Valid but not in Virtue of Form?

Some remarks of the Semantic Terrorist in the post on moral truthmakers got me to thinking. Here is what he said.

consider the following argument which is easily proven to be invalid despite the fact that many analytic philosophers would mistakenly classify it as valid:

1) George Bush is a bachelor.
? George Bush is unmarried.

This argument is in the same logical form as the following:

1) George Bush is a Texan.
? George Bush is unmarried.

As ST points out many analytic philosophers do take that argument to valid. It is standard in logic textbooks to point out that these arguments meet the definition of validity; it is indeed impossible for the premise to be true and the conclusion to be false, but as the point continues, this isn’t because of teh form of the argument. The form, as ST demonstrates, allows for counter-examples, and so the validity must be due to something besides the form of the argument. The reason for the impossibility of the truth of the poremises and the conjunction of the denial of the concusion is said to be due to the definition of ‘bachelor’.

All of this is standard, but why isn’t the argument above seen as having a supressed premise of the form ‘all bachelors are unmarried makes’? Then the argument is formally valid; it is just an instance of a very common categorical syllogism. The same is true of the texan argument, it just happens to have a false suppressed premise ‘all Texans are unmarried males’. I don’t see what the argument against positing the suppressed premise is supposed to be. It is clearly the only way to make the inference legitimate.

One thought on “Valid but not in Virtue of Form?

  1. LOGICAL VALIDITY VS. ANALYTIC VALIDITY
    Logical validity is a formal characteristic of arguments, and so is logical invalidity. To suggest that some arguments are “(logically) valid, but not in virtue of [their] form” confuses logical validity with a non-formal semantic property that’s sometimes called ‘analytic validity’ (or ‘analytical validity’). In my experience, however, analytic validity is rarely talked about; although the corresponding analogue of the relationship of logical implication — which is usually called ‘analytic entailment’ — is occasionally mentioned by philosophers with decent training in formal logic.

    LOOSE DEFINITION OF ‘ANALYTIC ENTAILMENT’
    ‘Analytic entailment’ can be loosely defined as follows: A set of propositions analytically entails a single proposition IFF the set of propositions that results by adding zero or more propositions that correctly define certain non-logical constants (that occur in one or more propositions belonging to the original set) to the original set yields a set of propositions that logically implies the single proposition.

    Technical Note: This definition is a bit loose because it treats non-logical constants as if they were parts of propositions, rather than parts of sentences that express propositions.

    Here’s a simple illustration:

    1) George Bush is a bachelor.
    ? George Bush is unmarried.

    This argument is analytically valid; insofar as a logically valid argument results by adding a premise that correctly defines the non-logical constant ‘bachelor’.

    Here, however, it must be pointed out that the term ‘bachelor’ is polysemous (i.e. multiply-ambiguous):

    Lexical definitions of ‘bachelor’:

    1. An unmarried man. [An unmarried adult male human being.]
    2. A person who has completed the undergraduate curriculum of a college or university and holds a bachelor’s degree.
    3. A male animal that does not mate during the breeding season, especially a young male fur seal kept from the breeding territory by older males.
    4. A young knight in the service of a more experienced knight in feudal times.

    The following argument is logically valid (i.e. formally valid):

    1) George Bush is a bachelor.
    2) Every bachelor is unmarried. [Notice that this premise does not define ‘bachelor’; although it’s implied by the relevant definition.]
    ? George Bush is unmarried.

    This argument has no counterargument. In other words, the argument is formally valid — or, in still other words, every argument in the same logical form as this argument is valid.

    By the way, ‘analytic validity’ has been defined in such a way that every logically valid argument is also analytically valid. (Note the phrase ‘zero or more’.)

    As far as I can tell, for someone to claim that some arguments are valid, but not in virtue of their form, indicates that they are unclear on the distinction between logical (i.e. formal) validity and analytic validity.

    ON SUPPRESSED PREMISES & ANALYTICAL VALIDITY
    Suppose I give the following argument, and insist that it’s valid:

    1) Every man is a mortal.
    ? Richard Brown is a mortal.

    Then suppose that you prove that my argument is logically invalid by producing the following counterargument:

    1) Every kangaroo is a marsupial.
    ? Richard Brown is a marsupial.

