When considering a logical argument, a person states premises that are true in order to draw a conclusion that is true - thus making a valid and sound argument.
Example:
If I oversleep, I will be late
I overslept this morning
Therefore, I was late
However, what if the preferences are personal opinion in nature? It seems like you could have a perfectly sound and valid argument, from the point of view of contructing a logical argument, even though it may very well be wrong.
Example:
I think {politician} is an idiot
I think people who vote for idiots are idiots
Therefore, I think people who vote for {politician} are idiots.
From a logical stance, it appears to be valid and sound, thanks to the qualifier ‘I think’ in both premises and the end conclusion. However, it just seems like there is a glaring hole in this to be considered complete and sound logic due to the extreme amount of personal opinion.
Is there a name for this type of thing? The closest I can come up with is the difference between logic and reasoning, but that doesn’t quite cover it. Or maybe it is actually perfectly valid and sound logic.
The second syllogism you create is perfectly valid. But an argument can be valid without its conclusion being true, because deductive logic manipulates false statements, and even nonsense, just as easily as it does true statements.
I don’t think it’s common knowledge what ‘formal’ means in the context of ‘formal logic’: It isn’t to do with decorum or politeness, except perhaps tangentially, but is entirely about using ‘formal’ to mean ‘of or relating to form’. That is, formal logic only concerns itself with the form, or shape, of arguments, not their content. As long as an argument is properly formed, it is valid as far as formal logic is concerned.
This is why the study of such things replaces all English (or other natural language) with mathematical symbols, so the meaning of real words doesn’t intrude and make it more difficult to see the underlying skeleton of the argument.
Objection. Assumes facts not in evidence. I think for this argument to be valid, it needs to be restated as:
I think {politician} is an idiot.
I think people who vote for those I think are idiots are idiots.
Therefore, I think people who vote for {politician} are idiots.
The minor premise must be modified because the major premise only states who you think are idiots, whereas your minor premise talked about those who voted for idiots, when we haven’t determined if anyone is an actual idiot.
Stated this way, it is a valid and sound argument about your own thoughts. But it says nothing about the world.
friedo is technically correct, I guess, but it is a bit of a nitpick. Basically the argument is sound, and the conclusion is true, so long as it remains qualified by “I think.”
One could make another nitpick here about the “I think” creating an intensional (yes, that is spelled correctly) context. (That may be the terminology that silk1976 is looking for: what makes this sort of argument different from ones based on facts about the word rather than about someone’s opinions.) Just because C follows from A and B, it is not necessarily the case that somebody who believes (thinks) both A and B will believe C. They may simply have failed to ever draw the inference. However, as the OP’s example is of someone who does draw the inference, this is a bit beside the point.
Skald Your point about the conclusion being true is part of what makes the line of thought in the second example somewhat confusing. At first I was thinking that there just HAD to be some reason why the second example was faulty logic - but having the qualifier ‘I think’ in every statement pretty much eliminates that. If someone thinks someone else is an idiot - kind of hard to refute that.
njtt expressed more clearly what I was thinking. The second example is based on personal opinion facts, as opposed to hard-world facts.
So far all I’ve come up with is that the logic is sound and valid (especially with the additional qualifier that friedo mentioned) - but the reasoning is full of holes and not necessarily universal. Maybe?
No. The reasoning is fine (modulo what freido said) so long as the reasoner does not take the additional step of assuming that the fact that he thinks something makes it more likely to be true. That is perhaps a temptation in cases like this, but no such false step was taken in your original example.
No, because the OP’s argument is perfectly valid. It just doesn’t prove what someone might think it does, because the “I think …” qualifier removes meaning.
Here’s a non-sequitur in a syllogism:
All of Skald’s threads on the Dope are primarily intended to amuse Skald himself.
I find all of Skald’s thread’s amusing.
Therefore I am Skald.
Now, as it happens, the conclusion is true; I am Skald. But it doesn’t follow from the argument, because there is nothing to establish that the set of people who find Skald’s threads amusing is limited to one person, or that Skald succeeds in amusing himself in all the threads he starts.
With the exception of Descartes’ cogito idiom, the phrase “I think” should be avoided generally. And Descartes was using the word “think” in a very different way. Opinion is not logic, although logic can be affected by opinion and vice versa.