h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

hi psi

Infection turned into full blown flu with bronchial infection as a complication. So have been completely hors de combat and awash with antibiotics which doctor prescribe over my objections. Apparently deems at my age some risk of pneumonia. Pah!

Starting to feel better so hopefully will reply in next couple of days.

bs

Hi Bx4,

I hope you have recovered.

ttfn

Hi psi

Apologies for delayed reply. Contracted a secondary infection and ended up in hospital. Now released and tying to catch up with our filosofickal debate.

In the meantime I thought you might enjoy this example from 'the s knows that p crowd' cited in William Lycan's 'The Gettier Problem Problem':

'S knows that h iff (i) h is true, (ii) S is justified [by some evidence e] in believing h…, (iii) S believes that h on the basis of his justification and…(ivg)…there is an evidence-restricted alternative Fs* to S’s epistemic framework Fs such that (i) ‘S is justified in believing that h’ is epistemically derivable from the other members of the evidence component of Fs* and (ii) there is some subset of members of the evidence component of Fs* such that (a) the members of this subset are also members of the evidence component of Fs and (b) ‘S is justified in believing that h’ is epistemically derivable from the members of this subset. [Where Fs* is an ‘evidence-restricted alternative’ to Fs iff (i) For every true proposition q such that ‘S is justified in believing not-q’ is a member of the evidence component of Fs, ‘S is justified in believing q’ is a member of the evidence component of Fs*, (ii) for some subset C of members of Fs such that C is maximally consistent epistemically with the members generated in (i), every member of C is a member of Fs*, and (iii) no other propositions are members of Fs* except those that are implied epistemically by the members generated in (i) and (ii).'

(Swain M. (1974). ‘Epistemic Defeasibility’. American Philosophical Quarterly, 11: 15-25.:

Compared with which Merricks' formulation seems a trifle jejeune

Ha ha ha superb.

hi psi

Returned home after ny involuntarily extended holiday so I have had to spend time getting back into the saddle, workwise. A busy day tomorrow but I'll try to reply to some of the points you raise. So in reply your 94

>>No it doesn't. The full quote makes this clear, I am rejecting the two quite distinct cases that a) you thought the circularity is due to the fiat and b) any other reason or argument you have used. When I posted this I wasn't sure whether you were using a) as well as b) and that's why I said we ought not to conflate the two.<<

Ok I hope we can now agree that I wasn't trying to conflate the two. My point was that while I find Merricks introduction of warrant by fiat a piece of somewhat dodgy filosofickal humptydumptyism however for the purposes of arguing that it is circular have to accept the fiction that it is not f. h.

>>No the original definitional premiss does not produce a circularity, what you have done is overlook its conditional property. I have tried to explain where I think you are going wrong,...<<

Merricks says:

'Warrant is “that, whatever precisely it is, which makes the difference between knowledge
and mere true belief.” S knows that p, therefore, if and only if S’s belief that p is warranted and p is true.

I have not overlooked the conditional since my argument is that Merricks' premise is the same as the conditional :

KcP iff BcP.WP.P (1)

which is to say that C know that P is true if and only //all// the atomic propositions that constitute the extended conjunction BcP.KP.P are true. If we expess (1) as a //strict// conditional:

BcP.WP.P-*KcP (2) (where -* tfor the non printable Lewisian 'fishhook' operator)

that is to say that the consequent cannot be false if antecedent is true. However the circularity does not lie in the conditional per se but in the fact that Merricks' //conclusion//, the title of the paper. 'Warrant entails truth', that is that WP so we have the argument from the premise BcP.WP.P-*KcP (2) to the conclusion that WP. Since the truth of the consequent is dependent on the truth of WP (as well as the other two atomic propositions), then the truth of the whole conditional is necessarily dependent on the truth of WP. But since:

'This sort of "reasoning" is fallacious because simply assuming that the conclusion is true (directly or indirectly) in the premises does not constitute evidence for that conclusion.'

['Fallacy: Begging the Question' http://www.nizkor.org/features/fallacies/begging-the-question.html]

So Merricks' argument is fallacious because it assumes that KP is true in the consequent of the premise and assumes that KP is true in the conclusion.

I am not clear why you think think the 'conditional property' of the premise affects its truth since it merely says that the consequent cannot be false if the antecedent is true. However in Merricks' argument if WP is false in the antecedent then WP is false in his 'conclusion which would still be a circular argument.

