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 Post subject: The overlap of deductive and inductive reasoning
PostPosted: Sat Apr 21, 2018 4:25 am 
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I wanted to get your thoughts on what I perceive to be an overlap in deductive and inductive reasoning and what practical importance, if any, this might have. To start with some simple definitions, deductive reasoning is, these days, defined generally as a form of reasoning in which the conclusion is guaranteed by the premises based on the form of the argument; whereas inductive reasoning is defined as a form of reasoning in which the conclusion is inferred from or warranted by the connection between the premises. These definitions are different from the older definitions of reasoning from general to particular (for deduction) and reasoning from particular to general (for induction). Moreover, today deductive arguments are analyzed in terms of validity and soundness, where validity has to do with the form of the argument and is truth preserving rather than truth making, and soundness has to do with both validity and the truth of the premises (so all sound arguments are also valid). Inductive arguments, on the other hand, are analyzed in two analogous terms: strength and cogency. A strong argument is one in which the premises strongly warrant the conclusion (without respect to their truth value), while a cogent argument is a strong one that also has true premises. There's a lot more that could be said about that and I have some questions even about those distinctions and some of their more precise relations, but I want to press on to get to the question that really interests me.

Inductive reasoning is not, we are told, a matter of form, but there are, still, certain common forms. The typical form a simple induction is something like:

1. Proportion Q of known instances of population P has attribute A
2. Individual I is a member of P
3. Therefore I probably has attribute A

An instance of this type of argument might be:

1'. Young men who live in the southeastern United States and who own trucks usually like country music
2'. John is a young man who live in the southeastern United States and who own trucks usually like country music
3'. Therefore, John probably likes country music

And this is said to be an inductive argument because the conclusion isn't guaranteed; after all, John might not like country music after all. Similar forms and instances could be made for generalizations, arguments from analogy, arguments from enumeration, etc. But now I have to wonder . . . isn't this example deductive and even necessarily true after all? Suppose it turns out that John does NOT like country music. Does it follow that 3' is false? On the one hand, it could seem obvious it is. If John doesn't actually like country music, then there is no probability that he does. I can say there is a 1:6 chance that when I roll this dice that it will land on a 2, but I have to say that before I roll it. Having rolled it, and seeing it land on a 2, I can't say it has a 1:6 chance of actually being a 2. I can say it had a 1:6 chance of being a 2. I can say it has a 1:6 chance of being a 2 on the next roll. But I must say it has a 1:1 chance of being a 2 now that actually is a 2, and a 0:6 chance of it being a 1, 3, 4, 5, or 6. Construed this way, again, 3' is false because there is no probability that John likes country music.

But doesn't 3' really just mean exactly what it says? There is a probability that John, as a member of a particular population, likes country music. There is a sense in which that probability remains regardless of whether John does or doesn't like said music. Statisticians, in fact, need that data and would build population distributions based exactly on that. In other words, we could interpret the syllogism along these lines:

1''. 84% of members of population that are {male; between the ages of 16-36; live in the states of Georgia, Alabama, Mississippi, South Carolina, North Carolina, Tennessee, or Arkansas; and are truck owners} [let this population be P] are also members of the population that {like country music} [let this population be Q]
2''. John is a member of population P
3''. Therefore, there is an 84% chance that John is a member of population Q

Now, technical matters aside on the relation between samples and population and how you actually figure out probability (I know I've overly simplified and misrepresented that part of the analogy) . . . grant that John is not, in fact, a member of population Q (he doesn't like country music). That doesn't chance the statistical fact that he still had a statistical probability of being with said group. The dice that landed on 2 still had a 5:6 chance of landing on some other number.

If this is correct, then I finally come to my question: is there not a real sense in which this argument is, in fact, a real deduction? That is, the conclusion is necessarily true, for even if John turns out NOT to like country music, the conclusion, as stated remains true, and that necessarily so. And if is in fact the case, then it seems to me that ALL induction is of this type, that ALL induction relies on a previous deduction.

Take this argument by analogy

1. I have a 1999 Toyota Camry
2. Tonya has a 1999 Toyota Camry, and her car gets 30+mpg
3. My car will get 30+mpg

Perhaps this isn't a strong argument, but it is still necessarily true as stated, so long as we interpret it probabilisticly. What this really means is that there is some statistical chance that my car gets 30+mpg. It seems to me that, so long as we are interpreting inductive arguments with reference to strength, then we necessarily are making them statistical and thus, in principle, a very specific form of deduction.

