Your work is technically very interesting neverthless I have some remarks.

1/ I don't always understand the claim that the Fitch Paradox threatens Anti-Realist philosophy.
If everybody accepts the Knowability Principle restricted to basic propositions,
it sounds more like a victory than a defeat for the knowability advocates.
It seems that what is threatened is more the capacity of modal logic to represent the knowability.

2/ In your intuitionistic frame, as you say in proposition 5.8, it is impossible to have 'A' and 'not K A' in the same world.
So the Fitch Paradox is avoided but the result is a very poor epistemic logic where you cannot express that some truths are unknown.

3/ more technically in the figure below the proposition 5.7
I don't understand what happens in the world y.
You have      y R_k y ;    y R_k z ;    y: p ;    z: not p
but you have not    'y: not K p' .
Does it stand that 'y: not not K p' ?
It is very counterintuitive.

Else I wrote a dissertation on these points.
I have published a - maybe insufi ... (read more)

I have a question...

A classical, Tarskian system standardly contains homophonic definitions as the base clauses, e.g.,

'G' denotes Gs.

This is understood to be a sentence of the metalanguage (ML) which defines a predicate of the object language (OL). And when ML contains OL, the standard assumption is that the expression 'G' used on the right-hand side is identical to the expression mentioned on the left...so that numerically one expression, 'G', is an expression of both ML and of OL.

However, if homophonic definitions are admissible, then (given the compositionality of negation) the following sentence also seems admissible into the system as a definition:

'G' denotes x iff x is ~G.

But such an interpretation suffices for paradox in OL. For instance,  'Socrates is G' will be true in OL iff it is not true in OL (contra PNC). So apparently the second definition is not admissible in a classical system. But (again by the compositionality of negation) that means the former cannot b ... (read more)

Hello

Please could someone help me with the above question.

For example, is there a difference between the propositions:

Edinburgh is the capital of Scotland.

and 

The proposition 'Edinburgh is the capital of Scotland' is true.

?

Given that the second proposition is a proposition about the first proposition, it seems to me that they can't be the same proposition.

Derrick

Here's an argument that you can't suppose the Liar, where the Liar is, basically, "this very sentence is false."

If you can't suppose the liar, then one common way of setting forth the argument leading to paradox won't work--since it requires you to suppose the liar.

(It's more common, probably, for it to require you to suppose the liar is true. Whether the below argument successfully extends to that supposition isn't something I've thought through yet.)

What do you think of the argument?

I worry about line 4. What do we know (or what do different people think they know) about how to individuate thoughts?

Should I be worrying about any of the other three premises?

Thanks for any comments. It's outside my field (as you can probably tell!) and doesn't really engage directly, as far as I can see, with any of the technical material people usually (need to) discuss when dealing with the liar paradox--which is probably a bad thing I'm afraid.

1.   A =­_def  A is false. (definition)<?xml:namespace prefi ... (read more)

notation : I use ! for 'not'

Perhaps you can avoid paradox but you have to admit this very strange proposition :
K !K x ->  !P K x
If you know that you ignore (x) it's impossible that you know (x)

I don't see how it could be compatible with the knowability principle :
x ->  P K x
else you can't have
(x) and (K !K x)

(excuse me if this message is out of place, I ignore the policy of tis forum,
excuse also my probable mistakes in english)

Hi!

coming from a bioinformatics background (aiming to represent the argumentative structure of research publications) I seek advice to clarify the concepts "argument" and "conditional".

Can these concepts, along with premise/antecedent and conclusion/consequent, interchangeably be used or are there actual differences in definition, meaning and/or use of these terms?

I'd be grateful for any advice on this and direction to relevant sources.

Christian

I'm currently a postgraduate studying philosophy of mind. I have studied logic, but only at undergraduate level, and it was over 30 years ago. So I apologise for the probable naivety of this question.
I'm going to take the liberty of quoting from Melvin Bragg's email newsletter about a radio programme on logic hosted by him, broadcast yesterday on the UK station BBC Radio 4. In a post-programme discussion between the participants,

A C Grayling, usually more slicingly exact than a Gillette razor, defended vagueness in the following terms: if he rushed into a bedroom at two o’clock in the morning and shouted “Fire!” this could open a wide range of possibilities for any logical person.  Was he talking about a candle being lit downstairs?  Was he talking about something that had happened in another place?  But we mere mortals would be vague enough to understand that the house was ablaze and rush out.  Something to be said for vagueness then. (Melvyn Bragg's In Ou ... (read more)

When we say that "P" is possible iff there is a possible world where "P" is true, we can continue and say that there is a possible world where "P" is true iff "A" is true, and "A" is not something about a non-actual possible world. Such an approach would allow us to use the vocabulary of possible worlds, while sustaining an agnostic or an anti-realist position about the the existence of non-actual possible worlds. Can such a reductive approach to possible worlds solve the problem of ontological commitmentt to the existence of non-actual possible worlds? And what do you think that "A" must be as non-actual possible worlds dont get implicated?

Cross-posted from http://mleseminar.wordpress.com/

...

