Definitions of Induction and Deduction -- Help a Confused Beginner

[Garrette]

In the thread There is no evidence for God, poster case#46cw39 used the terms "inductive" and "deductive" in a manner I thought to be incorrect, so I challenged him. He responded, and yy2bggggs chimed in on my side. For the record, SumDood also challenged case#46cw39's definition, but on different grounds than I did.

I am still not convinced that case#46cw39 is correct, but I am less certain than when I challenged him. I started this thread so as not to derail the other.

Here are the relevant posts from that thread:

case#46cw39 said in this post:

Right and I've said just that. But there are two possible negative options:
(%) God existing is implausible, or
(1) God existing is impossible (scientifically certainly true, .95%).

The prior is an inductive, probables conclusion meaning I dont know (for sure) and that means agnosticism. The other is a deductive (scientifically, virtually) certain conclusion based on "complete" evidence as deduction requires. That's what it means to be an atheist (or Theist). I have not seen that evidence that is complete (both acceptable and sufficient), and so I am an agnostic.

After I challenged that definition, case#46cw39 said in this post:

Well in reference to out current debate this is a good place to start - Internet Encyclopedia of Philosophy, a Peer reviewed Academic Resource ...

"...deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises, ...
http://www.iep.utm.edu/ded-ind/

[*So the the premises are said to be complete or able to guarantee the certain conclusion (scientific .95%) in deduction. The conclusion is merely probable in induction because the premises offer only partial support (incomplete).*]

For this debate of am I agnostic or an atheist the following is worth contemplating:

The difference between the two comes from the sort of relation the author or expositor of the argument takes there to be between the premises and the conclusion. If the author of the argument believes that the truth of the premises definitely establishes the truth of the conclusion due to definition, logical entailment or mathematical necessity, then the argument is deductive. If the author of the argument does not think that the truth of the premises definitely establishes the truth of the conclusion, but nonetheless believes that their truth provides good reason to believe the conclusion is probably true, then the argument is inductive.
http://www.iep.utm.edu/ded-ind/

An inductive, merely probable conclusion is supported by partial, incomplete evidence. It's equivalent to saying "I don't know (for sure)", and that equals agnosticism.

A deductive, definitely certain conclusion is supported by completely guaranteeing evidence. It's equivalent to saying "I know for sure."

I don't believe a deductive argument is possible, ergo I'm an agnostic. This is my take on it and how I use those terms. Someone asks me if I believe in God I say "I don't know for sure if there is no God or if there is. I'm an agnostic."

yy2bggggs responded in this post:

The phrase "for sure" does not belong in parentheses. Putting it there suggests that to know is the same as to know for sure.

I know my car is in my driveway. I don't know that for sure, though. I think the demand for certainty or the focus on lack of certainty is overrated. I think I still get to claim that I know my car is in my driveway.

I might be wrong, but I'm probably not wrong. I'm fine with that.

Follow by case#46cw39 in this post:

OK so it could be .. "I don't know for sure" meaning the virtual certainty of science set at .95%. If we say a conclusion is deductively certain true this is what we mean. And let's say that''s the same standard in life usually. So I type these letters and see them appear and am deductively certain (.95 % certain) my PC is working. So I would answer this question deductively in the affirmative: Yes. My computer certainly is working. Yes, your car is certainly in your driveway. This is a deduction and the 95% threshold of certainty we use. Some things we are certain of within this range, based on having complete deductive evidence.


This is equivalent to answering our "Is God a fiction? in the affirmative: Certainly yes. As deductively certain as you are of your car being in the garage or other scientific certainties, that magic 95+% scientific, deductive certainty of the atheist.

I can't get there.

My remembrance of induction and deduction is that the first is moving the specific to the general while the latter is moving from the general to the specific, but I suppose that may be another way of saying "less certain" vs. "certain." I'm just not convinced yet.

And to be clear: let's not get bogged down in a definition of "certain." We know that we're not dealing with mathematical certainty, but we should be able to understand, I think, the logical usage.

