Clear Language, Clear Mind

September 13, 2011

Time travel: reading material

Filed under: Metaphysics — Tags: , , , — Emil O. W. Kirkegaard @ 17:33

I am taking a metafysics class1 and last lectur’s topic was time travel. That is an issu i sort of like but i dislike the way people discuss it, in general. Ther is a widespred lack of clarity and lack of training in the relevant logics (that is, modal logics: alethic logic and temporal logic). A fine example of that is the first essay below.

John M. E. Mctaggart – Time Is Not Real

David Lewis The Paradoxes Of Time Travel

The followup essay (2nd abov) is certainly better than the first but not quite clear enof to my taste. I do generally agree with Lewis tho. I advice people interested in the subject to lern alethic logic (S5) and read the following materials.

http://www.sfu.ca/~swartz/time_travel1.htm

http://www.sfu.ca/~swartz/beyond_experience/index.htm Chapter 8.

And for those who like fiction about time travel and wants to see som fiction with time travel that seems to be non-contradictory.

Robert A. Heinlein – Time enough for love_ the lives of Lazarus Long

Robert A. Heinlein – All You Zombies

Notes

1Well, tecnically, i signed up for it but never turned up so far. I blame the timing. They put it at 0900, and even on the same day as another class (filosofical logic) altho not the same time. But it still implys that if i want to attend both lectures, then i hav to spend a lot of time on the university in one day. But i disfeel like spending that much time, unless ther is alcohol involved. :)

August 12, 2009

Validity and necessary truths

Filed under: Logic — Tags: , , , , , — Emil O. W. Kirkegaard @ 14:32

Validity is defined in a couple of ways. I like to define it like this: An argument is valid iff the superconjunction1 of all the premises and the negation of the conclusion is impossible. It sounds a bit unusual at first but it is worded that way to prevent confusion about modalities. A more common definition is: An argument is valid iff it is impossible for all the premises to be true and the conclusion false. I contend that mine is clearer when understood. Consider this argument:

n Proposition Explanation
1 P Premise
2 P→Q Premise
3 Q From 1, 2, MP

Anyone trained in logic will immediately recognize that this argument is valid (and the form valid too) for it has the form of MP and all arguments of that form are valid. To see this using my definition of valid above we can simply make the superconjunction of the argument and put it into a truth table:

P Q ¬Q P→Q P∧(P→Q)∧¬Q
T T F T F
T F T F F
F T F T F
F F T T F

Note that I skipped a conjunction step.

The superconjunction comes out as impossible.

And here comes the tricky part. Suppose that the conclusion of an argument happens to be a necessary truth. Consider this argument:

n Proposition Explanation
1 P Premise
2 ¬(Q∧¬Q) From 1

Is that argument valid? It is according to my definition and the usual definition of valid. A truth table will show that:

P Q (Q∧¬Q) P∧(Q∧¬Q)
T T F F
T F F F
F T F F
F F F F

Note that (Q∧¬Q) is equivalent to ¬¬(Q∧¬Q) which is the negation of the conclusion in the argument above. I skipped a double negation step.

Realize that whatever is conjoined with an impossibility such as (Q∧¬Q) will come out as false. So no matter the argument structure, an argument with a necessary truth in the conclusion is valid. This doesn’t seem to bad again, after all, we already know that anything implies a necessary truth and that an impossibility implies anything. Truth tables show that:

Necessary truth as consequent:

P □Q P→□Q
T T T
F T T

Note that Q is true on all rows.

An impossibility as antecedent:

□¬P Q □¬P→Q
F T T
F F T

Note that P is false on all rows.

But now consider that in the realm mathematics all propositions are either necessary truths or impossibilities. Thus, any mathematical argument that happens to have a necessary truth in its conclusion is valid, no matter the form of it. That seems like an odd conclusion.

1A conjunction has the form P∧Q. A superconjunction has the form P∧Q∧…∧T. I use it to avoid talking about sets.

Truth tables and necessary truths

Filed under: Logic — Tags: , , , , — Emil O. W. Kirkegaard @ 14:28

In the essay Validity and necessary truths I used truth tables with necessary truths and impossibilities in it. I did it like this:

P □Q P→□Q
T T T
F T T

Note that the modal operator is placed in the truth table also. It could also be done like this:

P Q P→Q
T T T
F T T

Note that Q is true on all rows. When thinking about a necessary truth or an impossibility we can simply choose only to look at the rows where the proposition is true. The truth table above is a part of this larger truth table:

P Q P→Q
T T T
T F F
F T T
F F T

We simply only looked at rows 1 and 3.

