*I*referred to

*him*as…

*a logician*. (Gasp!)

Specifically, I noted that

*that’s how he referred to himself*on his site.

I know, I

*know*.

*Nasty*stuff. But hey, I was in a bad mood that week – what with, you know, people like this very doofus calling me an “apologist for murder” and what not.

Still, the poor,

*poor*man. Apparently I hurt his feelings. You see, by “logician” he didn’t mean to portray himself as some especially penetrating thinker or anything. Just a guy who studies logic, that’s all. Or something like that. Anyway, he’s written a 1,254 word post explaining himself, so do read it, and disabuse yourself of the

*terrible*calumny I directed against him.

Because, you know,

*he*would never,

*never*misrepresent someone

*else’s*words. Nor would he ever ridicule someone else who defended himself against a libelous misrepresentation.

And Brian, I know you like to ridicule people for offering “lengthy” self-defenses – when you’re not ridiculing them for giving “non-replies,” that is. (The good old “Heads I win, tails you lose” strategy – clever one, Bri!) But please lay off this guy, huh? He’s

*very*sensitive…

UPDATE: Bored with the whole Leiter/"apologist for murder" thing? Me too. But see here for an epilogue, courtesy of Big Bad Brian himself, if you want one last chuckle (or groan).

## 15 comments:

It's useless, it's all diffuse and dissolute gamesmanship, one-upmanship, and sniffing, preemptive expressions of triumphalism and bravado. There isn't even a desire evidenced to seek basic suppositional/definitional clarity, much less a more sincere desire when it comes to the real problems that would need to be faced.

He's also enabled the censor/moderating option and has barred a comment which very simply asked if he is in fact presuming to prescribe all denotative and connotative senses of the term "logician." On one level, fine, but he's feigning sincerity, astonishment and a desire for genuine probative inquiry throughout.

Yup. "Doctor-killing enthusiast" is a nice touch too. Lying with style, minus the style.

Anyway, if there were ever any doubt about Anscombe's dictum re: the pointlessness of arguing with corrupt minds, this guy and his ilk provide all the empirical evidence one needs.

Professor Feser, I have a question about a common example mentioned by you (and many other philosophers) about 2+2=4 being a necessary truth (truth in any possible world) and, hence, impossible to conceive it in a different way.

However, I've read at least one philosopher to argue that that's not correct because, for example, in special aritmethics the rules could be different.

For example, in the aritmethic of a clock, 12+1=1 (because, if at 12 am you add 1 hour, you get 1 pm). Also, in the countries that use the 24 hours in the clock, 24+1=1 (not = 25)

In other words, 12+1=13 (or 24+1= 25) is not a necessary truth; it's only valid if we take for granted the conventional rules of normal aritmethics, but it doesn't apply to special aritmhetics and, hence, it is not a necessary truth.

Do you think such argument/objection is good?

Sorry, in the first example, if to 12 am you add 1 hour, you get 1 AM (not pm).

An obvious mistake of mine.

Also, if to 11 pm you add 2 hours, you get 1 AM (so, 11+2=1)

The point is that we can think in many possibilities where conventional aritmethics don't apply, and it argues against it being a necessary truth.

Hi Jime,

I could be off on this, but....

even in those cases no one is denying the content or value of a particular number. 1 is still 1 and 12 is still 12. The rules are still the same too: 1 added to 12 still only takes the result one value further (1am) opposed to 2am or 3am.

We could have no independent knowledge of what a clock was for but if we understood 2+2=4; if we were to look at a clock at 11pm and add 2 to it... by simply moving the hand of the clock based off of what we know 2 to be we would still come to the conclusion of 1am.

Jime: Arithmetic of the clock is basically a sort of cyclic base-12 (or base-24) arithmetic. There are many examples of base systems other than 10. The most famous are probably binary (1+1=10) and hexadecimal (f+1=10), used in computer systems. None of this changes the fact that 2+2=4 is true in the base-10 system. (or that the equivalent calculation is true in other base systems) It's simply that the numbers are represented by different notations. This is more like a language issue, i.e. the same idea (2+2=4) represented in different languages, rather than the idea itself being different.