>>Then it follows that KcP can only be true iff W is is necessarily true. <<
Modal scope fallacy alert. What is 'necessarily' doing here? It should be: Necessarily, KcP can only be true iff W is true. I agree.<<

I disagree that there is any modal scope fallacy here since as I point out above the 'KcP iff BcP.WP.P' construction is logically equivalent to the Lewisian strict implication, BcP.WP.P-*KcP.

In the modern version of strict implication the 'fishook' operator is replaced by

(a) @(BcP.WP.P->KcP) (where @ is the modal necessity operator)

Which from the Distribution Axiom K gives:

(b) @(BcP.WP.P)->@(KcP)

>> However, it does not follow that W -> P as I have explained, since you haven't ruled out the scenario that KcP is false and P is false and W is true<<

The conditional W->P forms no part of my argument but rather the conditional BcP.WP.P->KcP. Note tha in this case if P were false then the conjunction BcP.WP.P would be false if P were false, irrespective of whether WP is true or not and also KcP would be false.

>> If you can preclude that possibility then you have W -> P. The important thing to realise is that you cannot assume KcP!<<

This is not Merricks' argument which is rather as I have pointed out is rather:

KcP iff BcP.KP.P

I don't need to consider the case where P is false because Merricks definition explicitly says 'p is true'.

>>No, W is only true if you assume KcP which you are not entitled to do and Merricks doesn't. Merricks assumes that IF KcP is true THEN BcP.WP.P is also true. That is the difference you haven't distinguished as far as I can tell.<<

I think you are somewhat confused here. the equivalent of KcP iff BcP.KP.P (1) as a conditional is BcP.KP.P->KcP (2) and not KcP->BcP.KP.P (3). In (1) and (2) KcP is the //consequent// of the conditional whereas in (3) you have made it the //antecedent//.

>>See above.<<

Ditto.

>>This is the error you are making in a nutshell. Merricks' definition presupposes no such thing, any more than presupposing that 'if it is raining then it is wet' presupposes that it is raining.<<

No I am merely assuming the normal conventions of the modus ponens form:

If it is raining then it is wet. {Premise 1}

It is raining {Premise 2}

Therefore

It is wet. {Conclusion}

However had the argument been:

If it is raining then it is wet. {Premise 1}

It is raining {Premise 2}

Therefore

It is raining. {Conclusion}

Which I assume you will agree in terms meets the criterion for being a circular argument.


Excluding my doubts about the introduction of warrant by fiat I would have had no problem had Merrick's argument been:

If c believes that P and C's belief that P is warranted and P then c knows that P {Premise 1}

c believes that P and C's belief that P is warranted and P {Premise 2}

Therefore:

c knows that P. [Conclusion}


However his argument is rather:

If c believes that P and C's belief that P is warranted and P then c knows that P {Premise 1}

c believes that P and C's belief that P is warranted and P {Premise 2}

Therefore:

C's belief that P is warranted {Conclusion}

Which demonstrates an equivalent circularity.

bs

Hi Bx4,

I'm pleased that you seem to be on the mend.

>>Ok I hope we can now agree that I wasn't trying to conflate the two. My point was that while I find Merricks introduction of warrant by fiat a piece of somewhat dodgy filosofickal humptydumptyism however for the purposes of arguing that it is circular have to accept the fiction that it is not f. h. <<
Ok, so we are not conflating, that's settled.

>>I have not overlooked the conditional since my argument is that Merricks' premise is the same as the conditional :

KcP iff BcP.WP.P (1) <<
No, I said you have overlooked its conditional property and by that I mean that the above premiss is expressing conditions for knowledge. However Merricks has a conclusion that Warrant entails truth. You haven't addressed what happens if C doesn't know p; is it possible that p is still warranted even if p is false? Your response to this seems to be to keep pointing out that in order for KcP, each of the atomic propositions, including W must be true. This shows that you haven't understood what the conditional property does here in my view. We aren't dealing with the scenario that KcP, so it doesn't follow in a circular way that W. Rather, Merricks tries to show that if you assume that it is logically possible to have a warranted true belief you either get a contradiction, or you get a much less plausible set of commitments than that warrant entails truth.

>>So Merricks' argument is fallacious because it assumes that KP is true in the consequent of the premise and assumes that KP is true in the conclusion. <<
Could you point to where he does this? I don't think he does. He assumes the biconditional 'iff' statement is true. But that can be true if KcP and p are both false.