    If I want to be pig-headedly obtuse, I can maintain the ignorant position that you goofed it up because you didn’t understand the first argument properly; because I also meant, but did not say, that Richard Brown is a man. If I do so, however, you can just point out that the following two arguments are obviously distinct — since argument (A) is a two-premise argument whereas argument (B) is a three-premise argument:

    Argument (A)
    1) Every man is a mortal.
    ? Richard Brown is a mortal.

    Argument (B)
    1) Every man is a mortal.
    2) Richard Brown is a man.
    ? Richard Brown is a mortal.

    This raises an issue well worth thinking about concerning the notion of analytic validity. For many philosophers would classify argument (A) as analytically valid; despite the fact that the so-called suppressed premise does not define any non-logical constant involved in the premise(s) of the original argument. Instead the so-called suppressed premise merely concerns a bit of basic background knowledge which any audience to which argument (A) were presented could reasonably be expected to know (and, perhaps, automatically “fill in” for themselves).

    At any rate, you ended your post #0 with the following pair of sentences: “I don’t see what the argument against positing the suppressed premise is supposed to be. It’s clearly the only way to make the inference legitimate.”

    I’ll pretend that you said ‘cogent’, not ‘legitimate’; since I presume that that’s what you meant — and since I care about using proper terminology, as well as correct spelling.

    I answer that until one is clear on precisely what argument is in question it’s impossible to prove “the” argument either valid or invalid. But that hardly shows that some arguments are (logically) valid, but not in virtue of their form. On the contrary, all that shows is that one does not know the identity of the argument he is supposed to be evaluating.

    I also feel the need to say something about the difference between arguments and argument-texts. Every argument ultimately consists of nothing but propositions. An argument-text, on the other hand, consists of sentences, not propositions. [A type argument-text consists of type sentences. A token argument-text consists of token sentences.]

    Please keep in mind that I use the word ‘sentence’ to mean a string of symbols. Please also keep in mind that, as I use the term, a sentence need not have any standard or even natural interpretation.

    I am, of course, aware of the fact that you believe that an argument can have commands (and presumably also, requests, questions, exclamations, warnings, etc.) as premises. I, however, am convinced that this is a mistake. At any rate, no command, request, question, exclamation or warning can logically imply anything given the definition of ‘logical implication’ that I gave in post #14 of “Moral Truthmakers” — and which is the standard definition of the term.

    R. Brown; post #0: “I don’t see what the argument against positing the suppressed premise is supposed to be.”

    This objection (if that’s what it’s supposed to be) strikes me as irrelevant; especially since you’re free to posit whatever the hell suits your fancy. Indeed, so far as I can tell the question, “How do I know what argument is expressed by this particular argument-text?” rarely needs an answer anyway. Just specify all of the arguments that you reasonably suspect might have been intended to be expressed by the person who produced the token argument-text in question and then evaluate each argument individually. It may well turn out that some of them are merely analytically valid whereas others, which include one or more suppressed premises or smuggled premises, are logically valid.

    In any case, the only way that one can figure out which argument was intended is by requesting that the person who presented the argument re-express it, taking special care to mention every premise of the argument explicitly. [Of course, if the guy who presented the argument has been dead for 300 years, we can’t do that. And thus there will always be squabbles about what argument Locke or Hume or whoever really meant to express by saying such-&-such.] At any rate, if, after having made the request to a living person and gotten a response, he later objects that you’re still failing to recognize a suppressed premise, then he’s flat out guilty of the fallacy of premise smuggling. After all, it’s the argument presenter’s job to present his argument clearly, and with sufficient precision for the purpose at hand. Blaming one’s audience for failing to understand a poorly expressed argument is every bit as foolish as a bad writer’s blaming his readers for failing to understand what he badly wrote.

    PROPER TERMINOLOGY
    You already mentioned that you don’t much care about spelling; and even consider it “the lowest form of human knowledge.” I, in contrast, I do care about spelling — because I reckon it shows respect for my readers. I also care about using proper terminology because I care about clarity and precision — as well as matters of good taste vs. bad taste. In any case, here are a few pointers in case you might be interested.