Thanks Ricky and Chang, for your helpful comments.

Bear in min that nobody is arguing that 2+2=4 is false.

The question is: is 2+2=4 a NECESSARY truth (truth in every possible world)?

For example, you can't think in a circular triangle (it's necessarily false, such thing is impossible in every world. Even God couldn't make it)

But, if as Cheng argue "

None of this changes the fact that 2+2=4 is true in the base-10 system", then the truth is relative to a system (base-10 system) not an absolute truth in every possible world (in worlds of a different bases)In other words, what I'm asking is if 2+2=4 is false in at least some world; and therefore, if it is not a necessary truth ein every possible world.

The example of 2+2=4 seems to me to be disanalogous to the examples of square circles and other logically impossible propositions.

This have implications for philosophy of religion, because the ommipotency of God doesn't apply to logically possible propositions; but if we can conceive a world where 2+2=4 is false, then God also can.

This has implications too for discussions on conceptualism, nominalism and realism, as discussed by professor Feser in TLS.

Jime: I think the confusion here is the idea of 2+2=4 versus how it is expressed, e.g. the base notation it is written with. It doesn't matter if you write 2+2=4 (base-10) or if you write 10+10=100 (base-2). Or for that matter if you write II + II = IV.* In all these cases the idea expressed is the same. The abstract idea of 2+2=4 is unchanging, regardless of how we represent it using material symbolisms.

*In this case for example, you're not adding things and getting a medical device. :) You're still adding the same numbers, just written differently.

I hope I'm making myself clear here.

Chen, I've considered and thought about your point before. And it's a possible answer (and fact, the fist one that came to my mind).

But I'd suggest that it is not a mere problem of expression.

As english is not my first language, I'll try to express myself in the better way I can.

Take the following example:

In conventional aritmethics, when you add 1 to 12, you get 13. The abstract idea is 13, not other number.

But in the artitmethics of a clock, when you add 1 to 12, you get 1, not 13. (Is 1 "the same" than 13? Is the same concept? Is is onlt a difference of the mode of expression? Obviously not, because the whole idea that you make in your mind is different)

Is the above only a difference on expressions? Or, instead, it involves difference in the ABSTRACT CONCEPTS involved?

I think the difference is in the concepts, not in the mode of expression alone.

Again, 2+2=4 is unchanged IF we accept and assume that conventional aritmethics is the only one existing.

But in special aritmethics (e.g of a clock), 12+4=4! (not 16)

It is not only a difference of expression, the whole numerical concept has changed in that particular context.

Note also the following: Why the base-10 has so absolute status as to make 2+2=4 a necessary truth, when there are exists other systems (like base-2) where it is not truth?

It is not only a mode of expression, the whole abstract numerical concept change if you change the aritmethical system.

In his book on philosophy of mind, professor Feser explained the principle of conceivability: if you can consistently and logically think in something, that something is metaphysically possible (possible in some world).

It could be not possible in the actual known world, but it's possible in another world.

Therefore, if (by whatever means) I can consistently think that 12+4=4 (and not 16), then the conventional aritmethics (2+2=4) is not a necessary truth (= it's metaphysically possible to conceive otherwise).

Therefore, 2+2=4 is not a necessary truth (it's only truth in conventional/general aritmethics)

I'm open to other interpretations of this problem (and this is why I asked professor Feser about it), and Chen's opinion is important too (as I said, I also considered it before), but it seems to me, for the moment, to be unconvincing.

Thanks for all of your helpful comments.

Just food for the thought.

A bit OT, for Ben Burgis and Ryan Lake,

Your antics don't so much as rise to a level that warrants pity. To warrant pity something of substance needs to be on evidence. In this case and as applied to the subject at hand, something reflective of and more receptive to probative depth.