>>I am not clear why you think think the 'conditional property' of the premise affects its truth since it merely says that the consequent cannot be false if the antecedent is true. However in Merricks' argument if WP is false in the antecedent then WP is false in his 'conclusion which would still be a circular argument. <<
For a start it is a biconditional rather than an implication, but this is not the structure of his argument. I summarised the actual structure above.

>>I disagree that there is any modal scope fallacy here since as I point out above the 'KcP iff BcP.WP.P' construction is logically equivalent to the Lewisian strict implication, BcP.WP.P-*KcP.

In the modern version of strict implication the 'fishook' operator is replaced by

(a) @(BcP.WP.P->KcP) (where @ is the modal necessity operator)

Which from the Distribution Axiom K gives:

(b) @(BcP.WP.P)->@(KcP) <<
You had said "Then it follows that KcP can only be true iff W is is necessarily true.", which perhaps could be reconciled with necessarily(KcP) iff necessarily(BcP.WP.P). Perhaps you could go through the steps?

>>The conditional W->P forms no part of my argument but rather the conditional BcP.WP.P->KcP. Note tha in this case if P were false then the conjunction BcP.WP.P would be false if P were false, irrespective of whether WP is true or not and also KcP would be false. <<
I thought you were trying to establish circularity in Merricks' argument so I'm unclear how you avoid addressing W->P as that's his conclusion. You've got quite good at showing your own circularity though. KcP being false if P is false, yes I've mentioned that a few times, so what I'm trying to communicate to you is that even though the conjunction is false irrespective of the truth value of WP, what Merricks does is try to show that WP /can't/ be true if P is false. In other words, you can't have a warranted false belief.

>>This is not Merricks' argument which is rather as I have pointed out is rather:

KcP iff BcP.KP.P <<
See above.

>>I don't need to consider the case where P is false because Merricks definition explicitly says 'p is true'. <<
No, it is a conditional. His definition says you can know p iff p AND BcP AND WP. His definition doesn't say 'P is true' except as part of that conditional.

>>I think you are somewhat confused here. the equivalent of KcP iff BcP.KP.P (1) as a conditional is BcP.KP.P->KcP (2) and not KcP->BcP.KP.P (3). In (1) and (2) KcP is the //consequent// of the conditional whereas in (3) you have made it the //antecedent//. <<
In my view, the confusion is yours. As I've said above the definition is a /biconditional/, hence the 'iff'. So this quibbling about the consequentand the antecedent is irrelevant, the definition can be read in either direction.

>>Which I assume you will agree in terms meets the criterion for being a circular argument. <<
I do.

>>However his argument is rather:

If c believes that P and C's belief that P is warranted and P then c knows that P {Premise 1}

c believes that P and C's belief that P is warranted and P {Premise 2}

Therefore:

C's belief that P is warranted {Conclusion} <<
No that isn't Merricks' argument. The half of his argument that is on the logic side is:
"Suppose that S has a warranted belief that p, and p is false; S then
infers, from p, that p or Brown is in Barcelona. That S’s belief that p is warranted seems to
imply that S’s belief that p or Brown is in Barcelona is warranted. Further, suppose that, by
sheer coincidence, Brown is in Barcelona. Then S’s belief that p or Brown is in Barcelona is,
not only warranted, but true. Since warrant is what makes true belief knowledge, S knows that p
or Brown is in Barcelona. But surely S doesn’t know this. The supposition that S’s belief that p
is both warranted and false seems initially to lead to a contradiction"

I hope this clarifies.

ttfn

Hi Bx4,

Sorry I find proofreading with this software tricky. Where I said:

"Rather, Merricks tries to show that if you assume that it is logically possible to have a warranted true belief you either get a contradiction, or you get a much less plausible set of commitments than that warrant entails truth. "

I meant:

Rather, Merricks tries to show that if you assume that it is logically possible to have a warranted false belief you either get a contradiction, or you get a much less plausible set of commitments than that warrant entails truth.

ttfn

...and the formatting, good grief. The logic part of Merricks' argument again:

"Suppose that S has a warranted belief that p, and p is false; S then infers, from p, that p or Brown is in Barcelona. That S’s belief that p is warranted seems to imply that S’s belief that p or Brown is in Barcelona is warranted. Further, suppose that, by sheer coincidence, Brown is in Barcelona. Then S’s belief that p or Brown is in Barcelona is, not only warranted, but true. Since warrant is what makes true belief knowledge, S knows that p or Brown is in Barcelona. But surely S doesn’t know this. The supposition that S’s belief that p is both warranted and false seems initially to lead to a contradiction"

I hope that is clearer.

