[gerard.casey]

Mises007 (I like the name!)

You write: “1. Progressives who believe that nobody has the right to make choices for a woman over her own body are being inconsistent when they support the redistribution of wealth for the “common good” because (assuming we ignore the possible rights of the baby) both cases are essentially about protecting the rights of property (the mothers body and the fruits of ones labor) and liberty (the right to do what you want with your property).”

Let’s see if we can express your arguments in the foregoing paragraph formally:

Argument 1
Premise 1: If I own x, then I may do as I wish with x
Premise 2: I own whatever is in my body
Conclusion: Therefore, I may do as I wish with whatever is in my body

This argument is valid a form of the hypothetical syllogism—i.e. if its premises are true, its conclusion must be true as well

Argument 2
Premise I: If I own x, then I may do as I wish with x
Premise 2: I own the fruits of my labour
Conclusion: Therefore, I may do as I wish with the fruits of my labour

This second argument has the same form as the first and is similarly valid.

Your hypothetical ‘progressive’, while accepting the validity of both arguments, is very likely going to reject the truth of 2-2 (“I own the fruits of my labour”) so the soundness of the argument will turn on the defence of this premise. That defence will itself be either a matter of logic (based on yet another argument) or its truth will be a metter of some other kind of evidence, not excluding self-evidence.

The first argument, while valid, isn’t immune from critique on grounds of soundness (i.e. evaluating the truth/falsity of the premises). I’m not sure a libertarian would be willing to stand over the self-evident truth of premise 1:1 “If I own x, then I may do as I wish with x” without adding the rider “provided that in so doing, I don’t infringe upon the non-aggression principle”. The revised argument would now read:

Argument 1a
Premise 1: If I own x, then I may do as I wish with x, provided that in so doing, I don’t fringe upon the non-aggression principle
Premise 2: I own whatever is in my body
Conclusion: Therefore, I may do as I wish with whatever is in my body provided that in so doing, I don’t infringe upon the non-aggression principle

Now I think it become clear where the lines of the different positions are drawn. The question becomes one of whether or not in the case of abortion, one is or isn’t aggressing against another.

You write: “2. If one believes in late term abortion on the grounds that the child is living off of the mother and is a part of her body, then he/she should also be ok with abortion after the baby has been fully extracted from the mother but is still attached to the umbilical chord.)”

The elements of the argument here rest on (1) what it is to live off the mother, and (2) what it is to be part of the mother’s body.

Somebody supporting abortion but unwilling to countenance the killing of the child born alive but still connected via the umbilical cord to the mother might want to argue that such a child while living off the mother is no longer part of the woman’s body and that that fact makes a moral/legal difference.

Some people argue that the movement of an entity from one location to another doesn’t normally change an entity’s ontological or moral status, so that if abortion in utero is legal, there is no principled reason why infanticide should not also be legal. Of course, one can run this argument in the other direction and argue on the same grounds that if infanticide is (or should be) illegal, then so too should abortion!

[Moving away from the purely logical for a moment, I published a book some years ago, before I became a libertarian, on certain aspects of the law of homicide in the UK and USA pertaining to the very young. If anyone would like a PDF copy of this book, I’d be happy to send it along.]

The same considerations relevant to your second argument apply, more or less, to your third argument.

You write: “4. A quote from Ron Paul: “The fact is that a fetus has legal rights not to be injured or aborted by unwise medical treatment, violence, or accidents. Ignoring these rights is arbitrary and places relative rights on a small, living human being.
The only issue that should be debated is the moral one: whether or not a fetus has any right to life. Scientifically, there’s no debate over whether the fetus is alive and human—if not killed, it matures into an adult human being. It is that simple. So the time line of when we consider a fetus “human” is arbitrary after conception in my mind.”
Q: Is their anything illogical about his statement? Particularly the part about any determination of life after conception being “arbitrary” when everyone agrees that on some level a fetus is alive on some level at conception.”

Dr Paul’s point relates to the soundness of the various arguments on this issue. If something is what it is and has the rights that it has because of what it is, its size or its relative state of development don’t seem to be particularly relevant considerations. To take a ridiculous example: a very short person (e.g. 3’ 6”) isn’t entitled to be treated with only half the respect due to a tall person (e.g. 6’ 6”). If it’s the case that once a human being comes into existence as a foetus, it is and continues to be a human being until death, then it would seem to be arbitrary to deal with its right not to be aggressed against in different ways simply because of its state of development (or its location). Of course, those who do not accept Dr Paul’s position will argue that a more or less fundamental change of moral/legal status takes place at some more or less specific developmental stage (implantation, viability, 2nd trimester, etc.) and so the argument/s will proceed on these issues.

