Freethought & Rationalism Archive

pug846 · 02-09-2002, 05:33 PM

Edited because I missed something.

[ February 09, 2002: Message edited by: pug846 ]

Clutch · 02-09-2002, 07:42 PM

Quote:

CLUTCH: I think this is a case where understanding Franc's statement is made easier by knowing that he recommended a primer on Rand as a good introduction to philosophy. So, not real surprising that 'A=A' is written on stone tablets for him.

Quote:

FRANC28: Nice ad hominem, which only goes to prove my point that one who doesn't understand the axioms can't understand anything profoundly. Thank you.

Sorry, was the "stone tablets" ad hominem? I was just being a bit glib. Or was it just the Rand comment? Hmmm. I guess I was simply explaining to bd that your "baffling" view would make more sense if seen as coming from a disciple of Objectivism. If you're arguing that the insinuation that someone is an Objectivist amounts to an ad hominem slur...

Well..., okay. I guess you've convinced me.

Francois Tremblay · 02-09-2002, 09:07 PM

Here we go again. "a disciple of Objectivism", "your "baffling" view".

This is the first time I see someone on this board deviate from normal discussion. It's funny how, when someone is a known Objectivist, people stop discussing the arguments and attack the person... Do you have anything relevant to say about my post at all, or are you just showboating ?

[ February 09, 2002: Message edited by: Franc28 ]

Clutch · 02-10-2002, 04:17 AM

Franc,

Showboating.

(Well, except for that bit about having a point about the origin of the modern conception of proof in geometry, which you ignored in obsessing over my brief allusion to you.)

Anyhow, you already have some excellent feedback to your post from bd-kg. Why not answer some of those questions? My only addition to them would be this: Do you mean modal, intuitionistic, second-order, and quantum logic too? What about paraconsistent logic?

Really, the point of my crack about Objectivism was just that your post seemed to indicate someone who only had a hammer, and so had to treat everything like a nail -- and this is characteristic of Randians in my experience. If you're not committed to explaining all things philosophical (and political) by means of the impoverished conceptual vocabulary of that view, then my apologies. In that case, though, you should look at the varieties of logic out there, and especially look at them through the most general means of representing them, lattices. Then you'll see that A=A, the possession of a "1" element for such a lattice, in general fails to determine the other properties of the logic. Hence it is simply false that *any* logic, never mind logic in general, is a corollary of the Axiom of Identity.

Adrian Selby · 02-10-2002, 05:19 AM

Clutch, can you recommend some not too weighty reading regarding these last points on identity and logic. I've read some of Saul Kripke's work, but parts of it are flawed, I'm hoping you can recommend something a bit more plain english than degree level maths

Adrian

Clutch · 02-10-2002, 08:12 AM

Adrian, I don't know quite what you're asking for; and this is one of those topics where what one person finds nice and accessible is found unforgivably complex by the next person, and pointless and trivially easy by the next!

But I really like a new logic book called _Logical Options: An introduction to classical and alternative logics_ (Broadview 2001). It's formalized, of course, but the formalism is all introduced pretty carefully. The later chapters are excellent introductions to non-classical logic, and there's a section on lattices too.

If you were asking about something altogether different -- sorry! Let me know and I'll try again.

Francois Tremblay · 02-10-2002, 10:19 AM

And now with "Randian". I don't consider you as being seriously interested in discussion anymore either. I'm very lenient with insults because I'm used to it, but enough is enough. And he acts as if I'm gonna forget this and answer another poster, whom I consider facetious as well. Have fun arguing with yourself.

[ February 10, 2002: Message edited by: Franc28 ]

NialScorva · 02-10-2002, 08:39 PM

Anyway, to drag this thread back onto topic kicking and screaming...

I pondered the same thing not to long ago, sr. Consider what Hume was first and foremost: an empirical skeptic. As has been pointed out several times, logic itself is nothing more than symbol shuffling with a few definitions. It's consistent pretty much because contradictions are defined to be false. From a Humean point of view, we expect logic to be consistent with reality purely the habit of it being consistent with reality. I think from a Humean tradition, we can pretty much throw away the notion of anything being strictly proven. Hume, afterall, was the one who threw out the notion that we can know our own histories with assuredness.

What you have to consider then is which is the skeptically superior assumption, contradiction or non-contradiction. To doubt the consistency of logic, you have to posit a hypothetical theorem P such that P and ~P are both provable. To assume the consistency of logic, you merely don't have to accept such an unconfirm hypothesis. I would consider the latter the skeptically superior position, in that we do not need to assume a hypothetical contradiction.

mac_philo · 02-12-2002, 12:01 PM

Quote:

Originally posted by Clutch:
Adrian, I don't know quite what you're asking for; and this is one of those topics where what one person finds nice and accessible is found unforgivably complex by the next person, and pointless and trivially easy by the next!

But I really like a new logic book called _Logical Options: An introduction to classical and alternative logics_ (Broadview 2001). It's formalized, of course, but the formalism is all introduced pretty carefully. The later chapters are excellent introductions to non-classical logic, and there's a section on lattices too.

If you were asking about something altogether different -- sorry! Let me know and I'll try again.

If you are able to proclaim that Kripke is flawed, why are you searching for easy to read texts?

A good introductory text for sentential logic is Jeffrey's "Formal Logic:Its Scope and Limits." A nice introduction to modal logic is Hughes & Creswell's "Modal Logic."