Hi psi

I'm a bit time poor at the moment but i am noodling away at your #106. Two or three days hopefully until I have finished

bs

Hi Bx4,

As usual, I look forward to it.

ttfn

hi psi

Apologies for the rather delayed reply.

Yr (amended) #106

>>No, I said you have overlooked its conditional property and by that I mean that the above premiss is expressing conditions for knowledge<<

I haven't overlooked the conditionality off Merricks' definition but rather focussed on the one condition under whih the conditional is true.

>>However Merricks has a conclusion that Warrant entails truth.<<

Indeed based on a conditional:

c knows that P is true if and only if the atomic propositions:

(a) c believes that P is true
(b) c's belief that C is true is warranted (whatever that means)
(c) P

are all true. That is to say KcP is true iff the extended conjunction BcP.KP.P is true. Merricks' conclusion 'warrant entails truth' is simply a

generalisation of KP(T); 'C's belief that P is true is warranted' is true.

>>You haven't addressed what happens if C doesn't know p; is it possible that p is still warranted even if p is false?<<

Since Merricks says of his definition 'This is a purely formal characterization of warrant.' and provides no description of (the properties of) warrant then

it seems there is no way of determining whether the truth conditions that would make warrant true are satisfied if P is false.

Situations in which any or all of the atomic propositions are false are irrelevant to my circularity point since I am discussing it in terms of Merricks'

//semantic definition// of the conditions under which KcP is true and such defnitions are true definitions are true a priori.

>>Your response to this seems to be to keep pointing out that in order for KcP, each of the atomic propositions, including W must be true. This shows that

you haven't understood what the conditional property does here in my view. We aren't dealing with the scenario that KcP, so it doesn't follow in a circular

way that W.<<

Not quite. The conditional KcP iff BcP.WP.P is equivalent to the Lewisian strict conditional BcP.WP.P->KcP, that is to say if the antecedent, BcP.WP.P is

true then the consequent is true (or a Lewis expressed it 'the consequent cannot be false'. So the 'conditional property' of Merricks definition is the truth

value of the antecedent which determines whether the consequent is true.

In fact the 'purely formal characterisation of warrant' is more properly a purely formal characterisation of the conditions under which one can assert that

'S knows that P' (is true). Since this assertion is wholly depends on the antecedent of the conditional, BcP.WP.P, being true. Moreover, the truth of the

antecedent is wholly //independent// of the conditional as should be obvious from the modus ponens BcP.WP.P->KcP:BcP.WP.P|=KcP.

The circularity is not implicit in the conditional but in the truth of the conjoined proposition BcP.WP.KP which can only be true if all its constituent

atomic propositions are true. I am quite puzzled that you cannot see the obvious circularity:

(d)If BcP.WP.P then WP;BcP.Wp.P|=WP (circular modus ponens)

>> This shows that you haven't understood what the conditional property does here in my view. We aren't dealing with the scenario that KcP, so it doesn't

follow in a circular way that W.<<

You seem to think that my argument for circularity is invalidated by conditions in which one or more of the atomic propositions in the antecedent are false.

However, since KcP is true by definition these are irrelevant just as

(e) If C is a bachelor then c is unmarried; P->Q

is true by definition the consideration of the condition that P is false is irrelevant.

>>Rather, Merricks tries to show that if you assume that it is logically possible to have a warranted false belief you either get a contradiction, or you get

a much less plausible set of commitments than that warrant entails truth. <<

Well, I have already expressed my reservations over Merricks's assertion by fiat that warrant exists but it is irrelevant to my point since if one accepts

that if Merricks' definition BP.WP.P->KcP is true //a priori// then if KcP is true then ¬BcP.WP is logically impossible.

>>I do...No that isn't Merricks' argument<<

Merricks (subsequent) argument is irrelevant to my point which is that his //a priori// definition of the conditions under which KcP is true requires that Wp

is necessarily true in the antecedent and therefore by (d) we have a circular modus ponens.

