When applying formal logic to a problem can the results ever be illogical and erroneous?
Yes
No
The qusetion is impenetrable and mind boggling
When applying formal logic to a problem can the results ever be illogical and erroneous?
Asking if it can is asking if it’s possible. Like with most tools, there are limitations to them, yet for the vast cases we come across where it’s not contrived to an extreme, applying formal logic will serve us well.
One of the silly criticisms of inductive arguments is that conclusions are not guaranteed. Well, they’re not supposed to perform the function of deductive arguments anymore than are drills suppose to perform the function of skill saws. So, if you come across a tool that DOES NOT perform a certain way, don’t consider it a FAILURE if the tool is not being used as it was designed to be used.
If memory serves me, there’s an old classic example where it’s shown that logic, even when applied properly, can lead us to faulty conclusions. It’s unlikely that one can travel from one side of the room to the other because between one side and the other is a halfway point (that even it) is unlikely to reach because between the start and that halfway point is yet another halfway point. Because there is no limit to the number of halfway points, it’s decreasingly unlikely for one to make progress such than the entire room can be traversed.
If it were worded right, we should be able to see that it’s logical. An underlying flaw that makes it obviously false doesn’t automatically render some part of the process illogical. Most people who see an obvious flaw or fault might deny that the process was logical, but it just might very well be logical—just not completely flawless.
The poll's question: Can using logic lead to ilogical and erromeous results?
The question is terminally messy.
So, yes, using logic can lead to erroneous results.
For example if the premises are wrong.
Or if logic is applied wrongly. This happens, all the time.
However, still today we don't know whether logic has intrinsic flaws or not. It is not only plausible, but probable that logic works near perfection for a range of problems but not outside of this range. The reason for that is simple: logic is a capacity of the human mind and the human mind is the result of natural selection. As such, logic is most likely faultless for those problems which have been operational in natural selection but there is no apparent reason that it should also be faultless for problems that haven't been tested at all but also for problems too infrequent to have made a dent in the evolution of logic.
The basic principle of biological functions generally is that they are fundamentally compromises between several constraints and are therefore never optimal in respect to any one of these constraints. A better logic would likely have required a much larger brain, probably to the detriment of other functions.
So, on probability, our logic must have intrinsic flaws and therefore using logic is likely to lead to faulty conclusions for specific problems, in particular for complex problems.
This wouldn't affect ordinary life problems.
However, with the development of scientific theories that are of increasing complexity, it seems inevitable that we hit the wall of invalidity at some point in the future. Computers could come to provide an extension of our logic, providing we're able to understand the problem and design the solution to begin with.
Now, your question was in fact about formal logic, presumably current mathematical methods of formal logic...
Then the answer is, yes, absolutely, and inevitably, and in very concrete terms.
EB
Last edited by Speakpigeon; 05-30-2019 at 09:27 PM.
Access a problem or situation, derive premises, draw a conclusion using logic rules. Can that be wrong? Or is logic always 'right'?
Well the universe seems to work the way we predict and we know we know very little about it.
I think they already answered this. Since derived premises can be wrong, any conclusion logically derived from them can be wrong, even if that conclusion is logically valid (which simply means it follows from the given premises).
Premises themselves can be wrong b/c they cannot be based purely on deductive logic, unless they are definitional/neccessary truisms such as "All cats are not birds." Contingent truths require empirical verification that the contingencies that make it true have been met. Since empirical verification always has some non zero probability of being incorrect, all premises that are not simple definitional truths have some probability of being incorrect, therefore all logically valid conclusions drawn from them have a probability of being incorrect.