I think my confusion is rooted in the two ways to interpret the conclusion of the inductive argument (so see my comments on the dice example). But I wonder if this isn't getting at an error, or at least an imprecision, in the definition proposed for "inductive reasoning." For it truly is necessarily true that some event has a certain probability of obtaining, and that whether it does or does not. We are deducing that probability. Is induction, then, merely taking the trivial step of predicting what will obtain based on those percentages (whether or not we've done the work of actual calculating the numbers or just going with our general perception)? Or have we gotten off at the very beginning of all this?

Sorry for the length, but those of you who have studied or even read anything on the philosophy of logic or know how modern logic compares to classical logic, if you could enlighten me on this and how to think about it, I would be appreciative.

Thanks

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Sat May 05, 2018 10:35 pm 
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So the forum has gone dead since this post....

I’m not responding to it as its way over my head. I still drinking the philosophical “milk” so to speak and am no where near eating the “meat”. Its a great discussion he’s written, but I think out of respect for Jack people don’t want to post anything else until someone has something to say in response.

So, after 191 views I thought, “I going to respond so that others will start posting again in this forum.”

I’ve don’t my part.

Discuss......

P.S. - sorry for the hijack.

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Sun May 06, 2018 5:57 am 
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If your point is that we use deductive reasoning to reach inductive conclusions, I agree. Where do we go from here?

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Sun May 06, 2018 6:15 am 
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I am very much interested in the comparison of modern vs classical logic as well.

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 11:32 am 
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Obi-Wan Kenobi wrote:
If your point is that we use deductive reasoning to reach inductive conclusions, I agree. Where do we go from here?

I guess where we go from here is to ask whether or not "inductive reasoning" is even a meaningful concept in modern logic, and if not, I'd ask is it a meaningful concept in classical logic. The older definition of inductive reasoning was reasoning from particular to general, whereas deduction was to reason from general to particular. Those definitions are widely rejected today. But it seems to me the price of that rejection is to actually say that there is no such thing as induction whatsoever. All of our so-called inductive arguments are merely probabilistic deductions, such that "inductions" is really just a short hand way of saying, "I don't feel like doing the hard work of working out the statistical probability of this statement being true, so I'm just going to say 'probably'." I suspect modern logicians would object to that characterization, but it still seems to me that's what happens.

So I'm asking, then, what ought we understand the precise nature of an inductive argument to be. If it isn't reasoning from the particular to the general (and maybe it is and modern logicians are just wrong on this point as they are, in my opinion, on several others), then what is it? Is it just deducing that X has a probability less than 100% of being true? But even that doesn't seem to help, because most classically understood deductive arguments would be the same.

All mammals are air-breathers
All whales are mammals
All whales are air-breathers

That's a typical deductive argument (AAA-1 in form). But the probability of this isn't 100% . . . maybe 99.99999%. For maybe we'll find a whale that isn't an air-breather after all. Or, perhaps, that whales just aren't mammals as we thought (no-true scotsman, anyone)? The point is that unless you are talking about analytical statements (i.e., all married men are bachelors), you always have probabilistic claims, even where that probability is near enough to 100% that we may justifiably treat it as 100%.

I ask this here because, as I understand it, classical thought isn't as concerned with mathematical certainty as we tend to be today. So I wonder how this effects our understanding of the nature of deduction and induction (because, later, this will have an impact on how I understand/classify/approach abductive arguments in relation to deductions).

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 11:40 am 
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As a former actuarial worker, I can say that many (most) probabilities are a lot less quantifiable than we like to think. So I'm not sure that you're accomplishing much more than hiding the uncertainty behind another layer--we're 95% sure that the probability is 84%. And I'm not sure that's much of an achievement.

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 12:01 pm 
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Peetem wrote:
So the forum has gone dead since this post....

I’m not responding to it as its way over my head. I still drinking the philosophical “milk” so to speak and am no where near eating the “meat”. Its a great discussion he’s written, but I think out of respect for Jack people don’t want to post anything else until someone has something to say in response.