>>"Suppose that S has a warranted belief that p, and p is false; S then infers, from p, that p or Brown is in Barcelona. That S’s belief that p is warranted

seems to imply that S’s belief that p or Brown is in Barcelona is warranted. Further, suppose that, by sheer coincidence, Brown is in Barcelona. Then S’s

belief that p or Brown is in Barcelona is, not only warranted, but true. Since warrant is what makes true belief knowledge, S knows that p or Brown is in

Barcelona. But surely S doesn’t know this. The supposition that S’s belief that p is both warranted and false seems initially to lead to a contradiction" <<

I think the problem here lies in:

'since warrant is what makes true belief knowledge'

references the //a prior definition// BcP.WP.P and so does not resolve the issue of circularity.

I think that there are quite a few other problems with the above but these are not relevant.

I am not clear why you find Merricks argument persuasive since it is simply a variant on the 'JTB+G' argument which fails to explain the 'G' is that

distinguishes 'knowledge' from 'true belief'.

Haven't had time todo a proper proof reading so opologies for any typos, solecisms, et.

bs

Hi Bx4,

Ironically, we seem to be going round in circles.

I'll see if I can think of a way to communicate my point to you effectively. I'm tempted to try an analogous argument, but I fear given our track record that this is unlikely to be effective. You are puzzled because you think I can't see a circularity, I'm puzzled because I don't understand why you think the circularity or your modus ponens has anything to do with Merricks' argument.

I'll try to reply fully after a think.

ttfn

hi psi

>>I'll see if I can think of a way to communicate my point to you effectively. I'm tempted to try an analogous argument, but I fear given our track record that this is unlikely to be effective.<<

I don't have a problem with analogies per se (though I generally find they obfuscate rather than clarify) but I do think if they are to be useful they need to be developed quite rigorously as in the TWA methodology:

>>http://www.csun.edu/science/books/sourcebook/chapters/10-analogies/teaching-analogies.html<<

>>You are puzzled because you think I can't see a circularity, I'm puzzled because I don't understand why you think the circularity or your modus ponens has anything to do with Merricks' argument.<<

I am not interested in Merricks argument as but in his somewhat dodgy conclusion 'Warrant entails truth' since this is implicit in his 'S knows that p, therefore, if and only if S’s belief that p is warranted
and p is true.

I think our difference may be that we have a quite antithetical views as to the merits of Merricks 'argument which seems to me nothing but a clever but entirely specious descent into semantic legerdemain.

>>I'll try to reply fully after a think.<<

I look forward to it.
bs

Hi Bx4,

I like the TWA methodology for analogies but I haven't found one that I think avoids the usual pitfalls. I don't think the issue is that I view Merricks' argument more favourably than you do. That's probably the case but it is separate to whether it is circular. I'll keep thinking of analogies and if I find one that works I'll present it using the TWA method.

In the meantime, let's try a different tack. Do you agree that if the argument is circular then this is structural rather than dependent on the semantics or meaning of the variables? In other words, you think the following is circular:

P1: p iff q.r.s

[additional premisses and deductions as required here]

Conclusion: r entails s

...because the circularity is contained in P1? (premiss 1)

This seems to be what you have argued, but this must be true regardless of any meanings assigned to p,q,r and s.

In that case, perhaps you could set out the argument for circularity in a clear logical format and ignore the context?

I don't think there is a circularity there. Of course a circularity could be introduced in the square bracket section, but this isn't the source you have identified in your arguments so far is it?

I think that would clarify things.

ttfn

hi psi

>>I like the TWA methodology for analogies but I haven't found one that I think avoids the usual pitfalls<<

Indeed. Inadequacy in mapping seems to be inherent in most analogies which is why I think they are best avoided.


>>. I don't think the issue is that I view Merricks' argument more favourably than you do. That's probably the case but it is separate to whether it is circular.<<

Except that your more favourable view of Mericks' paper might predispose you to ignore its many flaws including its (to me) obvious circularity.

>> Do you agree that if the argument is circular then this is structural rather than dependent on the semantics or meaning of the variables?<<

I don't think I have suggested otherwise. The problem lies not in the semantics but in the logical structure of the argument.

>> In other words, you think the following is circular:

P1: p iff q.r.s

[additional premisses and deductions as required here]

Conclusion: r entails s

...because the circularity is contained in P1? (premiss 1)

>>

Not quite.

P0: q.r.s iff |q|r|S (Law of conjunction where |x indicates that x is independent atomic proposition)

P1: p iff q.r.s

[additional premisses and deductions as required here]

Conclusion: |r (r entails truth)

(Note that the only //valid// conclusion from P1 is KcP and //not// |r nor your 'r entails s'.)

