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persuasive but invalid arguments
An argument can't be both sound+invalid, but maybe it can be persuasive+invalid.

persuasive but invalid arguments

hatsoff
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Posted 07/22/09 - 11:23 AM: Subject: persuasive but invalid arguments	#1
An argument, I am told, cannot be both sound and invalid. But, what then do we say about arguments which are persuasive and invalid? Consider the following: Premise: Jim mows the lawn every Saturday. Conclusion: Therefore, the grass is somewhat longer on Friday than on Sunday. This is a flat-out invalid argument. And so then by definition it is unsound. But clearly it has some persuasive power. It makes sense to assume that if Jim mows the lawn every Saturday, that he probably has a weekly mowing schedule. And if that is the case, then we can expect the grass to be longer at towards the end of that cycle (Friday) than the beginning (Sunday). What, then, do we say about such arguments? It doesn't seem fair to simply dismiss them as unsound and invalid. So, what terminology does a logician use to describe them?

MoeBlee
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Posted 07/22/09 - 12:06 PM:	#2
It's persuasive because we supply the missing premise ourselves. We don't need for the argument to be formally correct for us to recognize that if we supply an unstated premise then the argument would be formally correct. Though, in everyday life, most people don't even think at all about formal correctness. So the argument you mentioned is taken as persuasive just by the ordinary habit of mind of skipping past tacit assumptions. I think the word for a tacit premise is 'enthymeme'.

xzJoel
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Posted 07/22/09 - 12:07 PM:	#3
hatsoff wrote: An argument, I am told, cannot be both sound and invalid. But, what then do we say about arguments which are persuasive and invalid? Consider the following: Premise: Jim mows the lawn every Saturday. Conclusion: Therefore, the grass is somewhat longer on Friday than on Sunday. This is a flat-out invalid argument. And so then by definition it is unsound. But clearly it has some persuasive power. It makes sense to assume that if Jim mows the lawn every Saturday, that he probably has a weekly mowing schedule. And if that is the case, then we can expect the grass to be longer at towards the end of that cycle (Friday) than the beginning (Sunday). What, then, do we say about such arguments? It doesn't seem fair to simply dismiss them as unsound and invalid. So, what terminology does a logician use to describe them? Today is Wednesday, therefore tomorrow is Thursday. That is an invalid argument, so what? It is still true. Why would you dismiss an argument merely because it is invalid? The way in which we communicate does not exist in a vacuum. Each sentence exists in a context that allows a person to understand it. This context can consist of axioms, premises, assumptions or whatever else you want to call them. On the one hand a logician may try to state the context explicitly so that a seemingly unsound argument is shown to be sound, while on the other hand the logician may let an invalid argument stand unchallenged because the argument works as needed even if it is technically invalid. (My argument is an example of the former, yours is an example of the latter.) Sure, the grass could have died from one Saturday to the next such that there is some Friday where the grass is less tall than it was the previous Sunday, but such a problem is easily solved by qualifying most statements with the word "generally" or the phrase "one would expect". Generally language is probabilistic in nature rather than being absolute. To those who care about logic, you would call an argument invalid when it is invalid. You wouldn't make up a word to say, "Yes it is invalid, but since it is a typical fallacy that we'd rather not call fallacious, we have this nice word "x"". Remember, logic is primarily concerned with the form of argument, not with the actual contents of a particular statement. Lots of fallacies are useful, convincing, and often true, but that doesn't mean that they aren't fallacies. P.S. I have no idea what I am talking about, so when an actual logician walks in and says, "The word is "x"", I will freely concede that I did not know the answer but felt like answering it anyway. P.P.S. An "enthymeme" is correct, but it addresses arguments only of the type that I gave in my example. Your example is just invalid no matter how many premises we state because your statement is unqualified.
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Octopus
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Posted 07/22/09 - 04:24 PM:	#4
xzJoel wrote: Today is Wednesday, therefore tomorrow is Thursday. That is an invalid argument, so what? It is still true. Only true if we supply the missing premise(s) at which time it is no longer invalid?

xzJoel
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Posted 07/22/09 - 06:48 PM:	#5
Octopus wrote: Only true if we supply the missing premise(s) at which time it is no longer invalid? That is correct, the argument would become valid if the missing premises are provided. Today is Wednesday. If today is Wednesday, then tomorrow is Thursday. Therefore, tomorrow is Thursday. W W>T T A simple example of the valid argument form modes pones. It was a sound argument because at the time it was stated (like it is now) the day actually was Wednesday so the premise was true. Tomorrow, the argument will be valid but unsound.
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chadlee
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Posted 07/23/09 - 03:10 AM:	#6
hatsoff wrote: An argument, I am told, cannot be both sound and invalid. . . What, then, do we say about such arguments? It doesn't seem fair to simply dismiss them as unsound and invalid. So, what terminology does a logician use to describe them? It seems that you've attached some sort of emotive or pejorative association with the notion of invalidity. Assessment of an argument needn't end upon determination of its invalidity, rather that is usually where assessment of most arguments begins. Generally, what you describe is merely the distinction between deductive and inductive logic. Deductive logic is simply the part of logic that concerns tests for validity and invalidity. Inductive logic investigates the process of drawing probable - though fallible - conclusions from premises. All arguments in which the truth of the premises makes likely - but not necessary - the truth of the conclusion are invalid arguments. If an argument is invalid, inductive logic may still investigate whether the argument is strong or weak. Inductive reasoning is often called statistical (or probabilistic) reasoning, and forms the basis of experimental science.

aufbau87
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Posted 07/23/09 - 11:11 PM:	#7
This is a pretty elementary question. I recommend C. Stephen Layman's book The Power of Logic (any edition, older ones are probably cheaper). In it, he makes the following distinctions of different types of arguments: Valid Arguments: Either (1) Deductively Sound (all true premises) OR (2) Deductively Unsound (at least one false premise). Invalid Arguments: Either (1) Strong (and either Inductively Sound or Inductively Unsound) OR (2) Weak (in which case it is neither Inductively nor Deductively Sound). The argument you give is what I'd classify as an Invalid and Strong argument (in short, an inductively strong argument). It's Invalid because it's premises can be true whilst its conclusion false. It's Strong because if the premises are true, then it is likely (though possibly false) that the conclusion is true. Is it Inductively Sound? That depends on whether or not the premise is true, which I do not know how to pass judgment on. Certainly we can phrase it so it is Inductively Sound: P1. There is someone (in the world) that mows his/her lawn every Saturday (say from age 21 to 35, to give a time-frame of his/her life when this premise is supposed to apply). C. Therefore, every Friday, the grass is longer than it was on Sunday. This, I would say, is Inductively Sound. But we can assuredly make it even better by stating relevant data, e.g. Grass grows such-and-such cm per unit of time; there is a modest area of the world where grass can grow virtually unperturbed; etc. But mind you, many logicians aren't concerned with this type of reasoning; and if they are, they are generally classified as philosophers of science, for it is the scientist that makes the most profound use of this reasoning. Logicians, in the full-blooded sense, are typically going to be concerned with deductive validity. Hope that helps! Any Q's, feel free to ask.

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