April 23, 2009

Why something rather than nothing? An argument for the necessity of a something-world

Filed under: Philosophy — Tags: , , , , , — Emil O. W. Kirkegaard @ 20:31

PDF due to mathematical expressions that WordPress does not support.

why-something-rather-than-nothing_-an-argument-for-the-necessity-of-a-something-world

April 20, 2009

Motivation, reason, the impossible

Inspired by reading of David Hume’s Enquiry concerning the principles of Morals (EPM) edited by Tom L. Beauchamp.1

“Hume is often interpreted as arguing that no value judgment–however extreme, obscene, or cruel–is reasonable or unreasonable, just as no value judgment is factual. This interpretation needs careful assessment. A passion is ‘unreasonable’ for Hume not because the passion is inappropriate, as we suggest today when we say, ‘It was unreasonable of him to be angry’, but because the passion is based on an erroneous judgment, as when we say, ‘It is unreasonable to have a desire to do what is impossible’. For example, if I desire to see my dead grandfather at a restaurant tonight and this desire together with my peculiar belief that he will be there lead me to go to the restaurant, my desire is unreasonable because the judgment that he is alive and will be at the restaurant is unreasonable. Hume thinks that the judgment, not the desire, is unreasonable.”(Ibid. 47)

It is not Hume’s idea I will comment on here but I agree with it.

It is the idea of the commentator that desiring something impossible in unreasonable. His grandfather example seems fine though. Here are two counter-examples:

It is impossible to achieve a perfect society and not unreasonable to desire.

It is impossible to remove all suffering in the world and not unreasonable to desire.2

One way to defend his view is that the case is some continuum such as the perfectness of society or the amount of suffering in the view, the claim does not hold.

1This one: http://www.elounge.com/pages/ProductDetails.aspx?ProductIndeks=1891812

2I’m using possible in the same collateral sense that he is, not any strict logical sense.

April 17, 2009

A journey into possibility land

Filed under: Uncategorized — Tags: , , , , , , — Emil O. W. Kirkegaard @ 03:27

Intro and types

I’ve been paying very close attention as of late to a special type of discourse: Namely, about what is possible and what is impossible. This study has led me to be very careful about my language use when speaking of such things because there are multiple types of possibilities: Logical, epistemic, physical, metaphysical, practical, technological etc. I have even created a modified version of modal logic that can handle multiple types of possibilities.i Logical possibility we ought to call L-possible, epistemic possibility we ought to call E-possible etc.

Modal fallacy

And before that I discovered the modal fallacy, which occurs when people confuse the scope of the possibility used. It may be about a single proposition or an entire implication.ii

Versions: Hypothetical and absolute

And then I discovered that even a single type (and pay close attention to the words used) of possibility is used in multiple ways. Let’s call these versions. There is the absolute version and then there is the hypothetical version. I did not invest these terms; Liebniz did.iii

Since I have already written of the aforementioned let me skip them and proceed on defining absolute and hypothetical modaly. Absolute modality is the one I’ve always been talking about and hypothetical is the one that others often talk about, which confuses matters a lot, and ultimately ends up wasting a lot of time.iv

Definitions

But that is not clear enough, so let me define the first. A proposition is absolutely necessary iff the negation is a contradiction (which has the form [p∧¬p]). A hypothetical impossibility is a proposition which if added to a set of propositions would result in a contradiction. This is the kind of impossibility that we’re talking about when making reductio arguments: “If something, then some contradiction, but that it impossible, so something can’t be true.” Yes, it can in the absolute sense. We ought not to confuse them.

In a later article I attacked a hypothetical impossibility for being an absolute impossibility.v

The value of the hypothetical impossibility term?

I ask now what value we have of this term. What need do we get covered by accepting this term into our collection of words? None but confusions as far as I can tell. We might as well stop called the hypothetical impossibility for an impossibility at all, and then while we’re at it, we should be very careful in our usage of the necessarily-operator when writing conditionals, so we don’t commit the modal fallacy. It doesn’t matter if we call it ‘must’, ‘cannot’ ‘has to be’ or something else. We must be very clear in our language about this matter, for if anything is certain (meant non-literally), it is that the plain English language is not at all good enough for handling modalities. Clarity is the way forward.

ihttp://deleet.dk/2009/02/09/flere-slags-muligheder-i-en-s%C3%A6tning/

iihttp://deleet.dk/2009/01/07/the-modal-fallacy/

iiiIt is discussed here: http://maverickphilosopher.powerblogs.com/posts/1159490720.shtml but originally from here: http://www.class.uidaho.edu/mickelsen/texts/Leibniz%20-%20Correspondence.htm

ivhttp://www.freeratio.org/showthread.php?t=264125

vhttp://deleet.dk/2009/04/07/does-a-sound-lpoe-establish-that-god-is-impossible/

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