How do nominalists account for the laws of logic?

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jeeprs
 
Reply Mon 29 Mar, 2010 02:00 am
@spiltteeth,
you ought to look up Graham Priest and Dialetheism (that there are true contradictions.)

Also for what it is worth, I don't think it makes any sense to say that maths is 'subjective' or 'arbitrary'. Ugaibhu keeps saying that math is arbitrary and then produces these incomprehensible (to me anyway) arguments in support of it. But I think there are some`very heavy hitting scientists, mathematicians and philosophers who are mathematical and even platonist realists.
 
ughaibu
 
Reply Mon 29 Mar, 2010 07:29 am
@spiltteeth,
spiltteeth;145460 wrote:
to repeat my original point, Logical absolutes are conceptual by nature, but I don't see how they are dependent on space, time, physical properties, or human nature etc
But logics are designed by human beings, and dont have any "absolutes".
 
spiltteeth
 
Reply Mon 29 Mar, 2010 02:24 pm
@Deckard,
Deckard;145471 wrote:
It is important to remember that Descartes meditation is a project of radical skepticism. After establishing certainty of his own existence Descartes then finds his way to the certainty of God's existence and then the truth of laws like A and not A cannot both be true. Kant took a different second step and did not feel the need to establish the existence of God but rather he bracketed* off all experience as phenomenal and conditioned by the subjective mind. For Kant, the law "A and not A cannot both be true" is something the subjective mind brings with it, something that is impossible to escape and yet nevertheless phenomenal. So for Kant it is a difference between saying "it is impossible to think otherwise" and "it is absolutely true".

"Nominalism is true" and "A and not A cannot both be true" are both true statements but only insofar and only because this is the way our subjective minds structure and condition reality. They can never be true in the universal and absolute sense without this phenomenological caveat. For Kant, these statements are not necessarily true (though it may be) outside of phenomenal experience.

I'm not sure why Peirce said that Kant's philosophy would have been more straightforward had he been a realist.

As I am writing this I am wondering that there must be a profound connection between the subjective/objective and nominalism/realism. Starting from the subjective truth of the cogito one has the opportunity to be a nominalist. Starting from A and not A cannot both be true one can only be a realist. It is almost as if the one reduces to the other. Again it is a matter of where one begins to philosophize. Descartes radical skepticism or some other alternative such as Plato's or Aristotle's.


*The term "bracketing" I think traces back to Husserl so I am a little worried that I am conflating Kant with Husserl but the term seems to fit.



That's very useful - thanks.

Also, I like yr sig - perhaps if I end every statment I make with "Thus spoke Spiltteeth" I'll start getting more respect at work! :bigsmile:

The thing is Decarte presupposes the laws of logic as true because he uses them to prove he exists - "I think therefor I am"

If the laws of logic weren't true he couldn't make that statement.

The thing is, IF the laws of logic are just subjective and from the mind etc then they are not absolute, but just a subjective preference for thinking.

First, to prove that they are subjective etc you need to USE the laws of logic.

And if they are not universal and unchanging then 4,000 yrs ago, or in the future, or in another culture, one could logically say A and -A are both true.

So the example I used : If I say the statement "2+2 =4 and 2+2 does not =4" is contradictory and therefore not true, then a person could say, "well, thats just using subjective logic, and I prefer to use a different kind of logic that says it sometimes is true, its not absolute.

Unless the laws are universal and unchanging, then, being subjective, nothing can ever be said to be absolutely true. Someone can say, in my logic 2+2=5 sometimes.

---------- Post added 03-29-2010 at 04:27 PM ----------

jeeprs;145475 wrote:
you ought to look up Graham Priest and Dialetheism (that there are true contradictions.)

Also for what it is worth, I don't think it makes any sense to say that maths is 'subjective' or 'arbitrary'. Ugaibhu keeps saying that math is arbitrary and then produces these incomprehensible (to me anyway) arguments in support of it. But I think there are some`very heavy hitting scientists, mathematicians and philosophers who are mathematical and even platonist realists.


Oh thanks, I did look it up - very interesting!

I agree, if there are not true contradictions nothing can ever be absolutely true including the statement "nothing can be absolutely true" !

I agree with you that saying logic is subjective results in a bit of silliness:

To say its subjective is to say one day 2+2 may = 6!
 
Deckard
 
Reply Mon 29 Mar, 2010 03:14 pm
@spiltteeth,
spiltteeth;145745 wrote:
That's very useful - thanks.

Also, I like yr sig - perhaps if I end every statment I make with "Thus spoke Spiltteeth" I'll start getting more respect at work! :bigsmile:

The thing is Decarte presupposes the laws of logic as true because he uses them to prove he exists - "I think therefor I am"

If the laws of logic weren't true he couldn't make that statement.

The thing is, IF the laws of logic are just subjective and from the mind etc then they are not absolute, but just a subjective preference for thinking.

First, to prove that they are subjective etc you need to USE the laws of logic.


Of course you have a point. Here's what Stanford Encyclopedia of Philosophy and Descartes say about it.