A fanstastic, clear introduction to logic/computability is Epstein & Carnelli's "COMPUTABILITY:Computable Functions, Logic, and the Foundation of Mathematics."

NialScorva · 02-12-2002, 12:13 PM

Just for more logic fun:
<a href="http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm" target="_blank">Bibliography of non-standard logics</a>
<a href="http://www.cc.utah.edu/~nahaj/logic/structures/" target="_blank">John Halleck's Logic System Interrelationships</a>

Neither is a beginner's guide, but the latter shows many different logics and how they are related by adding, changing, and removing axioms.

02-09-2002, 05:33 PM	#11
pug846 Veteran Member Join Date: Mar 2001 Location: Somewhere Posts: 1,587	Edited because I missed something. [ February 09, 2002: Message edited by: pug846 ]</p>

02-09-2002, 09:07 PM	#13
Francois Tremblay Banned Join Date: Sep 2000 Location: Montreal, QC Canada Posts: 876	Here we go again. "a disciple of Objectivism", "your "baffling" view". This is the first time I see someone on this board deviate from normal discussion. It's funny how, when someone is a known Objectivist, people stop discussing the arguments and attack the person... Do you have anything relevant to say about my post at all, or are you just showboating ? [ February 09, 2002: Message edited by: Franc28 ]</p>

02-10-2002, 10:19 AM	#17
Francois Tremblay Banned Join Date: Sep 2000 Location: Montreal, QC Canada Posts: 876	And now with "Randian". I don't consider you as being seriously interested in discussion anymore either. I'm very lenient with insults because I'm used to it, but enough is enough. And he acts as if I'm gonna forget this and answer another poster, whom I consider facetious as well. Have fun arguing with yourself. [ February 10, 2002: Message edited by: Franc28 ]</p>

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02-10-2002, 04:17 AM	#14
Clutch Veteran Member Join Date: Oct 2001 Location: Canada Posts: 3,751	Franc, Showboating. (Well, except for that bit about having a point about the origin of the modern conception of proof in geometry, which you ignored in obsessing over my brief allusion to you.) Anyhow, you already have some excellent feedback to your post from bd-kg. Why not answer some of those questions? My only addition to them would be this: Do you mean modal, intuitionistic, second-order, and quantum logic too? What about paraconsistent logic? Really, the point of my crack about Objectivism was just that your post seemed to indicate someone who only had a hammer, and so had to treat everything like a nail -- and this is characteristic of Randians in my experience. If you're not committed to explaining all things philosophical (and political) by means of the impoverished conceptual vocabulary of that view, then my apologies. In that case, though, you should look at the varieties of logic out there, and especially look at them through the most general means of representing them, lattices. Then you'll see that A=A, the possession of a "1" element for such a lattice, in general fails to determine the other properties of the logic. Hence it is simply false that any logic, never mind logic in general, is a corollary of the Axiom of Identity.

02-10-2002, 05:19 AM	#15
Adrian Selby Senior Member Join Date: Jan 2002 Location: Farnham, UK Posts: 859	Clutch, can you recommend some not too weighty reading regarding these last points on identity and logic. I've read some of Saul Kripke's work, but parts of it are flawed, I'm hoping you can recommend something a bit more plain english than degree level maths Adrian

02-10-2002, 08:12 AM	#16
Clutch Veteran Member Join Date: Oct 2001 Location: Canada Posts: 3,751	Adrian, I don't know quite what you're asking for; and this is one of those topics where what one person finds nice and accessible is found unforgivably complex by the next person, and pointless and trivially easy by the next! But I really like a new logic book called _Logical Options: An introduction to classical and alternative logics_ (Broadview 2001). It's formalized, of course, but the formalism is all introduced pretty carefully. The later chapters are excellent introductions to non-classical logic, and there's a section on lattices too. If you were asking about something altogether different -- sorry! Let me know and I'll try again.

02-10-2002, 08:39 PM	#18
NialScorva Veteran Member Join Date: Jan 2001 Location: Median strip of DC beltway Posts: 1,888	Anyway, to drag this thread back onto topic kicking and screaming... I pondered the same thing not to long ago, sr. Consider what Hume was first and foremost: an empirical skeptic. As has been pointed out several times, logic itself is nothing more than symbol shuffling with a few definitions. It's consistent pretty much because contradictions are defined to be false. From a Humean point of view, we expect logic to be consistent with reality purely the habit of it being consistent with reality. I think from a Humean tradition, we can pretty much throw away the notion of anything being strictly proven. Hume, afterall, was the one who threw out the notion that we can know our own histories with assuredness. What you have to consider then is which is the skeptically superior assumption, contradiction or non-contradiction. To doubt the consistency of logic, you have to posit a hypothetical theorem P such that P and ~P are both provable. To assume the consistency of logic, you merely don't have to accept such an unconfirm hypothesis. I would consider the latter the skeptically superior position, in that we do not need to assume a hypothetical contradiction.

02-12-2002, 12:13 PM	#20
NialScorva Veteran Member Join Date: Jan 2001 Location: Median strip of DC beltway Posts: 1,888	Just for more logic fun: <a href="http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm" target="_blank">Bibliography of non-standard logics</a> <a href="http://www.cc.utah.edu/~nahaj/logic/structures/" target="_blank">John Halleck's Logic System Interrelationships</a> Neither is a beginner's guide, but the latter shows many different logics and how they are related by adding, changing, and removing axioms.

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