It would be a useful exercise to attempt to formulate your arguments in categorical or hypothetical logical form or, if that’s not possible, to construct an informal argument as clearly as possible.

[gerard.casey]

A re-submission of the previous post

[gerard.casey]

JohnD: With what you call your ‘minor changes’, we get:
“Let A = Rand rejects initiatory force because it violates man’s inalienable rights.
Let B = Rand permits retaliatory force against man’s inalienable rights.
Let H = Human beings have inalienable rights.
The form of the argument would then be the same:
(1e) If A, then H.
(2e) If B, then not H.
(3e) Both A and B.
Therefore, (4e) both H and not H, a contradiction.
So, if the premises are true, then Rand’s thoughts are shown to be inconsistent here.”

Putting your reformulation into English, you get
(1e) If Rand rejects initiatory force because it violates man’s inalienable rights then human beings have inalienable rights
(2e) If Rand permits retaliatory force against man’s inalienable rights then it is not the case that human beings have inalienable rights
etc.

The trouble with the new (e) version is that it has a hint of the self-referential—you’ve got the ‘inalienable rights’ stuff appearing twice in each premise. I’m not sure that you really want to do this or need to do this; in any event, it certainly reduces the clarity. Furthermore, the new B is possibly question-begging.

Whether or which, the key to the discussion (it seems to me, unless I’m completely missing the point, which is certainly possible) is the distinction between the initiation of force against another, which violates the rights of the other, and the response to such force by the person who is aggressed against which is not only not a violation of the right of the attacker but must be available to the person aggressed against, otherwise you would have rights that were, in principle, incapable of defence. This, I think, might address the issue you raise under your ‘3rd Part’: the attacker who is physically resisted doesn’t have his inalienable rights infringed.

I got a little lost in the rest of your posting, being unsure whether you were responding to me or to Jerryb225 or making some completely new point! If there is something in your post you would like me to comment on, perhaps you could isolate it from the larger context and let me see it on its own.

Jerryb225: Congratulations on doing so well with the syllogism exercises. If you’d like me to take a look at your work at any stage, I’d be happy to do so.

[gerard.casey]

Jerryb225: As I mention very early on in the lectures, there are always gaps between our natural reasoning and any formal system of logic. Sometimes, elements of our natural reasoning seem to be incapable of being ‘captured’ by our formal system; at other times, our formal system seems, as it were, to have a mind of its own and to come up with inferences that are, on the face of it, non-intuitive.

The traditional system of logic I teach in the course has two basic types: the first, where we can analyse the internal structure of the proposition (categorical proposition) and derive inferences from that; the second, where we are concerned with the external relationships between propositions taken as a whole (the hypothetical syllogism). [Have you got to the section on the hypothetical syllogism yet?]

If JohnD were to reformulate his argument, it might be susceptible to an analysis in the logic of the categorical proposition.

As things stand, however, I give an analysis of his argument in the logic of the hypothetical syllogism upon which it turns out the argument is valid. That being so, our attention now turns to the truth of the premises. I suggested that premises 1d and 3d were most likely true (their truth to be established by extra-logical means) and that the problematic premise was 2d. The truth of this has to be established either on the basis of non-logical evidence or as the conclusion of yet another argument.

As you can see from all this, logic is not a universal solvent for all our conceptual problems. In the end, the truth of our premises is, for the most part, derived from empirical evidence, history, and only occasionally by pure thought. Logic’s strength, however, is that, by allowing us to distinguish clearly between validity and soundness, it enables us to focus our attention where it needs to be rather than being distracted by the inessential.

[gerard.casey]

JohnD: At last I have the opportunity to respond to your posts. Your reformulation of the argument runs like this:

(1) Rand objects to the initiation of force because humans have inalienable rights.
(2) Rand permits retaliatory force against these inalienable rights.
(3) 1 and 2 are either inconsistent or incoherent. If the rights are inalienable, then upon what basis is retaliatory force that alienates them permitted? If the rights are not inalienable, then the statements are incoherent.
I’m going to try to address the issues that have been raised in logical terms rather than in substantive terms.

First part: As things stand, your propositions 1 and 2 are not immediately inconsistent. What would be inconsistent would be (making minor verbal changes) either
(1a) Rand rejects the initiation of force because humans have inalienable rights
(2a) Rand accepts the initiation of force because humans have inalienable rights
or
(1b) Rand rejects retaliatory force against inalienable rights
(2b) Rand accepts retaliatory force against inalienable rights
If your 2 were translatable into 2a (keeping 1 as 1a) or your 1 were translatable into 1b (keeping 2 as 2b) then we’d have a clear case of inconsistency but neither translation is obviously possible without changing the semantic content of the propositions.