 

[Denver]

My recollection, is that deduction is logically correct inference: If B is true given A, and then A is given as true, then B is true. This can still include probabilities: B is at least 80% likely to be true given A is at least 40% true. If A is given as 50% likely to be true, then B is at least 80% likely to be true. Given the data, it would be 'certain' than B is as least 80% true. So you really have to understand the domain and the data to speak of certainty, even in a deductive environment.

Induction is more probability or experience: You land on a new planet, and see one plant with red leaves. You explore the environment for days and miles, and each and every plant you see has red leaves. You get a twitter from a friend a few miles further away. He says he just landed in a field of plants. He doesn't mention their color. You induce they were red.

 

[case#46cw39]

My remembrance of induction and deduction is that the first is moving the specific to the general while the latter is moving from the general to the specific, ...

Well, that's the first problem..

Though many dictionaries define inductive reasoning as reasoning that derives general principles from specific observations, this usage is outdated.[2]

The premises of an inductive logical argument indicate some [partial/incomplete] degree of support (inductive probability) for the conclusion
but do not entail it; that is, they suggest truth but do not ensure it [due to evidence not being deductively complete.]

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


As I've described it is the new usage.

 

[Garrette]

Okay, Denver, I certainly follow the example about induction as that follows my understanding exactly.

The bit about deduction makes sense as you state it and is, I suppose, a more rigorous explanation than the layman's phrase of moving from the general to the specific. In your example with probabilities, the deductive (certain) conclusion isn't B but is, instead, that B is 80% likely to be true. Am I getting that right?

 

[Garrette]

Well, that's the first problem..

Though many dictionaries define inductive reasoning as reasoning that derives general principles from specific observations, this usage is outdated.[2]

The premises of an inductive logical argument indicate some [partial/incomplete] degree of support (inductive probability) for the conclusion
but do not entail it; that is, they suggest truth but do not ensure it [due to evidence not being deductively complete.]

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


As I've described it is the new usage.

Thanks. I'm still reading this and some other stuff on line. I've got commitments today so don't know when I will be able to post again, but I'm not ignoring you.

 

[case#46cw39]

Actually I've been cherry picking from a book I'm writing. Gotta stop doing that.

 

[69dodge]

And to be clear: let's not get bogged down in a definition of "certain." We know that we're not dealing with mathematical certainty, but we should be able to understand, I think, the logical usage.

I always thought that "deduction" did refer to deriving conclusions with mathematical certainty.

 

[drkitten]

I always thought that "deduction" did refer to deriving conclusions with mathematical certainty.

The most general formulation that I've seen is that in deductive reasoning, the conclusion is certain; with inductive reasoning, the conclusions need not be certain.

But you have to be careful about exactly what you consider to be the conclusion, especially when the conclusion involves probabilities.

For example, it can be deductively shown that a fair die has one chance in six of showing an ace. In this case, the conclusion is the complete statement "`this die will come up a one' is true with probability 1/6.'

In other words, we have the statement 'B' ("this die will come up a one") and statement 'A' ("B is true with probability 1/6). A can be shown deductively from the assumption that the die is fair; B can never be shown deductively, but can be shown inductively to be true with probability about 1/6 by testing.

And we can also show A to be true inductively by that same testing, but in that case, we don't have a dead cert, just the statistical confidence.

 

[Robin]

But induction does not mean just any argument where the conclusion is not certain.

It means a very specific thing - it means arguing from the particular to the universal.

 

[Robin]

Also, not all forms of induction lead to uncertain conclusions.

The conclusion of an argument using mathematical induction is deductively valid.

It qualifies as induction because it does argue from the particular to the universal.

 

[case#46cw39]

Also, not all forms of induction lead to uncertain conclusions.

The conclusion of an argument using mathematical induction is deductively valid.

It qualifies as induction because it does argue from the particular to the universal.

Though many dictionaries define inductive reasoning as reasoning that derives general principles from specific observations, this usage is outdated.[2]
http://en.wikipedia.org/wiki/Inductive_reasoning


Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of rigorous deductive reasoning.
http://en.wikipedia.org/wiki/Mathematical_induction

 

[I Am The Scum]

I think one of the problems with this discussion is that many, when observing an argument, attempt to analyze our certainty of the premises in order to infer our certainty of the conclusion. This is not a valid distinction between inductive and deductive. I'll give an example.