If you want to be taken more seriously, especially so when it comes to an intractable and Gordian Knot subject such as abortion, and attendant subjects, then raise the level of your arguments above that of question begging sneers and arrogations based upon moral and other qualitative incomprehensions. The Gordian Knot quality of pivotal aspects of the debate/disagreements are themselves indicators that a more sober and a far more fertile and receptive approach is needed. By contrast, you both come across as a couple of slope-shouldered light weights, heavily reliant upon self-regard. In the respective links, Ryan's arguments are especially obtuse, diffuse and uncomprehending, but the same for Ben's once the gloss is seen for what it is. Sad, perhaps, but too bloodless and self-infused to be worthy of so much as pity.

Others, both in agreement and disagreement, may kiss your Marvel Comics ring and take you more seriously. Their choice.

Jime: Actually, in "clock arithmetic," when you say 12+1=1, the second 1 *is* 13. It's the number that comes after 12 and is 1 greater. In fact, in 24-hr clocks that is 1300 hours. The only thing is that the clock wraps around at 12 or 24.

Now I might have sowed the confusion by the diversion into different base notations, (sorry about that) but clock arithmetic is totally explainable in terms of arithmetic. A good summary is here:

http://en.wikipedia.org/wiki/Modular_arithmetic

In short, there is no new math needed.

Chen, I think you haven't understood my point, maybe I haven't explained myself well.

I'll try again.

In clock aritmethics (of clocks that works with 12 hours, not with 24), 12+1= 1 (not 13, because 13 doesn't exist in such clocks!) (See my citation below of the link of wikipedia that you provide)

But let's to suppose that we addopt the 24 hours clock. In such case, what would occur in 24-hr clocks when you add 1 to 24? Do you get 25? No, you get 1.

If in such clocks 24+1= 25 were true (and it is not) and given that time is continous, then you'll never get any hour below 24 anymore, since every hour will sum after the 24 (e.g 25, 26, 27, 283920202382020 hours, ad infinitum.).

The simple fact that everyday we have a 2 am or a 5 pm, proves that the addition of new hours don't add to 24 in the way of conventional aritmethics.

This is the point. In fact, this point is made clear in the wikipedia link you provided:

"

Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; there is no "15 o'clock"Look the "usual addition" doesn't work in clock aritmethics (what is precisely what I'm arguing for!)

Likewise, usual addition proves that 4= 2+2 (I'm reversing the terms here for higher understading of my example); but in clock aritmethics 4 = 12+4!

In short, there is no new math needed.But I haven't argued for a new aritmethic. My point is not if maths is new or old, of if there are new math systems.

My point is purely philosophical.

My original question is if 2+2= 4 is NECESSARY truth; in other words, if such proposition is truth in every possible world.

In other words: is it possible to conceive a world (e.g. some aritmethical system) where 2+2=4 is false?

If it's so, what implciations (according to the principle of conceivability) have to the metaphysical status of the proposition that 2+2=4?

Please, don't misunderstand my point. My question is philosophical, I'm thinking hard about this question, since I have interest in realism, conceptualism and nominalism, and what examples and counterexamples count for each theses.

It's philosophical thinking is all about, doesn't it?

For the record, the idea that 2+2= 4 is false in

someworld (and therefore, not a necessary truth), doesn't argue against the existence of God.It only would prove that we can't use that example anymore as an example of a necessary truth. Only that.

The case for God existence doesn't depend or rest on maths.

Jime, I wasn't even thinking about God at all with this discussion. My interest here is in arithmetic systems and the abstract ideas behind them.

A clock system really doesn't change any of the rules of arithmetic systems. The only thing that happens is the wrap-around at 12, (or 24) which is a notation needed for convenience, since days are cyclic. So like I said before, no new arithmetic system is needed. (what I meant to say by "no new math") This is only a matter of notation, and not of different philosophical worlds.

2 + 2 = 4 is not a necessary truth, it is a formal truth, because all the objects involved are formal contructs.

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