Second part: If we could get the argument into proper logical form, then we could assess it using the rules of formal logic. You will recall that arguments (formal arguments) can be criticized on two levels. If a formal argument is invalid, then we need proceed no further in our criticism. If, however, it is valid, then our attention turns to the question of the truth of the premises. Should the premises of our arguments turn out to be true and the argument valid, then the conclusion must be true as well.
As things stand, propositions 1 and 2 are not obviously categorical in form. I have made several attempts to translate them into categorical form but nothing I’ve produced has been satisfactory.
I next tried to see if I could deal with them using the forms of the hypothetical syllogism. The way in which you phrase the argument suggests we have something like a dilemma with this significant difference: in a dilemma, we have a disjunction between two propositions as constituent parts of the overall complex argument whereas in your argument, we seem to have a conjunction instead. Let me see if I can illustrate what I mean.

Third part:
Let A represent the proposition “Rand rejects initiatory force”
Let B represent the proposition “Rand accepts retaliatory force”
Let H represent the proposition: “Human beings have inalienable rights”
The argument you give now seems to run:
(1d) If A then H (If Rand rejects initiatory force, then human beings have inalienable rights)
(2d) If B then not H (If Rand accepts retaliatory force, then human beings do not have inalienable rights)
(3d) But (and here comes the conjunction) both A and B (Rand rejects initiatory force and Rand accepts retaliatory force)
Therefore, (4d) both H and not H (Human beings have inalienable rights and human beings do not have inalienable rights)
This argument is valid and its conclusion, being a contradiction, is necessarily false. That being so, the premises taken together must be inconsistent, that is, they can’t all be true together. If, as seems antecedently likely, 1d and 3d are true then the most likely culprit for falsehood is 2d.

Fourth part: The burden of the messages that you and Jerryb225 have posted seem to circle around this premise (or something closely resembling it). A Randian might claim that 2d should read: If B then H (rather than if B then not H) and if pressed for his reason for asserting this, might respond that retaliatory force and initiatory force while both involving physical violence and so being indistinguishable from a physical perspective, nonetheless are morally distinct; just as if I were to drive your car away, what would be physically presented to us would be identical whether I was driving it with your permission or without your permission. Your grant of permission makes no difference to the physical dimension of the act but changes the moral (and legal) character of it completely.
Having read all this (if you haven’t gone to sleep!) you may agree or disagree with this analysis totally or agree or disagree in part. In the end, logic helps to line one’s argument up in the most perspicuous way (or sometimes shows that this can’t be easily done) but, in the end, if an argument is valid, then we have to assess the truth (categorical or probable) of the premises and that is not the direct concern of logic, unless one or more of the premises are themselves conclusions of further argument.

[gerard.casey]

JohD &B Jerryb225: I’ve read your interesting posts and am mulling them over. It’s 8.30 a.m. here in Ireland and my day is just beginning. It’s a pretty full day with lectures, student consultations, entertainment of a colleague from Germany, and finishing with a debate in Maynooth University tonight on “Libertarianism vs Statism” sponsored by the Maynooth Skeptics Society! It will probably be sometime tomorrow before I can respond substantively to your posts.

[gerard.casey]

JohnD: This argument would seem to embody a fallacy of equivocation on the word ‘initiate’. In one sense of ‘initiate’, every action is initiated; in a second sense, where one has a sequence of actions and reactions, only the first action in the sequence is initiated in a way that is relevant to the libertarian prohibition. When Rand (and libertarians) object to the initiation of force, they are objecting to the first action in such a sequence, not to any forceful action at all. Applying this distinction to the argument you give, the word ‘initiate’ simply drops out of premise 2 and there is no inconsistency between premises 1 and premise 2.

[gerard.casey]

Jerryb225: Your worked example is correct. Where ‘-‘ stands for a complement:

HAS becomes -SA-H, by contraposition (contraposition valid on O and A types)
-SA-H becomes -SEH by obversion (obversion valid on A, E, I, O)
-SEH becomes HE-S by conversion, (conversion valid on I and E types) and
HE-S becomes HAS by obversion (obversion valid on A, E, I, and O)

I think you’ll agree that it’s not easy to see the equivalency of these four propositions in English!

[gerard.casey]

JohnD: You’re welcome! Keep the posts coming. If something is odd, unusual or inexplicable to you, the chances are that it is so to others as well. You’re doing everybody a favour by posting.

[gerard.casey]

Chris and John: I can see why you might think as you do. The names of these fallacies comes from what happens in the non-hypothetical premise, not from what happens in the conclusion!

