, and likely irrational.

... Because tentatively adopting a conclusion supported by the data we have so far and willingness to change views in the face of new/better data is EXACTLY like pure speculation?

  • Scientific inquiry shows us that there are far more stars in the sky than can be seen with the naked eye, that many of those stars have planets and that there are whole categories of weird things out there in space that we couldn't have even guessed at only a few hundred years ago. This is EXACTLY as valid as speculating that God's janitor, Barry, goes out each night to hang the stars one-by-one on a big velvet curtain over our heads?
  • Scientific inquiry has brought us the tools we rely on to diagnose and treat diseases far better than at any point in our history, greatly contributing to the unprecedented quality and duration of our lives. Microbiologists can even show us pictures of the pathogens that make us sick, and toy companies can turn those pictures into cute plushies. This is EXACTLY as valid as speculating that illness is brought on by demons, imbalance of humours, bad fung-shui or curses by witches?
  • Scientific inquiry has unearthed a fascinating story of the planet we live on, of how plate tectonics floating on a molten mantle change the face of the planet over unfathomable timescales; of the ever-changing forms of life populating the land, sea and air; of wild changes in climate and of catastrophic mass-extinction events. This is EXACTLY the same as speculating that we live on a 10,000-year-old, four-cornered flat earth resting under a dome held aloft by pillars at the world's edge?

So while everything we know through science may be wrong in the sense of not being 100% correct, we know that we're less wrong today than we were yesterday. I wrote a lengthier response addressing this in the 'Fallibilism' thread.

Is a conclusion based on induction rational or irrational? Does it always work?

Yes and no, respectively (and depending on what you mean by 'work').

It is entirely rational to hold a conclusion to be tentatively true based on the weight of evidence to date. Let's go back to the swans for a moment and try a slight variation (literally) with a combination of induction and deduction:

  • All swans I have seen so far are white.
  • Genetic variation, mutation and other extremely well-established principles of biology can trivially introduce changes in pigmentation.
  • It is not rational to conclude that all swans must be white. (Though I can rationally posit that most are if my sample size warrants)

Remember that science isn't some stamp-collection of facts, it's an interconnected web of facts, theories, experiments, etc. If we are using induction and arriving at wrong conclusions, we can usually remedy our error by including more data - either by going out to find it or by considering sources we may have neglected at first.

Not all swans are white, but are all heavenly bodies bigger than asteroids - that is: rocky planets, moons of sufficient size, gas giants, stars, etc. - (roughly) spherical?

  • All naturally-occurring heavenly bodies above a certain size threshold observed so far are (roughly) spherical
  • There are known mechanisms (gravity, etc) that explain the shape and slight deviations and why there is a size threshold and why other shapes would be unstable
  • It is rational to conclude that all naturally-occurring heavenly bodies are roughly spherical
Is deduction rational or irrational? Does it always work? ( assuming something can be rational always works, which may or may not be the case)

As others have pointed out, if the rules of logic are followed properly then yes the deduction is rational. If the premises are correct you'll get the added bonus that the conclusion will be correct. Depending on your definition of 'work' that'll translate to a 'yes' or a 'no'.

Can the conclusion that there is a creator of the universe be rational?

A very heavily qualified, theoretical 'yes'. IF valid premises lead to the logical conclusion, yes. HOWEVER: my assessment of the facts, as well as that done by many extremely knowledgeable people, have come to the conclusion that the universe we happen to find ourselves in does not support any of the premises required to arrive at a conclusion that our universe was created by some outside entity, much less that there's a cosmic being out there that has any concern for our little blue-green planet or the creatures thereon.

So when you ask:

Also please watch this. Is the logical proof for god valid?

I will refer you to this excellent index of creationist claims.

Hamza (person in the video) makes the argument that we can make a logical conclusion that a person is likely to have a great great great great grandparent. But isn't that assumption purely based on the evidence of his own existence, and thus induction?

Again, there's a whole body of knowledge that we've built through repeated observation, experiment, rigorous testing, etc. over the last few hundred years.

Induction is a powerful tool when you combine multiple lines of evidence into a succinct but powerful and predictive conclusion. Remember, though, the lesson of the black swan - all conclusions should be held tentatively, not absolutely.

However, the more we learn the closer our conclusions come to the truth. A black swan goes against our hypothetical notion that all swans are white, but at least there is a mechanism where we could accept - even predict - that an outlier would be found. Some claims, however, violate multiple well-supported lines of evidence. We would be foolish to accept a claim that Hamza sprang full-formed from the split skull of his father, violating everything we know about physics and biology, without an exceptionally comprehensive body of supporting evidence to back the claim!

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With respect to the first part of your question: induction is impossible. No knowledge has even been created by induction. Nor will any knowledge ever be created by induction. Explanations do not follow from observations in any sense. Nor do observations prove any idea. Nor can any observation make any idea one jot more probable. Inductivism is just another variety of justificationism: the idea that it is possible and desirable to prove ideas true or proably true. In reality, you can't prove any position or show it is probable. Any argument requires premises and rules of inference and it doesn't prove (or make probable) those premises or rules of inference. If you're going to say they're self evident then you are acting in a dogmatic manner that will prevent you from spotting some mistakes. If you don't say they are self evident then you would have to prove those premises and rules of inference by another argument that would bring up a similar problem with respect to its premises and rules of inference.

In reality all knowledge is created by conjecture and criticism. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem. Experiments are useful only as criticism. Ideas can't be derived from experiment any more than from any other set of premises. Rather, the idea is that you work out how the consequences of one theory differ from those of another. Then you conjecture ideas about experimental setups that would enable you to see the relevant consequences and criticise them. Once you have a setup that works about as well as you can make it work you use it to do the test. If the results are compatible with one theory and not the others then you may have successfully refuted some false ideas. Sometimes a purported successful experimental test will be successfully criticised because a test is a conjecture about something that happened and that conjecture may be wrong, so experiments don't prove anything.

What about deduction? Deduction is just working out the consequences of a conjecture. It may be used as part of a rational argument or an irrational attempt at argument. For example, if you start an argument by ignoring a criticism of your position, then the rest of the argument is just elaborating on something that may be a mistake: it is an irrational waste of time.

With respect to the grandmother issue, we know you grandmother exists in the same way we know everything else: conjecture and criticism.

The logical "proof" for the existence of God starts with the false assumption that God is a possible solution to the alleged problem of why the universe exists, but this is not true. The problem is as follows. Suppose that God exists, then one of the following is true.

(1) He made the universe on a whim, in which case we might as well say that "shit happens."

(2) He made the universe according to some principle X, in which case we can just say "the laws of physics respect principle X".

A further problem is that if God exists then there are no laws of physics or of morality or of biology or of anything else since God could choose to change them all. So the existence of God explains nothing and destroys all existing explanations. God does not exist.

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