1. All men are mortal.
2. Socrates is a man.
C. Socrates is mortal.

It doesn't matter how certain you are of premises 1 and 2. This is a deductive argument, in that, if the premises are true, then the conclusion must be true. On the other hand...

1. Most men are mortal.
2. Socrates is a man.
C. It is more likely than not that Socrates is mortal.

That's inductive. Given the premises, we can't say with certainty that Socrates is mortal. However, we are still somewhat justified in concluding that he is.

There is no sliding scale between inductive and deductive. As an inductive conclusion becomes more certain, it does not get "closer" to becoming deductive. It's either one or the other.

 

[Denver]

Okay, Denver, I certainly follow the example about induction as that follows my understanding exactly.

The bit about deduction makes sense as you state it and is, I suppose, a more rigorous explanation than the layman's phrase of moving from the general to the specific. In your example with probabilities, the deductive (certain) conclusion isn't B but is, instead, that B is 80% likely to be true. Am I getting that right?

Yeah that sounds right: it is that the original statement (if A-stuff is true, then B-stuff is true) holds. whatever B-stuff is. In this case, it's B's probabilities (or B's colors, or B's age, etc).

Another way it can be defined is making implicit knowledge, explicit. So if 1) A is true, then B is true, and 2) A is true. Implicitly, B is true in there someplace. When you actually pull it out and state B is true, that statement, that new rule, that addition to your explicit knowledge base, was generated via deduction.

There is another inference type, called abduction. If I instead said: 1) If A is true then B is true, and 2) B is true, abduction might allow me to say, you know, maybe A could be true. It's a good one to watch for, because it is not deduction, but some people true to use it as such. I.e: A) if God created the universe, then B) The tides would come, and go out, with no mis-communication. Since B is true, then A is true. Abduction.

 

[I Am The Scum]

There is another inference type, called abduction. If I instead said: 1) If A is true then B is true, and 2) B is true, abduction might allow me to say, you know, maybe A could be true. It's a good one to watch for, because it is not deduction, but some people true to use it as such. I.e: A) if God created the universe, then B) The tides would come, and go out, with no mis-communication. Since B is true, then A is true. Abduction.

Actually, that's just affirming the consequent^WP.

 

[Denver]

Actually, that's just affirming the consequent^WP.

Yes, as is explained under abductive reasoning^WP

Abduction allows inferring a as an explanation of b. Because of this, abduction allows the precondition a to be abduced from the consequence b. Deduction and abduction thus differ in the direction in which a rule like "a entails b" is used for inference. As such abduction is formally equivalent to the logical fallacy affirming the consequent or Post hoc ergo propter hoc, because there are multiple possible explanations for b.

 

[Robin]

Though many dictionaries define inductive reasoning as reasoning that derives general principles from specific observations, this usage is outdated.[2]
http://en.wikipedia.org/wiki/Inductive_reasoning


Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of rigorous deductive reasoning.
http://en.wikipedia.org/wiki/Mathematical_induction

I would hardly regard Wikipedia as an authority.

It is not just dictionaries (such as the Oxford English Dictionary) Boole, De Morgan and Mill all defined induction as I have done. It is normally how Aristotle's "epagoge" is translated and Aristotle's word referred to arguing from the particular to the universal. I see no evidence that this is outdated.

Whenever we hear of the "problem of induction" it is always used in this sense. Think of the iconic example of the problem of induction - about seeing only white swans. That is arguing from the particular to the universal.

And the reason that mathematical induction is so-called is that it is a method of arguing from a particular member of the set to the whole set.

The idea that induction and deduction were mutually exclusive was then shown to be wrong.

 

[case#46cw39]

I would hardly regard Wikipedia as an authority.

It is not just dictionaries (such as the Oxford English Dictionary) Boole, De Morgan and Mill all defined induction as I have done. It is normally how Aristotle's "epagoge" is translated and Aristotle's word referred to arguing from the particular to the universal. I see no evidence that this is outdated.