You have the hypothetical premise, then you affirm the consequent (problem) and then you mistakenly conclude with the antecedent. Similarly, you have the hypothetical premise, you deny the antecedent (problem) and then mistakenly conclude with the negation of the consequent.

In the end, names are names but the important thing is to recognize the fallacy, whatever you want to call it.

[gerard.casey]

Hello Dorian. Yes, the books I list in the course all contain exercises of various kinds. The McCall book is particularly good. But almost any book on logic that you can find in your local library (if it’s a good one) or your local college or university library should have sections of exercises.

I’m a great fan of the internet and I’m sure that a search there with terms such as ‘logic exercises’, ‘simple conversion’ etc. etc. should turn up some interesting material.

If there was a demand, I could put together a Word file with some exercises on any topic that students of the course might find useful. I’m not in a position to do this immediately (rushing to finish writing deadlines!) but, if people thought it useful, it’s something I should be able to do in about three weeks or so.

Hope you are finding the course interesting. Don’t forget, if you have questions or comments, you can add to existing posts or start one of your own.

[gerard.casey]

David Konietzko: Apart from its perhaps being the case that outlawing self-referentiality is merely ad hoc, and thus unsatisfactory, it also has the effect, as you correctly note, of outlawing perfectly respectable sentences such as “This sentence is in the present tense”.

JohnD: You write “The thought of ALL THOSE DIFFERENT LOGICS is quite disturbing. I thought since logic is the science of necessary inference (proper thinking) that we could rely on it to yield certain truths. But with so many logics to choose from, where does that leave us???”

I can appreciate your concern. When you consider all the possibilities that I mentioned in my previous post, it can induce a kind of intellectual vertigo. Perhaps an analogy will help. The basic theory of modern physics seems to be in trouble. Just how many basic particles do we have? Is string theory the answer to our questions? However, whatever may be the case with theoretical physics, we have no difficult getting on with our daily lives, weighing things, measuring them, comparing them, and so on. The inferential core of logic is like our everyday practices of weighing and measuring; the fact that theoreticians may be at odds and special extreme cases may cause us headaches, doesn’t in any way affect, say, the invalidity of the fallacy of the undistributed middle or the validity of the conversion of E-type propositions. This analogy may (or may not!) help: all analogies limp. The disquiet expressed in your post was one reason why I was suggesting that while these topics which we are discussing are interesting and exciting, it can be confusing and distracting to focus on them at the same time as one is trying to come to grips with a basic formal logic system.

David Konietzko: You write:”A sentence has a certain meaning precisely because people interpret it to have that meaning. Therefore, if it is in principle impossible to understand the meaning of a sentence, then it simply doesn’t have a meaning.”

The syntactically-in-order sentence “The kronxite instrumentality befummels reflexiveness cromulently” doesn’t mean anything because some of its key words don’t mean anything in English. Failure to understand it is not a fault in anyone’s understanding; no one can possibly understand it. This is to agree with the second sentence in your post.

The first sentence in your post is possibly ambiguous depending on whether ‘people’ means, assuming we’re using English, some particular special group of people who are competent in English or competent English speakers in general. A sentence could be well-formed in English and understandable to all competent English speakers; or it could be well-formed and understandable only to a proper subset of competent English speakers. In all cases, it would have meaning.

[gerard.casey]

One of the charms (is that the word I want?) of logic is that it leads to topics such as the one under discussion here. This topic, however, properly belongs either to metalogic or the philosophy of logic (it’s not always easy to distinguish one of these from the other). Metalogic, as the name suggests, takes formal logical systems and makes them the object of formal study. Philosophy of Logic (as in Susan Haack’s book, Philosophy of Logics – note the plural) also takes the various logics as objects of study but the questions it raises are of a philosophical rather than a formal nature. And then, arising from the perceived limitations of modern logic (such as the Paradoxes of Material Implication) we have the development of Modal Logic which then ramifies into a whole system of so-called deviant logics – epistemic logic, deontic logic, 3-valued logic, multi-valued logic and the seemingly paradoxical fuzzy logic!