    ‘Counterargument’ and ‘counterexample’ are not synonymous terms. A counterargument is an invalid argument that’s in the same logical form as some argument that one intends to prove invalid, or whose validity is in dispute. Not every counterargument is a known counterargument. For this reason it’s possible to discover a counterargument. In contrast, every known counterargument is an argument that’s both known to be invalid and known to have the same logical form as the disputed argument in question.

    It’s very important to keep in mind that a counterargument may be a known counterargument for one person and not be a known counterargument for a second person. Similarly, it’s possible for an unknown counterargument to become a known counterargument; because one gains knowledge that it’s in the same form as the disputed argument; or because one already knows that but gains the knowledge that it’s invalid.

    Here it might well be useful to briefly comment upon your accusation that I got the form of Sorenson’s zero-premise argument wrong. I claim to have presented a known counterargument to Sorenson’s argument; which therefore proves that his argument is invalid. Your objection amounts to saying that my proposed counterargument (about unicorns) is not really a counterargument to Sorenson’s argument; because, although you admit that my argument about unicorns is invalid, you disbelieve that it’s in the same logical form as Sorenson’s argument — and thus you do not know that it’s in the same form as his argument — and thus it’s not a known counterargument (to Sorenson’s argument) for you (at this time). This naturally raises the question as to whether it really is a counterargument, but you just haven’t gained knowledge of that fact yet. Expressed in a way that instead favors your position, it raises the question whether I really know that my argument about unicorns is in the same logical form as Sorenson’s argument.

    ‘Counterexample’ is virtually always defined as an individual that makes a false universal proposition false. For example, my puppy dog, Tanger, is a counterexample to the false universal proposition that every mammal is a cat. [Again, it’s often important to distinguish between a counterexample and a known counterexample — despite the fact that few philosophers are sensitive to the distinction.]

    I maintain that the standard definition of ‘counterexample’ is slightly but interestingly goofed-up; because only a fact (or something very much like a fact) can be a falsemaker for any false universal proposition. And so, for example, I claim that it’s the fact that Tanger is a mammal that’s not a cat that really serves as a falsemaker to the universal proposition that every mammal is a cat. And this can be a fact even if no one knows it, or yet knows it.

    Please also notice that the word ‘falsify’ has both an ontic and an epistemic interpretation; as do such phrases as ‘determine the truth-value of’, ‘determine the truth’, ‘determine the falsity’, etc. For a person to determine the falsity of a proposition is for him to discover that it’s false — or at least judge that it’s false. But for a fact to determine the falsity of a proposition is for that fact to make the proposition false — independently of whether anyone has discovered, or even judged, that it’s false.

    It might also be worth explicitly stressing that both ‘counterargument’ and ‘counterexample’ are relative terms (or “role words”); in the sense that to be a counterargument is to be a counterargument for some invalid argument; and to be a counterexample is to be a counterexample to some false universal proposition.

    Since I’ve gone this far I might as well also mention that a proexample is an individual (or a fact) that makes some true existential proposition true. Thus, for example, Richard Brown (or rather the fact that Richard Brown is a Caucasian person) is one of millions of proexamples for the proposition “Some person is Caucasian.”

    You might find it interesting that I do not claim that every proexample must be a fact (or something very much like a fact). This is so because there are “effectively-singular” existential propositions, such as “Richard Brown exists”. And I take the individual, Richard Brown — whatever the hell he is — and without having to describe him in order to refer to him — to be a truthmaker for that proposition.

    It’s also interesting to notice that the term ‘proargument’ does not appear to be in use. One may, however, define it as a valid argument that’s in the same logical form as some argument whose validity is in dispute. It seems to me that the reason the term is virtually never used is that we never interestingly prove that any argument is valid by showing that it’s known to be in the same form as some argument that’s already known to be valid. Nevertheless, we can indeed prove validity in this way on certain occasions — and it’s highly pedagogically useful to do so whenever you get the chance in introductory logic courses.

    R. Brown; post #0: “…it is just an instance of a very common categorical syllogism.

    I’ve also noticed that you use the phrase ‘categorical syllogism’ incorrectly; or at least loosely. No categorical syllogism contains any singular propositions, such as “George Bush is a bachelor”. Put another way, according to the definition of ‘categorical syllogism’, each of a categorical syllogism’s two premises must be either an A, E, I or O proposition; and every categorical syllogism’s conclusion must also be either an A, E, I or O proposition. Put still another way, no categorical syllogism contains any proposition that’s expressed by a sentence in the argument-text that contains a proper name. [This fact is mentioned in most popular introductory logic texts that deal with categorical syllogisms. You probably learned this fact at some point in undergraduate school, but forgot it — since, after all, it’s rather trivial.]

