This post is just a note to say that I have started a podcast, called ‘Thoughtology‘. It is a series where I talk to professional philosophers about various interesting things. I have recorded two episodes so far, and plan to get one out every two weeks (schedule permitting).

In the first episode I talk with my friend Arif Ahmed, who is a well-known atheist philosopher, who, among other notable achievements, has debated William Lane Craig on several occasions. We talked about a paper he has recently published in the journal *Mind*. The topic is David Hume’s argument that it is always irrational to believe in reports of miracles. A well-known response to this is to argue that the combined weight of multiple witnesses could in principle overcome the scepticism one may have on hearing such a report. Arif explains how, when you look at the details of this in a Bayesian framework, the response fails.

In the second episode, I was very lucky to be joined by Graham Priest, who is one of the world’s most notable logicians and philosophers. He is famous for defending a highly controversial position called ‘dialetheism‘, according to which there are some true contradictions. We talked about dialetheism, paradoxes and the metaphysics of logic.

In the coming weeks and months I intend to interview various other professional philosophers, and have about 12 lined up so far. Many of them will be philosophers who are widely known, and many of them will be less established (but equally interesting) people. If you enjoy this blog, you should subscribe to the Thoughtology YouTube channel so that you get the content when it is released.

Thanks.

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I cannot disagree that dialetheism is very very very controversial. (Case and point…Spell correctors don’t care about it…LOL)

I always remember “Ex contradiction quodlibet” = “From a contradiction….anything follows”

(p∧¬p)

________

q

Prove:

1. (1) (p∧¬p) (Premise)

2. (1) p (Conjunction Elimination of 1.)

3. (1) p∨q (Disjunction Introduction with 2.)

4. (1) ¬p (Conjunction Elimination of 1.)

5. (1) q (Disjunctive Syllogism with 3. and 4.)

But clearly, assuming dialetheism, the Disjunctive Syllogism is NOT a valid rule of inference. Because in dialetheism ¬p DOES NOT IMPLY that p is false….therefore it is NOT the case that ¬p along with p∨q NECESSITATES q to be true. Because even when ¬p is true….p can ALSO still be true…which is sufficient for p∨q to be true, eve with q false.

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I am sure I’m mistaken about what follows….so please let me know about the problems below.

I believe that the BIG thing that dialetheism rejects is the “meaning” of the “not” (“¬”) unary operation. By saying “reject the meaning” I am saying that they don’t agree with the following “definition of ¬”.

Let P be an arbitrary proposition that has truth value of either true or false.

Then, “¬” operates on P in the following way (consider this the definition of “¬”)

_____________________

If P is true, then ¬P is false

If P is false, then ¬P is true.

_______________________

Basically, I am saying that “¬” is defined by its truth-table (and the its truth-table is the two sentences above). Clearly dialetheism doesn’t hold this definition of “¬”, because for them:

If P is true, then ¬P can still be either.

Going back to my previous comment, about how Disjunctive Syllogism is NOT valid in dialetheism…i think the source for this invalidity is that “¬” doesn’t have the meaning that we are familiar with.

¬¬P ≠ P

In dialetheism there is also no double-negation-cancellation. Rejecting dialetheism does allow us to cancel by going back to the definition of “¬”…and doing case by case:

If P is true, ¬P is false….so ¬¬P is true (same as P).

If P is false, ¬P is true….so ¬¬P is false (same as P).

So, simply using the definition of “¬” we show that the truth-value of P is equivalent to the truth-value of ¬¬P in all cases…thus, giving us cancellation.

But no such thing can be conclude in dialetheism, where “¬” doesn’t hold its classical definition.

Most probably, all of this is wrong…I say “most probably” because I refuse to belief that experts in the field haven’t looked into this and show its flaws.

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A couple of suggestions I have would be David Atkinson and Jeanne Peijnenburg for their work on probabilistic skeptical reasoning and infinite regresses:

https://link.springer.com/article/10.1007/s11229-018-1883-8

https://books.google.com/books?hl=en&lr=&id=XtpCDwAAQBAJ&oi=fnd&pg=PR7&ots=MuJUP8r8eE&sig=3X6l9sCvlV0hFNWe0V-vJsXCCPg#v=onepage&q&f=false

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