And you do it too!
Inference
with predicate logic and other such logic is a powerful and beautiful
mechanism, but somewhat paradoxically, its reliability turns out to be
its main weakness. Unless the conclusion follows from the premises with
an absolute 100% certainty, the conclusion does not logically follow at
all and it is therefore not possible to infer it. Adding in a
conclusion that is only 99.9999% likely to be true still risks the
possibility of a logical contradiction, which would break the whole
system entirely since it becomes possible to infer anything at all.
Predicate logic and other such logics can be useful only if the problem domain is simple enough to allow such axiomatization. For most real-world domains, it is simply not possible to come up with a working list of axioms that describes the domain sufficiently for nontrivial reasoning to be possible. Any uncertainty or vagueness, ragardless of whether it is due to inherent vagueness or randomness in the domain or the impossibility of perfect observation, makes logical axiomatization impossible. A good example is medicine, where it is not even remotely possible to write a set of logical axioms with which one could mechanistically infer the diagnosis from the observed symptoms. And even if the facts were straight, we rarely argue about the facts themselves but optimal actions (e.g. the chosen treatment in medicine), to choice of which falls under additional vague and nonlogical constraints.
For all its glory, logic is virtually useless in any real-world reasoning and argumentation task. Nobody actually expresses their ideas logically, except in some rare circumstances where the discussion is about some microworld domain for which logical reasoning is possible in principle. Usually even the word "logical" itself essentially really means "sounds good to me, I like it". And logic is used even less in coming up with the ideas and positions.
In this light, the weight that the first logic and argumentation textbooks give to propositional logic is absolutely hilarious. I doubt that there has ever been a single situation anywhere where someone has successfully come to a solution and argued his case to others using propositional logic, for some nontrivial real-world issue.
Instead of using the predicate logic and other such 100% in-principle-reliable logics, various forms of informal logics tend to be used in real-world argumentation. These logics produces results which are probably true and kind of common sense, but not absolutely entailed by the premises. I was once amused to notice that the popular lists of logical fallacies are practically isomorphic with the lists of techniques of informal logic and argumentation. The only difference between a logical fallacy and an informal logic argumentation technique is that the former leads to a false conclusion and the latter leads to a true conclusion: other than this, there seems to be no structural difference between the two whatsoever. Since it is not possible to tell the difference between a logical fallacy and a valid informal logic argumentation technique unless one knows whether the conclusion is true, this renders all argumentation at best useless. After all, if you already know whether the conclusions are true or false, what do you need any kind of reasoning mechanism for?
For example, "Affirming a disjunct" is a logical fallacy in which from two formulas "A or B" (where or is the logical or which allows for both A and B to be true, and not the exclusive or that makes A and B complements) and "A" one erroneously infers "not-B". For example, from "Bill came in or Bob came in" and "Bill came in" one infers that Bob didn't come in, which doesn't necessarily follow. However, suppose your burglar alarm is ringing and you realize that "There is a burglar in the house or your cat is playing with the sensor". Checking the sensor, you notice that your cat is playing with it, causing it to blare. Is it now really such fallacious thinking to conclude that there is no burglar in the house?
Or consider "Ad hominem", the most beloved of all logical fallacies. I am sorry, but I still don't consider the representatives of the multibillion dollar tobacco institute to be very credible when they claim that smoking is not harmful to health. Or "Appeal to authority". I again apologise, but for some reason I just tend to trust Richard Dawkins over a sideshow creationist preacher.
"Appeal to authority" seems to be a special fallacy in that its definitions often like to present conditions under which it is not a fallacy. Comically these conditions are themselves various fallacies or meta-fallacies. For example, consider the Wikipedia definition linked above. It says that the appeal to authority is legitimate if "The expert should be reasonably unbiased (not unduly influenced by other factors, such as money, political considerations, or religious beliefs)." Now, am I missing something, or why isn't this straightforward Ad hominem? Or consider "A technique is needed to adjudicate disagreements among equally qualified authorities. If scientific testing of the claim is not possible, then the majority of expert opinions is sometimes used to develop a consensus." And here I thought that using the majority opinion was the fallacy of "Argumentum ad populum".
