Tuesday, May 05, 2009

The Limits of Logic

Let’s examine those syllogisms I presented in the last post and find out which are valid and which are not:

Syllogism A:

No Gox box when in purple socks.
Jocks is a Gox wearing purple socks.
Therefore Jocks does not now box.

Many people struggle with this syllogism, even though its logical structure is quite simple. The difficulty arises from the confusing, unfamiliar, even silly subjects of the syllogism. If presented in terms of more familiar objects, it becomes so easy that even a child can figure it out. Take, for example, the following syllogism, which has the same structure:

No cars run when they’re out of fuel.
My car is out of fuel.
Therefore my car does not now run.

Obviously, both syllogisms are valid. But as Morton Hunt notes, “if we were truly logical thinkers, we would find the first [syllogism] just as easy to evaluate as the second one.”

Syllogism B:

Those who believe in democracy believe in free speech.
Fascists do not believe in democracy.
Therefore Fascists do not believe in free speech.

Many people assume this syllogism is valid because the premises and conclusion all seem to be true. How, then, can it not be valid? Well, consider the following syllogism, which features the same structure:

Robins have feathers.
Chickens are not robins.
Therefore chickens do not have feathers.

Obviously, we confronting an invalid syllogism. The reason so many people are fooled is because they don’t use logic when they evaluate the syllogism, they use there own experience and knowledge. This is one of the critical findings of cognitive science. People don’t think logically, they think experientially, in terms of what they know.

Syllogism C:

Whatever makes for full employment is socially beneficial.
Being in a state of war tends to make for full employment.
Therefore war is socially beneficial.

Here we are confronted by a syllogism, the premises of which appear, at least superficially, as true, yet which has a conclusion that seems false. Yet the syllogism itself is valid. What gives on this one?

People tend to think this syllogism is invalid because the conclusion is wrong. They often don’t notice that the first premise is dubious, because it seems reasonable enough at first glance. What this syllogism demonstrates is the tendency for human beings to judge arguments based solely on whether they agree (or disagree) with the conclusion. Again, logic is ignored.

Syllogism D:

If it’s raining, the streets are wet.
The streets are wet.
Therefore it’s raining.

This is another syllogism that gives people great difficulty. Why? Because it exhibits a natural form of reasoning that is useful in ordinary life—so they are inclined to regard it as valid. But it isn’t valid—not logically. Even if the streets are wet, this doesn’t necessarily mean it must be raining. The streets may be wet for some other reason, such as a broken water main or a street-washing machine. To be sure, in real life, these alternative explanations aren’t very likely and can usually be ignored. That is why such reasoning, though logically invalid, often leads to correct conclusions and is used with great effectiveness in the real world.

Syllogism E:

Disease X is known to produce various symptoms, including A, B, and C.
This patient has symptoms A, B, and C.
Therefore this patient has disease X.

This is not a syllogism that was used to test logical ability in cognitive science experiments. On the contrary, it is the form of reasoning routinely used by doctors when analyzing patients. Logically, it is an invalid form of reasoning. But, as Morton Hunt notes, “it is a highly plausible way to begin a diagnosis.”

Syllogism F:

Some of the beekeepers are artists.
None of the chemists are beekeepers.
Therefore… some of the artists are not chemists.

This is the most difficult to get right (and you don’t have a 50% chance of guessing, like you do with the others). If we make the terms a little more sensible and familiar, it’s easy at least to evaluate as to its validity:

Some birds can swim.
No fish are birds.
Therefore some animals that can swim are not fish.