Whenever we hear of the "problem of induction" it is always used in this sense. Think of the iconic example of the problem of induction - about seeing only white swans. That is arguing from the particular to the universal.

And the reason that mathematical induction is so-called is that it is a method of arguing from a particular member of the set to the whole set.

The idea that induction and deduction were mutually exclusive was then shown to be wrong.

Well there has been a contemporary shift and what you say, while it's how it used to be taught, is no longer the case.

The wiki quote had a [2] citation which referred to the Internet Encyclopedia of Philosophy which is "a Peer-Reviewed Academic Resource". So let's agree that this and the Stanford Encyclopedia of Philosophy are good resources.

FROM: http://plato.stanford.edu/entries/induction-problem/ ...
"The Oxford English Dictionary defines “induction”, in the sense relevant here, as follows: The process of inferring a general law or principle from the observation of particular instances (opposed to DEDUCTION, q.v.).

That induction is opposed to deduction is not quite right, and the rest of the definition is outdated and too narrow: much of what contemporary epistemology, logic, and the philosophy of science count as induction infers neither from observation nor from particulars and does not lead to general laws or principles. This is not to denigrate the leading authority on English vocabulary—until the middle of the previous century induction was understood to be [that] ..."

and it goes on ...

"Although inductive inference is not easily characterized, we do have a clear mark of induction. Inductive inferences are contingent, deductive inferences are necessary. ... Of course, the contingent power of induction brings with it the risk of error. Even the best inductive methods applied to all available evidence may get it wrong; good inductions may lead from true premises to false conclusions. (A competent but erroneous diagnosis of a rare disease, a sound but false forecast of summer sunshine in the desert.) An appreciation of this principle is a signal feature of the shift from the traditional to the contemporary problem of induction."
http://plato.stanford.edu/entries/induction-problem/

So:

Deduction leads to necessary conclusions based on "complete" evidence, meaning complete to guarantee the truth of the conclusion ... it MUST be true. The same can't be said for inductive conclusions which are at best probably true , and could well be false.


Induction leads to probable but not necessary conclusions based on "incomplete" evidence, meaning not enough to guarantee the conclusion, but just to conclude there is a certain probability it's true (but could be false).

So I stand by my descriptions of induction and deduction.

 

[fuelair]

Induction is when you use a magnet and a coil of wire to produce electrical current.
Deduction is when you have money removed from your pay to keep you from spending it all on drink and wild women - or so the government can spend it all on same.
Hope this helps!!

 

[case#46cw39]

I think one of the problems with this discussion is that many, when observing an argument, attempt to analyze our certainty of the premises in order to infer our certainty of the conclusion. This is not a valid distinction between inductive and deductive. I'll give an example.

1. All men are mortal.
2. Socrates is a man.
C. Socrates is mortal.

It doesn't matter how certain you are of premises 1 and 2. This is a deductive argument, in that, if the premises are true, then the conclusion must be true. On the other hand...

1. Most men are mortal.
2. Socrates is a man.
C. It is more likely than not that Socrates is mortal.

That's inductive. Given the premises, we can't say with certainty that Socrates is mortal. However, we are still somewhat justified in concluding that he is.

There is no sliding scale between inductive and deductive. As an inductive conclusion becomes more certain, it does not get "closer" to becoming deductive. It's either one or the other.

Very clear. And I agree with it all. It's in the structure of the deductive argument that makes the conclusion guaranteed. No matter how much the probability of an inductive argument like your example changes, its structure remains the same, an inductive structure, which can never guarantee its conclusion.

Your inductive argument sample:

1. Most men are mortal.
2. Socrates is a man.
C. It is more likely than not that Socrates is mortal.

So what's the difference? Premise 1 went from a universal premise (All men are mortal.) to a particular premise having a numeric probability. Technically it's just a "some" sentence:

Some (x%) men are mortal.

And this premise structure does not ever produce a guaranteed conclusion:

Some men are mortal
Socrates is a man
--------------------
No guaranteed, deductive conclusion possible

 

[I Am The Scum]

Actually, the more I think about my example, the less I like it. I'm gonna have to rethink this one.