In this light, I bet it would be interesting to see someone present an argument for some nontrivial issue that is relevant to everyday life, in a way that the individual steps of the argument are made explicit and the argument does not contain any part that is structurally isomorphic with some well-known logical fallacy. I wonder if anyone could point me to an actual example. Until I see such an example, I think I stay in my opinion... or am I now committing the dreaded "Argument from ignorance" ?
Predicate logic and other such logics can be useful only if the problem domain is simple enough to allow such axiomatization. For most real-world domains, it is simply not possible to come up with a working list of axioms that describes the domain sufficiently for nontrivial reasoning to be possible. Any uncertainty or vagueness, ragardless of whether it is due to inherent vagueness or randomness in the domain or the impossibility of perfect observation, makes logical axiomatization impossible. A good example is medicine, where it is not even remotely possible to write a set of logical axioms with which one could mechanistically infer the diagnosis from the observed symptoms. And even if the facts were straight, we rarely argue about the facts themselves but optimal actions (e.g. the chosen treatment in medicine), to choice of which falls under additional vague and nonlogical constraints.
For all its glory, logic is virtually useless in any real-world reasoning and argumentation task. Nobody actually expresses their ideas logically, except in some rare circumstances where the discussion is about some microworld domain for which logical reasoning is possible in principle. Usually even the word "logical" itself essentially really means "sounds good to me, I like it". And logic is used even less in coming up with the ideas and positions.
In this light, the weight that the first logic and argumentation textbooks give to propositional logic is absolutely hilarious. I doubt that there has ever been a single situation anywhere where someone has successfully come to a solution and argued his case to others using propositional logic, for some nontrivial real-world issue.
Instead of using the predicate logic and other such 100% in-principle-reliable logics, various forms of informal logics tend to be used in real-world argumentation. These logics produces results which are probably true and kind of common sense, but not absolutely entailed by the premises. I was once amused to notice that the popular lists of logical fallacies are practically isomorphic with the lists of techniques of informal logic and argumentation. The only difference between a logical fallacy and an informal logic argumentation technique is that the former leads to a false conclusion and the latter leads to a true conclusion: other than this, there seems to be no structural difference between the two whatsoever. Since it is not possible to tell the difference between a logical fallacy and a valid informal logic argumentation technique unless one knows whether the conclusion is true, this renders all argumentation at best useless. After all, if you already know whether the conclusions are true or false, what do you need any kind of reasoning mechanism for?
For example, "Affirming a disjunct" is a logical fallacy in which from two formulas "A or B" (where or is the logical or which allows for both A and B to be true, and not the exclusive or that makes A and B complements) and "A" one erroneously infers "not-B". For example, from "Bill came in or Bob came in" and "Bill came in" one infers that Bob didn't come in, which doesn't necessarily follow. However, suppose your burglar alarm is ringing and you realize that "There is a burglar in the house or your cat is playing with the sensor". Checking the sensor, you notice that your cat is playing with it, causing it to blare. Is it now really such fallacious thinking to conclude that there is no burglar in the house?
Or consider "Ad hominem", the most beloved of all logical fallacies. I am sorry, but I still don't consider the representatives of the multibillion dollar tobacco institute to be very credible when they claim that smoking is not harmful to health. Or "Appeal to authority". I again apologise, but for some reason I just tend to trust Richard Dawkins over a sideshow creationist preacher.
"Appeal to authority" seems to be a special fallacy in that its definitions often like to present conditions under which it is not a fallacy. Comically these conditions are themselves various fallacies or meta-fallacies. For example, consider the Wikipedia definition linked above. It says that the appeal to authority is legitimate if "The expert should be reasonably unbiased (not unduly influenced by other factors, such as money, political considerations, or religious beliefs)." Now, am I missing something, or why isn't this straightforward Ad hominem? Or consider "A technique is needed to adjudicate disagreements among equally qualified authorities. If scientific testing of the claim is not possible, then the majority of expert opinions is sometimes used to develop a consensus." And here I thought that using the majority opinion was the fallacy of "Argumentum ad populum".
In this light, I bet it would be interesting to see someone present an argument for some nontrivial issue that is relevant to everyday life, in a way that the individual steps of the argument are made explicit and the argument does not contain any part that is structurally isomorphic with some well-known logical fallacy. I wonder if anyone could point me to an actual example. Until I see such an example, I think I stay in my opinion... or am I now committing the dreaded "Argument from ignorance" ?
Comments