So what does all this prove (or at least suggest)? Namely this: that individuals rely far more on experiential and/or plausible reasoning when they judge the validity of arguments than they do on logic. And why is experiential/plausible reasoning more important than logic? Because, as Morton Hunt puts it,

logical reasoning is in large part abnormal, unnatural, and not generally applicable to everyday experience and to the problems of survival. [Logic] consists of a set of artificial rules that we can learn and can apply—indeed, must apply—in order to solve certain kinds of problems, but it is not a means by which our minds can effectively interpret the larger part of the reality around us; our natural way of reasoning, however, is just such a means…

Logic enables us to judge the validity of our own deductive reasoning, but much of the time we need to reason nondeductively—either inductively, or in terms of likelihoods, or of causes and effects, none of which fits within the rules of formal logic. The archetype of everyday realistic [i.e., experiential] reasoning might be something like this: This object (or situation) reminds me a lot of another that I experienced before, so probably I can expect much to be true of this one that was true of that one. Such reasoning is natural and utilitarian—but logically invalid.

9 comments:

Anonymous said...

"People don’t think logically, they think experientially, in terms of what they know."

Why do we only have to be *one* type of thinker? Thinking logically might not give us the answer, but it does often tell us what the answer can't be.

For example, in Syllogism E, that's a great way to kill a bunch of patients, just treating them for a disease X because that disease has symptoms A, B, and C.

What if there's a disease Y which has symptoms A, B, C, and D, but the treatment for disease X kills people who have disease Y?

Just because "much of the time we need to reason nondeductively—either inductively, or in terms of likelihoods, or of causes and effects" to begin with, that doesn't mean we shouldn't then submit what we've figured out to deductive reasoning.

Objectivists may be playing games by calling things that are only 'verifiable' by the term 'logical' but attack that, not the importance of logic itself.

Xtra Laj said...

Once we switch from "logical" to "verifiable" to "best guess inference", which is really what most human beings use when they aren't hardcore empirical scientists in their fields of expertise, then the attitudes of Objectivists towards skepticism and error becomes very unbecoming.

Anonymous said...

I got all them right, save for the last one (I couldn't figure out a conclusion). Do I get a cookie? ^_^

Wells said...

Actually Syllogism C Or

Whatever makes for full employment is socially beneficial.
Being in a state of war tends to make for full employment.
Therefore war is socially beneficial.

is still not logically valid.
The second line uses 'tends to', therefore the third line must also use 'tends to' rather than 'is' in order to be logically valid, since language that will weaken a claim will percolate down to the conclusion.

Here's why
The first line says,

Whatever makes for full employment is socially beneficial.
Or
Full Employment -> Socially Beneficial
Pretty stright forward.

However, the second line says
Being in a state of war tends to make for full employment.

Here you cannot assume that a state of war will result in full employment. Since you used 'tends to' what is being said is that war might result in full employment, which is a different claim from that it will.

More mathematically the statment says
(There Exists) a war that will result in full employment.
AND
(There Exists) a war that will not result in full employment.

So now we have two types of wars, One of which results in full employment, and the other of which does not. The one that does can, of course, be used to make the syllogism logically valid. The other cannot. While it could be possible for a war that does not result in full employment to nevertheless be socially beneficial, that conclusion does not follow from the premises.

gregnyquist said...

Anon: "For example, in Syllogism E, that's a great way to kill a bunch of patients, just treating them for a disease X because that disease has symptoms A, B, and C."

I think Anon has missed the point here. Sure, you could kill a lot of patients if this reasoning was the conclusion of the diagnosis—but as the start of the diagnosis, it's pretty good. In other words, this invalid form of reasoning is useful for coming up with a hypothesis (one can use "inductive" forms of reason as well for this sort of thing). But then, once you get the hypothesis, you start testing. Even this will not get you a definitive diagnosis, just well corroborated one.

Red Grant said...

Wells, brilliantly conceived and implemented arguement.

One of the very best I've read anywhere.

Actually, I had the same inkling, thought about making a point as you've made here, but I got distracted by E, and F.

Still, I don't think I would have made as succint and convincing arguement as you've made.


Well done!