This seems to be what you have argued, but this must be true regardless of any meanings assigned to p,q,r and s.

Not quite. See above. I have never claimed that the /validity/ of a logical deduction is dependent on its semantic content:

'A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false...an argument is valid if the truth of the premises logically guarantees the truth of the conclusion.'( Validity and Soundness: Internet Encyclopedia)

>>This seems to be what you have argued, but this must be true regardless of any meanings assigned to p,q,r and s.<<

We were discussing Merricks' argument, so using |B,|W and |P rather than |r,|s| and |t makes little difference because I was addressing his argument's validity not its soundness.

>>In that case, perhaps you could set out the argument for circularity in a clear logical format and ignore the context?<<

See above. You seem somewhat taken with the notion that I consider the 'context' of any relevance. I don't and have never so claimed.

>>I don't think there is a circularity there. Of course a circularity could be introduced in the square bracket section, but this isn't the source you have identified in your arguments so far is it?<<

No. Because they are irrelevant to my point that the source of the circularity lies in P0 as I have pointed out severally in previous posts. For example in my #105:

'I have not overlooked the conditional since my argument is that Merricks' premise is the same as the conditional :

KcP iff BcP.WP.P (1)

which is to say that C know that P is true if and only //all// the atomic propositions that constitute the extended conjunction BcP.KP.P are true. If we expess (1) as a //strict// conditional:

BcP.WP.P-*KcP (2) (where -* tfor the non printable Lewisian 'fishhook' operator)

that is to say that the consequent cannot be false if antecedent is true.'



Now you might make the point that Merricks' argument has no P0 to which I would reply that the his P1 presupposes P0. Generally any //valid// logical argument in classic propositional logic presupposes that it laws are true, which is why they need not be explicitly stated in the deduction, and the Law of Conjunction is one such

>>I think that would clarify things<<

I hope it has.

bs

hi psi

>>I like the TWA methodology for analogies but I haven't found one that I think avoids the usual pitfalls<<

Indeed. Inadequacy in mapping seems to be inherent in most analogies which is why I think they are best avoided.


>>. I don't think the issue is that I view Merricks' argument more favourably than you do. That's probably the case but it is separate to whether it is circular.<<

Except that your more favourable view of Mericks' paper might predispose you to ignore its many flaws including its (to me) obvious circularity.

>> Do you agree that if the argument is circular then this is structural rather than dependent on the semantics or meaning of the variables?<<

I don't think I have suggested otherwise. The problem lies not in the semantics but in the logical structure of the argument.

>> In other words, you think the following is circular:

P1: p iff q.r.s

[additional premisses and deductions as required here]

Conclusion: r entails s

...because the circularity is contained in P1? (premiss 1)

>>

Not quite.

P0: q.r.s iff |q|r|S (Law of conjunction where |x indicates that x is independent atomic proposition)

P1: p iff q.r.s

[additional premisses and deductions as required here]

Conclusion: |r (r entails truth)

(Note that the only //valid// conclusion from P1 is KcP and //not// |r nor your 'r entails s'.)

This seems to be what you have argued, but this must be true regardless of any meanings assigned to p,q,r and s.

Not quite. See above. I have never claimed that the /validity/ of a logical deduction is dependent on its semantic content:

'A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false...an argument is valid if the truth of the premises logically guarantees the truth of the conclusion.'( Validity and Soundness: Internet Encyclopedia)

>>This seems to be what you have argued, but this must be true regardless of any meanings assigned to p,q,r and s.<<

We were discussing Merricks' argument, so using |B,|W and |P rather than |r,|s| and |t makes little difference because I was addressing his argument's validity not its soundness.

>>In that case, perhaps you could set out the argument for circularity in a clear logical format and ignore the context?<<

See above. You seem somewhat taken with the notion that I consider the 'context' of any relevance. I don't and have never so claimed.

>>I don't think there is a circularity there. Of course a circularity could be introduced in the square bracket section, but this isn't the source you have identified in your arguments so far is it?<<

No. Because they are irrelevant to my point that the source of the circularity lies in P0 as I have pointed out severally in previous posts. For example in my #105:

'I have not overlooked the conditional since my argument is that Merricks' premise is the same as the conditional :

KcP iff BcP.WP.P (1)

which is to say that C know that P is true if and only //all// the atomic propositions that constitute the extended conjunction BcP.KP.P are true. If we expess (1) as a //strict// conditional:

BcP.WP.P-*KcP (2) (where -* tfor the non printable Lewisian 'fishhook' operator)

that is to say that the consequent cannot be false if antecedent is true.'