To return to the topic under discussion: a number of approaches have been taken to the so-called Liar Paradox. One approach is to outlaw self-referentiality so that propositions are not allowed to refer to themselves. This (probably) works but it has a disturbingly ad hoc air about it which may be intellectually unsatisfying. Another approach, to which I am drawn, is to hold that all propositions make an implicit claim to truth so that the Liar sentence simultaneously asserts and denies the same thing and so is a contradiction and so is false. But there are other attempts at a solution and no general agreement is to be found on how this is to be handled. These attempts at a solution and some others are discussed in this Wikipedia article
http://en.wikipedia.org/wiki/Liar_paradox

When I was a student I found these kinds of questions practically irresistible, much to the detriment of my other studies and my social life. While I would encourage people to think hard about such topics, it probably isn’t a good idea to do so at the same time that one is attempting to learn the nuts and bolts of a primary formal system. Furthermore, to take part in current discussions you really need to familiarise yourself with modern Proposition and Predicate Logic, some Modal Logic, some metalogic and some philosophy of logic. If you want a short DIY introduction to elementary modern logic to get you started, send me an email (gerard.casey@ucd.ie) and I’ll get my material to you.

Finally, to see how logic can allow one to focus on aspects of philosophical discussions that might otherwise remain out of sight, consider the following snappy 6-line proof for the existence of God (I think I stole this from Charles Hartshorne but I’m not 100% certain):

Let G stand for the proposition ‘God exists’; let § stand for the phrase (modal operator) ‘it is necessary that….;’ and let * stand for the phrase (modal operator) ‘it is possible that…’

Line 1: *G (It is possible that God exists)
Line 2: If G then §G (if God exists, then God necessarily exists)
Line 3: If *G then *§G (If it is possible that God exists, then it is possible that God necessarily exists) We arrive at this by applying the * operator to each side of line 2
Line 4: *§G (it is possible that God necessarily exists) We get this by putting lines 1 and 3 together, using the modal version of the rule called Modus Ponens
Line 5: §G (God necessarily exists) We get this from line 4 by using a modal logic rule that allows us to dispense with all but the last modal operator in front of any given proposition.
Line 6: G (God exists) This comes from the most basic rule in modal logic; whatever is necessarily true is true

The premises of this argument are plausible; it doesn’t seem unreasonable to think that it is possible that God exists. Similarly, if God isn’t to be thought of as a rock or a tree, it seems reasonable to think that if He exists at all, He exists necessarily. Grant these two premises and the rules of modal logic (up to a certain level) and the conclusion (God exists) pops out!

I like to tease my atheist friends with this bit of modal prestidigitation. The serious side of the argument is that it forces one to look again at whether the premises are, in fact, obviously true (perhaps it’s not even possible that God exists or perhaps God might exist but not necessarily!). On the more purely logical side, it leads to a consideration of the plausibility of the various systems of modal logic, in particular, the rule used in line 5 that allows you to reduce a proposition prefaced by a mixed string of modal operators to just the last operator. Here, as elsewhere on the borderlands of logic, our intuitions tend to run into the sand.

There is much more that could by said on this and related topics but not by me tonight!

[gerard.casey]

Dear Brendan,

In formal English, two negatives = affirmative. But in colloquial English, if some says “I’m never going to do nothing, nohow, noway….” what they are doing is asserting a very strong negative. and in some language, a double negative is routinely a way of making a strong denial.

In serious disputation, it is indeed necessary to be clear, to define your terms and so on. Often, however, a substantial portion of any discussion involves getting to that stage. That’s human nature, I’m afraid, and also the nature of language.

If I may make a suggestion? I would recommend moving on through the logic lectures until the level of understanding really starts to drop, then go back and repeat the viewing. If you do this, you will find that some at least of what was earlier problematic is no longer so. I can’t guarantee that this will happen but that has been my experience over the years.

Keep up the study and thank you for your interesting posts.

[gerard.casey]

When you have a proposition without an explicit quantifier (and it’s obviously not singular) then you have to choose between taking it as universal and taking it as particular. If you’re speaking to someone, you can of course ask him to clarify his meaning; likewise, if you’re emailing or texting or phoning – this is a point you have yourself correctly noted. However, if you’re not in contact with the speaker or writer then, unless the context unambiguously requires you to take a proposition universally, you should take it particularly, as that commits the utterer of the proposition to a more defensible position. [See my brief discussion of the principle of charity under the ‘All or some’ topic.]

In the particular example you discuss – “Men are sometimes dishonest” – not only is there nothing in this proposition considered simply in itself to suggest universality which, under the principle of charity, would be enough to take it as particular, but further, the adverb ‘sometimes’ gives you a further positive push in that direction.

Your third paragraph contains a ‘therefore’ which, as I hope you may come to see, is not strictly justified. There is a difference between one proposition’s implying another and one proposition’s being consistent with another. This should become clearer when we come to take a look at inference.

Finally, translation is an art, not a science. Your task in translation it to do your best to go from one language to another without semantic falsification or semantic addition. In most cases in our logic, the translation is straightforward; in a few cases, there is genuine room for disagreement.

I have found from experience that some of the problems people have with translation are retrospectively clarified once they move on to a consideration of inference.

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