[gerard.casey]

Yes, you’ve got it. Well done and well put. Logicians don’t mind if your evidence is about everything but your conclusion only about some things; but they get very upset if from a limited range of evidence you start drawing conclusions about everything.

GC

[gerard.casey]

David,

Switching them around as you did:

BIC
CAD
therefore BAD

would give you an invalid syllogism as it would fail rule 6. As you noticed, it also fails rule 2! Are you on the right track? Yes. You put the essential point very well – using your language, you can go from large to small (validly) but not from small to large.

Here’s an example of an invalid syllogism that fails only rule 6:

PEQ
QIR
therefore POR

If you run the six rules over this, you’ll see that if passes the first 5 but fails no. 6.

If you start a new thread, email me at gerard.casey@ucd.ie to let me know.

Keep up the good work.

Best wishes,

GC

[gerard.casey]

David, the second case you mention [BAC, ????, therefore BID] is in fact a valid syllogism if you add, as the second premise, CAD.

Rule 6 on distribution goes from bottom (conclusion) to top (premises), not the other way around. What rule 6 prohibits is having a term distributed in the conclusion and not distributed in the premise in which it occurs. There’s no problem having a term distributed in a premise and not distributed in the conclusion. Roughly, the idea is this.
If in my premises I haven’t been using a term to refer to all the things that it can refer to, it’s hard to see how I can start doing so in my conclusion. On the other hand, it’s perfectly in order to use a term to refer to all of the things it can refer to in a premise, and then not to do so in the conclusion. You can validly go from all to some, but not from some to all.

So, if you check the complete syllogism according to the six rules, you get:

BAC
CAD
therefore, BID

Rule 1 satisfied (at least one universal)
Rule 2 satisfied (vacuously – no particular premise so no need to check further)
Rule 3 satisfied (at least one affirmative premise)
Rule 4 satisfied (vacuously – no negative premise so no need to check further)
Rule 5 is satisfied (the middle term, C, is distributed in the second premise)
Rule 6 is satisfied (vacuously, since no term in the conclusion is distributed)

I hope this clears things up?

If you have any other queries or questions, please do let me know. And if you start a thread, please send your initial post directly to me, otherwise I might not see it for some time.

Best wishes,

GC

[gerard.casey]

Thank you, David. This came up before and I posted a correction in the thread ‘Errata’ but since someone might miss the correction, I’m redoing the lesson and it will be reposted. Here’s what I said in the Errata thread:

“I’d like to pretend I put that error in deliberately just to check if people were paying attention but the truth is that Homer nodded. Well spotted! I don’t quite know why that error happened – I can only think that I must have been looking at the MIR/RIM on the line immediately before the erroneous statement.

Here’s the situation.

In lesson 13, problem 5 (starting at 6.04 on the video) asks you to find (if possible) a conclusion that, if added to the syllogism fragment, would give you a valid syllogism.

The fragment is
[1st premise] MIN
[2nd premise] NER(complement)
[Conclusion] ???

By obverting our 2nd premise, we get as our fragment,

MIN
NAR
???

At 6.36, having shown that the premises as they now are together with MIR or RIM as a conclusion will satisfy the first four rules of the syllogism, I go on to say:

“However, the middle term is N and N is distributed in neither premise so no valid conclusion is possible”

This, of course, is incorrect! The middle term is ‘N’ and ‘N’ is distributed in the second premise. That satisfies rule 5.

Rule 6 requires that any term distributed in the conclusion be distributed in the premise in which it occurs. As we have seen, the only possible candidates for a conclusion are:

MIR or RIM (which, by conversion, are the same proposition)

As this is an ‘I’ type proposition, neither term is distributed so that rule 6 is vacuously satisfied.

So, MIR or RIM will, if added to the fragment, give us a valid syllogism.”

[gerard.casey]

If I understand what you say about Bahnsen’s work, David, there would appear to be no possibility of a discussion between a believer and an unbeliever. Of course, a person may accept another’s presuppositions ‘for the sake of the argument’ with a view to examining their consistency or the validity of deductions from them without really accepting them. This is common practice. But to require another to commit to your presuppositions which are the very point at issue comes close to begging the question.