Now you might make the point that Merricks' argument has no P0 to which I would reply that the his P1 presupposes P0. Generally any //valid// logical argument in classic propositional logic presupposes that it laws are true, which is why they need not be explicitly stated in the deduction, and the Law of Conjunction is one such

>>I think that would clarify things<<

I hope it has.

bs

erratum

Apologies I omitted >> << from

>>This seems to be what you have argued, but this must be true regardless of any meanings assigned to p,q,r and s.<<

Not quite. See above. I have never claimed that the /validity/ of a logical deduction is dependent on its semantic content:

Hi Bx4,

>>Except that your more favourable view of Mericks' paper might predispose you to ignore its many flaws including its (to me) obvious circularity.<<
I don't think it has. You seem to be mistaken about the circularity and perhaps its apparent obviousness is obscuring this.

>>I don't think I have suggested otherwise. The problem lies not in the semantics but in the logical structure of the argument.<<
Nor am I suggesting that you had, I'm just seeking agreement on some basic points.

>>Not quite.

P0: q.r.s iff |q|r|S (Law of conjunction where |x indicates that x is independent atomic proposition)<<
As you point out later, the law of conjunction is an implicit prerequisite for this discussion, so it is not clear how making it an explicit premiss is useful. It certainly does not bring you any nearer to demonstrating the required circularity.

>>(Note that the only //valid// conclusion from P1 is KcP and //not// |r nor your 'r entails s'.)<<
I can't make sense of this I'm afraid. P1 doesn't involve KcP. One might conclude KcP from KcP iff BcP.W(P).P given the additional premisses BcP, W(P) and P. I can't see the relevance of this.

>>Not quite. See above. I have never claimed that the /validity/ of a logical deduction is dependent on its semantic content:<<
In that case we agree and you should have said 'quite' rather than 'not quite'?

>>We were discussing Merricks' argument, so using |B,|W and |P rather than |r,|s| and |t makes little difference because I was addressing his argument's validity not its soundness.<<
If you could demonstrate circularity using either then there would be progress.

>>See above. You seem somewhat taken with the notion that I consider the 'context' of any relevance. I don't and have never so claimed.<<
I saw above but found no argument for circularity in a clear logical format. I was wondering whether the context was distracting you, if not then fair enough, but you haven't demonstrated the circularity in Merricks' argument, which introduces the notion of warrant via the KcP definition in order to leave W(P) non specific. He then uses other premisses and arguments to arrive at the conclusion that warrant entails truth. I can't find any circularity there and you don't seem to be able to either.

>>No. Because they are irrelevant to my point that the source of the circularity lies in P0 as I have pointed out severally in previous posts. For example in my #105:<<
The law of conjunction is a given. The fact that given P1, KcP can only be true if each and every one of BcP, P and W(P) is true, does not introduce a circularity. I have pointed out lots of times why not- KcP needn't be true! So Merricks still has to show that you can't have a warranted false belief. He seems to do this without circularity.

So I ask again, could you please set out a clear logical argument to demonstrate circularity? (You can have P0 as well as P1 if you wish).

ttfn

Hi psi

Somewhat engaged in transferring CDs and LPs to my shinee new Brennan JB7 at the moment so It might be Sunday before I can reply to your somewhat hectoring*** last

**What is clear to me is clearly not clear to you. So it goes.

bs

Hi Bx4,

Sorry I did not intend my post to seem hectoring at all.

What is clear to me seems not to be clear to you. This is indeed how these tend to go.

Consider this though. Suppose in any logical argument involving propositions, p,q,r and s, we have a premiss

P1: p iff q.r.s

and a conclusion,

C: r entails s

Even if you introduce a version of P0 to explicitly include the law of conjunction, there is no circularity introduced by P1 in the above.

This is clear if we look at the truth table for P1. We see that iff can be written <-> and P1 can be true if all of p, q, r and s are true, or if p is false and any number >=1 of q,r, and s are also false. So it just isn't the case that the truth of W(p) in the original argument is smuggled in with the definition premiss.

So it is clear to me that your argument for circularity in Merricks' argument is mistaken. This is not clear to you. So it goes.

ttfn

hi psi

extende delay in replying due to excessive time poverty Taking a few days off later in week so hopefully will manage a reply then
bs