___________________________________

I think Anon has missed the point here. Sure, you could kill a lot of patients if this reasoning was the conclusion of the diagnosis—but as the start of the diagnosis, it's pretty good. In other words, this invalid form of reasoning is useful for coming up with a hypothesis (one can use "inductive" forms of reason as well for this sort of thing). But then, once you get the hypothesis, you start testing. Even this will not get you a definitive diagnosis, just well corroborated one. - Greg
___________________________________





I agree, even though I still would say it's neither necessarily valid nor necessarily invalid on E.

Anonymous said...

gregnyquist and Red Grant:

Remember, the post where the syllogisms were first presented started out with this quotation from Leonard Peikoff:

"Logic is man’s method of reaching conclusions objectively by deriving them without contradiction from the facts of reality—ultimately, from the evidence provided by man’s senses."

Now, if the point of these two posts was to show that, as you said:

"Sure, you could kill a lot of patients if this reasoning was the conclusion of the diagnosis—but as the start of the diagnosis, it's pretty good."

Then these two posts use the Peikoff quotation as a strawman: you can't exactly attack someone's statement about how "Logic is man’s method of reaching conclusions" if your point is only about "starts" and not "conclusions."

I'm not saying there isn't plenty in Rand/Objectivism to attack when it comes to their insistence on logic, it's just that the attack should be that when someone Objectivists disagree with presents evidence in support of their conclusion, Objectivists dismiss it as "intuition" or "mysticism" or "faith"; when an Objectivist does the same thing, well, that's just 'provided by man’s senses'.

The real weakness in the Objectivists' defense of their philosophy (and not necessarily the philosophy itself) is that they create exceptions to their rules through which you can basically fit almost any other ideology you want as long as you dress it up in Objectivist terms. Allowing in that which is "provided by man's senses" as "evidence" is exactly that sort of exception: you could even bring in 'gut feelings' if you wanted by calling it 'data provided by the Enteric Nervous System'

However, don't start off with a quote about conclusions, and then make a point, well, not about conclusions.

Mark Stouffer said...

"People don’t think logically, they think experientially, in terms of what they know."

Isn't it logical to base your ideas on what you know, what you have experienced?

Also, doesn't Rand say "All knowledge is contextual"?

gregnyquist said...

Isn't it logical to base your ideas on what you know, what you have experienced?

Technically, no. But often logic is used in a non-technical sense. Instead of meaning the study of valid reasoning, it's simply used as a sort of vague synonym for "rational." Of course, one could come up with logical arguments in support of the proposition. But how many people actually bother doing that?

Also, doesn't Rand say "All knowledge is contextual"?

In the context of this post, what on earth is this supposed to mean? Does this mean that in some contexts (e.g., science, mathematics, geometry), logic is the appropriate method, and in other (e.g., some if not most everyday experience) it isn't? Well, in that case, there's no difference between my position and Rand's. But that surely can't be the case. It's extremely unlikely that either Rand or any of her orthodox followers would concede to my view (based on extensive cogsci research no less) that everyday practical reasoning is not strictly logical. Indeed, I doubt that they could even understand my view. Objectivists tend to forget that there's a lot more to logic than merely avoiding blatant contradictions. Nearly everyone recognizes and abhors people who speak out of both sides of their mouth, saying one thing one moment and the exact opposite the next. But logic is a lot more exacting and subtle than merely asserting that A is A and it is wrong to say otherwise. There are all sorts of inferences that are useful in practical life (because they lead to true conclusions in the majority of instances) but are technically invalid and illogical. I don't find in Objectivism any appreciation of this interesting fact.

I would also note that logic is far more useful when it comes to testing conclusions than it is at arriving at conclusions. This is really the larger point in all my criticism of the Objectivist over-emphasis on logic. I contend that Rand placed way too much emphasis on processes of thought: on focusing one's mind, concept-formation, logic, etc. Rand appears to have believed that she was right and everyone who disagreed with her was wrong because she knew how to think. That is an arrogant attitude that is contrary to science and practical wisdom. The presumed quality of thought that goes into one's conclusions about matters of fact in no way objectively validates or confirms or even corroborates them.