One might wonder if, in any rational conversation, there are always some presuppositions or other that are necessarily accepted by both interlocutors (a la Habermas) and if so, whether such commonality is enough to get a genuine conversation up and running.

That being said, exchanges between believers and unbelievers are often a conversation of the deaf (and not only in religious matters but in matters of economics, history, philosophy, climate change, and so on.)

[gerard.casey]

I am familiar with the term ‘presupposition’, David, but not as it’s used by van Til and Bahnsen. That being so, there’s nothing sensible I can say about the use of the term in those contexts.

More generally, the idea of presupposition arise in the context of real-life argument analysis. You are, let us say, reading a scholarly article and you come upon a particular argument. This argument may very well be internally valid but may be sound (i.e. valid with true premises) only upon certain things being taken for granted (presuppositions). Such a strategy is not necessarily unwarranted as we don’t always have time to prove everything to everybody and sometimes we just have to take things for granted. In particular, when our arguments are addressed to particular audiences, we are justified in taking their positions as starting points that do not need to be argued for.

[gerard.casey]

Hello again, Dean.

Someone might respond that your analogy of the aspirin is significantly disanalogous to the MW case. Drugs interfere with the body’s natural operation and may (and generally do) have side effects. Usually, you want to take the minimum amount of the drug to produce the beneficial effect and avoid side-effects.

This would not seem to be the case with MW. Other things being equal, higher wages are better (for the worker) than lower wages and there is no necessary element, as there is in the case of drugs, of any side effects that need to be avoided.

The anti-MW argument (which appears again in today’s Mises Daily by Walter Block) is effectively a challenge to the MW proponent to say just why the MW should be set at X rather than at X+delta. If, as is expected, the answer is that X+delta couldn’t be afforded by employers, then the anti-MW arguer will continue the challenge and ask why the MW proponent thinks that X can be afforded. This then focuses the argument on economic rather than on social factors and the discussion can proceed from there.

Anyway, there you have my 2-cent’s worth for the moment. I’d be interested to see what others have to say.

[gerard.casey]

Sorry for the delay in responding to your query, Dean. I’ve just got home to Ireland having attended the 2013 Austrian Economics Research Conference at Auburn. I had a wonderful time (as usual) not least occasioned by the company and conversation of the proprietor of this Classroom! While I was away normal service was somewhat disrupted but I’m back at work now. However, I’m still a little jet-lagged so let’s hope I don’t make some madly egregious blunder! And I know you addressed your query to all and sundry not just to me so let’s see what others have to say.

I’m not sure there’s a logical fallacy of any kind here though a defender of a minimum wage (MW) might respond that he’s promoting a minimum (underscored) wage, not a large, handsome or quasi-maximum wage (as would be the case with $100 per hour or $1,000 per hour) and so might take exception to your rhetoric.

The economic argument against MW is simple and elegant and takes the form of a trilemma: (1) If MW equals the (discounted) marginal value product (DMVP) of labour, then it’s redundant; (2) if MW is less than the DMVP then it’s again (economically) pointless; (3) if MW is greater than the DMVP then it will reduce employment (actual and/or potential), labour-retention laws to one side. The more MW exceeds DMVP, the greater the unemployment effect – hence the typical argument strategy you started with.

[gerard.casey]

Remember, definitions are invariably universal, so, “triangles are plane figures bounded by three straight lines” and “gold is a metal” can only sensibly be taken as universal. If someone said to me “triangles have 3 x 60 degrees angles” I’d say, “You are talking about equilateral triangles, aren’t you?” If there’s no way on interviewing your interlocutor, you could take this proposition (as I think you are suggesting) as being an elliptical “(Some) triangles have 3 x 60 degree angles” and thus true or, alternatively, as a quasi-definition and thus false.

[gerard.casey]

Thank you for the kind compliment, Kristopher.