This week we discussed some unpublished material by Antony on ‘might’ counterfactuals. The handout is here, and the paper is here.

We thought a bit about cases in which ‘could’ and ‘might’ come apart. In the paper, Antony discussed sentences like

33b)  If we’d left the gate open, the dog could have got out; yet if we’d left the gate open, it isn’t the case that the dog might have got out.

The felicity of such sentences seems to show that at least some ‘might’ counterfactuals shouldn’t be analysed in terms of ‘could’, but instead should be given an epistemic reading. Antony isn’t averse to this idea – in fact, his final view is that ‘might’ is ambiguous in counterfactual contexts between the epistemic reading and the ability reading. However, this does invite the further question of what determines the appropriate reading for some given ‘might’ counterfactual.

Fron 33b we naturally conclude though the dog has the ability to get out, it is ... (read more)

Cross-posted from http://mleseminar.wordpress.com/

...

The handout for this week is here, the original paper is here.

I found this a particularly interesting paper. I’m in firm agreement with the main gist of Williams’ view- that the notion of typicality is in principle better adapted to deal with chancy similarity than the notion of ‘non-remarkableness’. That said, we found plenty of potential pressure points.

- Firstly, I’m not sure that quantum mechanics really has as wide-reaching consequences as is assumed in the paper. Depending on your response to the measurement problem, it could be that outcomes such as plates flying off sideways are not genuine quantum possibilities after all, because the low-amplitude branches are in some way ‘lost in the noise’. Although I think this issue is worth further investigation, I don’t think it’s critical to the debate between Williams, Hawthorne, and Lewis. Their worries can be raised about considerably less unlikely events – in fact, we can restrict ... (read more)

Cross-posted from http://mleseminar.wordpress.com/

...

You can find the handout for this week here. I thought this was a really good paper, and we didn’t find all that much to criticise in it. It was a bit frustrating not to hear more about Fitelson’s positive story, in particular about the bridge principle that he would endorse instead of the various versions of RTE that he criticises. He’s clearly saving the juicy stuff for his book.

In particular, I find it hard to see how he plans to steer a middle ground between the Carnap/Williamson-style ‘a priori priors’ version of objective bayesianism, and the subjective bayesian approach. My naive take on the matter is that you either think that there’s a unique correct set of priors or you don’t. Maybe these priors aren’t a priori knowable (contra the Carnap/Williamson approach), although it seems that a position like this would be committed to complete epistemic rationality being in principle unattainable.

I wasn’t sure how strongly Fitelson m ... (read more)

Cross-posted from http://mleseminar.wordpress.com/
...

This week we discussed Cian Dorr’s ‘There are no abstract objects’, which isn’t currently available online, but is in ‘Contemporary Debates in Metaphysics’. Here’s the handout instead.

As we had Cian on the spot for this meeting, the discussion mostly took a question-and-answer format. So here are what I recorded of some questions and some answers, with a few that I didn’t get time to ask thrown in at the end. Apologies if my paraphrases of Cian's answers misrepresent him!

Q: What about people who would resist the paraphrase strategy (p.37) because they think that counterpossibles are all vacuously true (Williamson takes this line in The Philosophy of Philosophy).
A: Nominalism/anti-nominalism are both contingent theses. But even if you think that nominalism is necessary if true, there will be certain kinds of truths like ‘there are possibly some things with a number-like structure’ which can be used to ground the relevant counterfactua ... (read more)

Cross-posted from http://mleseminar.wordpress.com/
...

Boris Kment - Counterfactuals and Explanation

A really interesting paper this week - it can be found here, and the presentation is here.

Kment's main proposal is that match of matters of particular fact should be relevant to closeness of two worlds for the purposes of evaluating counterfactuals if and only if the matters of fact have the same explanation in both worlds. Secondarily, he proposes that we should allow for laws to have exceptions, and hence that all worlds which share the same laws as ours should be closer to actuality than any world with different laws.

We quite liked the main proposal, but worried about the individuation of explanations it relies upon. What are the conditions for two events to have the same explanation? For example, consider the counterfactual 'if I had tossed the coin five minutes earlier, it would still have come up heads'. This seems false, but perhaps Kment can account for this falsity by sayi ... (read more)

             

From MATHEMATICAL REVIEWS.

MR2398883

Nolt, J. 2008 Truth as an Epistemic Ideal. Journal of Philosophical Logic. 37: 203-237.

 

            The abstract of the paper being reviewed is as follows.

“Several philosophers—including C. S. Peirce, William James, Hilary Putnam, and Crispin Wright—have proposed various versions of the notion that truth is an epistemic ideal. More specifically, they have held that a proposition is true if and only if it can be fixedly [sic] warranted by human inquirers, given certain ideal epistemic conditions [emphasis added]. This paper offers a general critique of that idea, modeling conceptions of ideality and fixed warrant within the semantics that Kripke developed for intuitionistic logic. It is shown that each of the two plausible notions of fixed warrant faces difficulties and that, moreover, “truth” defined in terms of either of them is distressingly dependent on one’s conception of idealized inquiry and perhaps also upon one’s standards of warrant.”

    ... (read more)