    MORE ON ANALYTIC VALIDITY VS. BASIC BACKGROUND KNOWLEDGE
    As I hinted above, most philosophers who aren’t clear on the distinction between logical (i.e. formal) validity and analytic validity also tend to confuse cases of analytic validity with cases involving the smuggling of a premise (or a suppressed premise) that concerns basic background knowledge.

    I noticed an interesting feature of your post #0 that might help you to appreciate this point better. Recall this argument:

    1) George Bush is a Texan.
    ? George Bush is unmarried.

    In commenting on this argument you said the following: “The same is true of the texan argument, it just happens to have a false suppressed premise ‘all Texans are unmarried males’.”

    What I find interesting about this comment is that you included the word ‘males’, rather than say ‘kangaroos’. This may seem like a strange observation; but compare the following three logically valid arguments:

    1) George Bush is a Texan.
    2) All Texans are unmarried [individuals].
    ? George Bush is unmarried.

    1) George Bush is a Texan.
    2) All Texans are unmarried human males.
    ? George Bush is unmarried.

    1) George Bush is a Texan.
    2) All Texans are unmarried kangaroos.
    ? George Bush is unmarried.

    Do you see my point? Your basic background knowledge that ‘Texan’ almost certainly was meant to mean a Texan human being affected your understanding of the argument; even though that information is not included in the premise-set of the argument. Similarly, your knowledge of the fact that all bachelors are males affected your understanding of the argument; despite the fact that the argument in question says nothing about bachelors. Of course one can say that the argument is about a certain male human being because it is true that the argument is about George Bush; but the proposition that George Bush is a male human being is not a premise of the argument.

    Insisting upon the distinction between (formal) logical validity and analytic validity is not a matter of being pedantic. Rather it’s primarily motivated by a desire to avoid the sorts of extremely natural confusions that arise as soon as one instead says “Analytic validity is all that counts”. For losing sight of formal validity very quickly leads to loose reasoning that involves numerous sorts of difficult-to-detect additions of information.

    TWO LAST POINTS CONCERNING THIS TOPIC
    Richard Brown; post #0: It is standard in logical textbooks to point out that these arguments meet the definition of validity; it is indeed impossible for the premise to be true and the conclusion to be false…

    It’s standard practice for introductory logic textbooks to ignore the distinction between logical validity and analytic validity (or between logical implication and analytic entailment). Unless the author is incompetent, however, this is done for pedagogical reasons — not because the author is unaware of the distinction. For, as it turns out, the vast majority of students find the distinction to be overly-technical and unproductively confusing; and, given the highly limited goals of a typical introductory course in logic, most instructors find it far easier (and more pedagogically effective) to simply ignore the distinction.

    Your claim that “…it is indeed impossible for the premise to be true and the conclusion to be false…” is somewhat interesting. In order to make my point clearly, however, it’s necessary to reproduce the two arguments at issue:

    Argument (A)
    1) George Bush is a bachelor.
    ? George Bush is unmarried.

    Argument (B)
    1) George Bush is a Texan.
    ? George Bush is unmarried.

    No reasonably competent author of any introductory logic textbook would claim that argument (B) is analytically valid. However, I suppose that what you really meant, by referring to arguments (in the plural), was arguments like argument (A).

    By the way, this is poor writing on your part. You shouldn’t demand so much of your readers.

    In any case, your claim only holds for one of four lexical definitions of the word ‘bachelor’, or given a certain semantic but non-formal connection between the (relevant) concept of being a bachelor and the concept of being unmarried. For it is indeed logically (i.e. formally) POSSIBLE that these two concepts might not be related to each other in the way that they ACTUALLY are. Hence, in that stronger sense, it is not FORMALLY IMPOSSIBLE for the premise to be true and the conclusion false — although it is, in-fact-impossible (because these two concepts are, in fact, related to each other in such a way that every bachelor is unmarried).

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