In English (and, I presume, in other natural languages also), expressions such as “Women can’t drive” or “Men can’t navigate” have no explicit quantifiers on them. If such propositions have categorical import, they must be either universal, particular or singular. Now, it seems reasonably clear that they are not singular so that leaves us with a choice between universal or particular. It’s possible that someone might say this and intend by it a universal proposition. It’s also possible they might not. Where it’s not possible to receive clarification on intent, then we have a hermeneutical principle of charity which says that we should take a proposition in its most defensible form; and particulars are always easier to defend than universals. If the context indicates that a universal is the only sensible way to take a proposition, then take it as universal; otherwise the default in cases of ambiguity is particular. {I’m assuming you’ve read the exchanges above?}

You ask: “If the latter [taking the proposition particularly] is the answer why is it different in mathematical logic?”

I don’t know that it is different in mathematical logic. If I were using this example in the context of the predicate calculus, I would counsel translation in exactly the same way.

Remember, as I’ve said elsewhere on the forum, translation is an art not a science and our guiding principle, as in all translation, is to be as faithful as we can to what is being said and as accommodating as we can be to our interlocutors.

Let me know if this helps or if you’re still unpersuaded.

[gerard.casey]

Ted: Sorry for the delay in responding. I’ve only just seen your post.

In answer to the first part of you question: yes, PIR or RIP is correct. As you note, they are effectively the same proposition (by conversion) and are also equivalent to POR(complement) and ROP(complement) by obversion.

I’m not quite sure what you intend by the second part to your question. Did you miswrite ‘convert’ for ‘obvert’? Because what you did was to obvert the second premise, thereby getting rid of the complement on its predicate. You weren’t wrong to do this – it just wasn’t absolutely necessary as the two premises as they stood contained three and only three terms.

If I haven’t understood the second part of your question correctly, come back to me again.

I hope this helps somewhat.

[gerard.casey]

“Why did American colonists self-organize and start the war in the first place? British were not killing anyone, nor forcing anyone to become or stop being British – they mostly wanted to get their taxes, just like with any State of today.”

Many colonists were opposed to the break with Britain and still others were indifferent. The treatment of the loyalists (so-called) hardly bears scrutiny.

“Why would a rational adult choose to go to a war and bear a tremendous risk (of death or, even worse, horrific mutilation) for what? To get a tax break?? I know it’s a silly question, but right now I’m stuck on it.”

It’s not a silly question. Rightly or wrongly, some of the colonists regarded the imposition of taxes upon them which they had no say over as a form of tyranny. It is ironic that the so-called Whiskey Rebellion was an outbreak of tax resistance against the new Federal state!

“If a neighboring State tries a “gentle” takeover of an anarchic territory, by simply saying – we are here just to collect some taxes and that’s mostly it, then what incentive would anarchists have to fight and maybe lose their lives… it seems they would need to value their anarchy very dearly. Regular soldiers (conscripts of a State) do not need to value much of anything, many of them fight because they are forced to.”

The Roman Empire was largely concerned with collecting taxes from conquered territories. Broadly speaking, once the taxes were paid, the Romans weren’t too concerned about matters of religion or local government. Of course, if the taxes are not forthcoming then violence is used to extract them – nothing gentle about that.

[gerard.casey]

Matt: Your question is a good one; perhaps the most basic of all. What’s the point of this whole logic enterprise?

You dont have to inhabit the worlds of economics or politics for too long before you realise that there are major differences between people on fundamental issues. To know what’s what in these matters, it’s not just a matter of opening one’s eyes and taking a look. Different people ‘see’ different things and, as a consequence, do (and recommend doing) different things.

If we decline to use violence as a mind-changer, the only mode open to us is persuasion, and rational persuasion (i.e. not bribery or other inducements) makes essential use of argument.

Logic, then, is a way of coming to grips with the essentials of argument. It’s not a magic bullet that solves all your problems but it will help you to focus on the essential points instead of trivia. It will help you to know what information you would need to definitively establish a point.

As you move to consider what is called informal logic, you will be exposed to a method of organising and evaluating the commonest class of arguments we come across.

And even with a rudimentary exposure to what are called fallacies, you will recognise a whole class of dubious types of argumentative strategies, an acquaintance with which will put you in control of many discussions.

I sometimes say that learning logic is, putting it at its lowest estimate, a little like learning a system of intellectual self-defence.