So, after 191 views I thought, “I going to respond so that others will start posting again in this forum.”

I’ve don’t my part.

Discuss......

P.S. - sorry for the hijack.

I don't think you can hijack something not going anywhere . . . ;)

But thanks for the bump. These thoughts popped into my mind while preparing some lectures on introductory issues in logic. The chances of this coming up in class are almost non-existent, but they came up for me, and so I thought I'd ask here!

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 12:53 pm 
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I originally saw it at a bad time to reply and then promptly forgot about it. I'm glad Peetem bumped it.

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 2:25 pm 
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Obi-Wan Kenobi wrote:
As a former actuarial worker, I can say that many (most) probabilities are a lot less quantifiable than we like to think. So I'm not sure that you're accomplishing much more than hiding the uncertainty behind another layer--we're 95% sure that the probability is 84%. And I'm not sure that's much of an achievement.

But even in those cases you can assign confidence intervals. I doubt, though, that the difference in an inductive and a deductive argument is when you cross some confidence interval threshold, as in, if I'm less than 95% sure that the probability of X:Y is 87%, then it's an inductive argument, otherwise, it's deductive.

Consider this argument:

1. There are 100 marbles in this jar
2. Of four randomly drawn marbles, three are black and one is white
3. The next randomly drawn marble will be black

So this is a fairly strong and cogent inductive argument. We're inferring that most of the marbles in the jar are black (in fact, that could be the conclusion if you wish to substitute it). This is considered inductive precisely because it's not necessary -- the premises do not, by their form, entail the conclusion. And I certainly agree with that. It could well be that, by chance, I randomly drew out only three black marbles and the remaining 96 marbles are all white! The odds are low, but they are calculable and real. But when I press these definitions, this way of distinguishing deductive from inductive arguments doesn't seem to hold. After all, I can restate my conclusion as follows:

3' There is a probability [stated explicitly or not] that there are more black marbles in the jar than there are white marbles

Now I'd have to flesh that out a bit as this is something of an enthymeme, but my point is just that it could be done with minimal effort, and then this would be a proper deduction. For even if it turns are that it is FALSE that there are more black than white, it remains true--and this by entailment it seems to me--that there is, in fact, a probability that there are more black than white. Just so, I could deduce that I have an x% chance (give or take a few points within a certain confidence interval) of pulling a white marble.

What, then, is the dividing line between deduction and induction? At least from the examples I'm looking at, entailment of the conclusion by the premises does not seem like a sufficient delineation. More generally statement, having a probabilistic and uncertain conclusion does not seem like a sufficient delineation. Rather, it just seems that in some deductions, the entailed conclusion is such that it cannot be false, and with other deductions, the entailed conclusion is such that it allows for a range of possible outcomes with a corresponding probability function.

edit:

The more I write, the more I am convincing myself that the new definition is simply wrong, and the older is correct. I find myself thinking that inductive reasoning is real, but that it constitutes reasoning to the general based on the particular. On this view, I can deduce the probability that some statement is correct, but that is distinct from the generalization itself. The generalization would be a result of inductive reasoning . . . deduction would help me justify how strongly to hold to or defend my inductive claim. I'm biased towards that because it fits with the narrative I have against analytical philosophy generally, which is that it, historically, has tended to confuse a mathematically oriented description of a subject with the definition of the subject (and that creates a whole set of problems on its own . . . I'm thinking specifically here of the problems Henry Veatch points out in his amazing but very dense book, Two Logics).

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 3:35 pm 
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As you might guess, I am partial to the older definition.

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 4:07 pm 
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So I'm not off my rocker then with my discomfort with the way introductory texts on logic treat this subject! :cloud9:

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Mon May 07, 2018 4:17 pm 
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I might be off my rocker too. What are the odds?

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Thu May 10, 2018 7:39 pm 
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Obi-Wan Kenobi wrote:
I originally saw it at a bad time to reply and then promptly forgot about it. I'm glad Peetem bumped it.


Thanks.

I was trying to prevent Gherkin taking over.

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 Post subject: Re: The overlap of deductive and inductive reasoning
PostPosted: Thu May 10, 2018 7:40 pm 
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Who is this "Gherkin" of whom you speak?

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