On an historical note, logic (or dialectic) was one of the so-called ‘trivial’ subjects, called that because it was one of three, the trivium – grammar, rhetoric and dialectic that were considered to be the basic tools of learning. Grammar allowed you to read and to understand what you read; dialectic (logic) gave your control over the processes of argument; and rhetoric enabled you to find the available means of persuasion. Equipped with these skills, a student was ready to take on more substantive matters.

So, I encourage you to stick with it for a while to see what you can make of it.

If you have any particular questions, please do get in touch, either through the forum or directly to me by email. And thank you for the heads-up on starting this thread.

Good luck!

[gerard.casey]

On p. 10 of the book, I wrote: “I am painfully aware that there are many issues of importance I will not have touched on in the book. You will probably find the phrase ‘But what about…?’ forming in your head from time to time as you read. I can only plead in extenuation that in a book of such modest proportions I have had to be extremely selective in my choice of topics.” Since practical issues have been treated by such as Friedman (and, of course, Rothbard) and others, I concentrated more or less completely on the theoretical issues.

The problem you raise is a very important one and one that David Friedman makes a valiant effort to address. It is something I am thinking about at the moment, if somewhat obliquely, in the context of my next book project, which will concern itself with the relationship between freedom and authority.

In brief, however, here is what I think.

In a condition of terminal anarchy where there are no states, there will be no specific problem of national defence. However, unless and until that condition is reached, there will be a problem of how individuals or groups of individuals can defend themselves against aggression by remnant states

In anarchy, it will most likely be the case that defence against individual aggression will be provided by specialist agencies. This much is standard. However, not only would it be likely that defence agencies would have cooperative arrangements for the solution of individual disputes, it is not inconceivable that they could offer as a service the organisation of defence against group aggression, utilising effectively a militia strategy. By this I mean that in the extraordinary situation where a whole area or a whole group of communities is under attack, the people themselves would function as a defence force. Having your protection agencies provide the officering would then allow such a force to be effectively mobilised.

This idea is not pure speculation. It is, more or less, the historical situation that the Swiss cantons found themselves, surrounded as they were by the Austrian Empire, France, and some German states. The Swiss army is organised for purely defensive purposes. Every Swiss man of an appropriate age has a duty to be prepared to defend the whole and the organisational structure is light. The Swiss strategy might be described as ‘the hedgehog’, an animal that is unpleasant to eat and spiky and it has been remarkably successful.

These remarks are cursory and I’m sure that you will have no problem thinking up scenarios that might prove difficult to deal with. However, Getting from here (statism) to there (anarchism) throws up a whole raft of transition problems. My inclination at the moment is to think that a Proudhonian federalist solution of gradual dissolution is probably the best practical way forward but I haven’t fully thought these matters through and my views might change as I do more research.

[gerard.casey]

SusanB_NH: You are absolutely right! I’d like to pretend I put that error in deliberately just to check if people were paying attention but the truth is that Homer nodded. Well spotted! I don’t quite know why that error happened – I can only think that I must have been looking at the MIR/RIM on the line immediately before the erroneous statement.

Here’s the situation.

In lesson 13, problem 5 (starting at 6.04 on the video) asks you to find (if possible) a conclusion that, if added to the syllogism fragment, would give you a valid syllogism.

The fragment is
[1st premise] MIN
[2nd premise] NER(complement)
[Conclusion] ???

By obverting our 2nd premise, we get as our fragment,

MIN
NAR
???

At 6.36, having shown that the premises as they now are together with MIR or RIM as a conclusion will satisfy the first four rules of the syllogism, I go on to say:

“However, the middle term is N and N is distributed in neither premise so no valid conclusion is possible”

This, of course, is incorrect! The middle term is ‘N’ and ‘N’ is distributed in the second premise. That satisfies rule 5.

Rule 6 requires that any term distributed in the conclusion be distributed in the premise in which it occurs. As we have seen, the only possible candidates for a conclusion are:

MIR or RIM (which, by conversion, are the same proposition)

As this is an ‘I’ type proposition, neither term is distributed so that rule 6 is vacuously satisfied.

So, MIR or RIM will, if added to the fragment, give us a valid syllogism.

So, thank you SusanB_NH for bringing this to my attention. If you notice anything else of significance, please do let me know.

I hope you and your sons continue to enjoy the logic lessons.

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