Quote:
...much of the debate over whether the cogito involves inference, or is instead a simple intuition (roughly, self-evident), is preempted by three observations. One observation concerns the absence of an express 'ergo' ('therefore') in the Second Meditation account. It seems a mistake to emphasize this absence, as if suggesting that Descartes denies any role for inference. For the Second Meditation passage is the one place (of his various published treatments ) where Descartes explicitly details a line of inferential reflection leading up to the conclusion that I am, I exist. His other treatments merely say the 'therefore'; the Meditations treatment unpacks it. A second observation is that it seems a mistake to assume that the cogito must either involve inference, or intuition, but not both. There is no inconsistency in the view that the meditator comes to appreciate the persuasive force of the cogito by means of inferential reflection, while also holding that his eventual conviction is not grounded in inference. A third observation is that what one intuits might well include an inference: it is widely held among philosophers today that modus ponens is self-evident, and yet it contains an inference. There is no inconsistency in claiming a self-evident grasp of a proposition with inferential structure-a fact applicable to the cogito. As Descartes writes:[INDENT] When someone says "I am thinking, therefore I am, or I exist," he does not deduce existence from thought by means of a syllogism, but recognizes it as something self-evident by a simple intuition of the mind. (Replies 2, AT 7:140) [/INDENT]
I suppose that given enough intuitions with inferential structure and noticing the consistent pattern one might arrive at "A and not A cannot both be true" through inductive reasoning :bigsmile:.

Descartes' Epistemology (Stanford Encyclopedia of Philosophy)
 
HexHammer
 
Reply Thu 15 Apr, 2010 12:53 pm
@spiltteeth,
spiltteeth;145038 wrote:
How do nominalists account for the laws of logic?

I'm no expert, but it seems to me the laws of logic are universal; and they are certainly not material.
So if you don't believe in abstract objects how do you account for them?
Logic are often flayed when the premesis of solving a problem with logic are calculating with uncertain factors, ignorence, naivity and stupidity ..etc will obscure the uncertainty.
 
Reconstructo
 
Reply Thu 15 Apr, 2010 07:10 pm
@spiltteeth,
spiltteeth;145057 wrote:
Well, like I say, I'm no expert but Logical absolutes are conceptual by nature, but I don't see how they are dependent on space, time, physical properties, or human nature etc
They are not the product of the physical universe (space, time, matter), because if the physical universe were to disappear, logical absolutes would still be true.


You make a good point. I would add that space, time, substance, nature, etc., are all made out of concept. Concept and something else. We can use the word qualia, but qualia is a concept. What ever exists outside of concept we can experience but not think, as thinking is concept.

Yes, ask the nominalist where in nature nominalism hides. Have them point to it. And have them point to themselves. Perhaps we should view the issue on a spectrum, one that runs from a mystical belief in a reality beyond the senses to the non-mystical recognition that our sense experience is structured by concept, which is obviously detachable from sense experience.

Can logic be true w/o man? It's arguable not only that logic and man are inseparable but also that man and the universe or man and his environment are inseparable. To conceive of them in isolation is not accomplished in the isolation conceived. It seems to me that it is always and only individual human beings immersed in history and qualia who can conceptualize themselves as if independent from both. To what degree are our best philosophical abstraction simple negations, provided by a prefix? In-finite. Ab-solute. Im-material. I also suggest that concepts like the universe and matter and the self, etc., are all just that, concepts. And that if we compare the structure of reality and the structure of our concepts we will find they are the same..

Excuse the long response but it's a great issue. I like when philosophy wonders away from ethics sometimes to deal with issues like this. Smile

---------- Post added 04-15-2010 at 08:14 PM ----------

ughaibu;145555 wrote:
But logics are designed by human beings, and dont have any "absolutes".


You have a good point. Perhaps he is referring to the intuitions (for lack of a better word) that inspire the formalization of logic? Indeed, if such intuitions are absent, then what can such formal logics mean? I see formal logic and math as related in this. To understand P, for instance, as a sort of X. Can we avoid a foundation of the "self-evident"?

I think it's a great subject and I look forward to your thoughts on the matter. Smile
 
jeeprs
 
Reply Thu 15 Apr, 2010 07:22 pm
@Reconstructo,
Reconstructo;152549 wrote:
I would add that space, time, substance, nature, etc., are all made out of concept


'Made out of concept' is a most peculiar expression, I think. 'Given form by the manner in which they are perceived'...now that is a line that I have been tinkering with the last few months....It is just that when you phrase it like this, it seriously sounds like 'concept' is this massive all-purpose plastic out of which things are actually formed...

Actually I have been reading up on Descartes, Newton and Galileo again. It was the latter who said the book of nature was written in mathematics. This is such a profound observation although nowadays I am sure many people take it for granted. I had also not appreciated the manner in which Decartes had set the stage for this understanding by combining algebra and geometry to devise the first notion of mathematical functions (cartesian co-ordinates, and the like). I suppose, moving down the track a little, these in turn give rise to the possibility of algorithms. But to take a step back, the fact that these mathematical insights do have such universal applicability, and reveal things about the workings of nature that could never be ascertained by mere observation, is still amazing.
 
Reconstructo
 
Reply Thu 15 Apr, 2010 07:29 pm
@jeeprs,
jeeprs;152556 wrote:
'Made out of concept' is a most peculiar expression, I think. 'Given form by the manner in which they are perceived'...now that is a line that I have been tinkering with the last few months....It is just that when you phrase it like this, it seriously sounds like 'concept' is this massive all-purpose plastic out of which things are actually formed...


I agree. While I do go on to enlarge on this (concept and qualia), I'm not always careful enough. I should have put those words in quotes. how about this? Experience is the collision of concept and qualia. And language is concept organizing qualia, as well as its own concepts. And because concept can self-organize, philosophy is possible. Abstraction is the negation of the accidental, which is simultaneously the revelation of the essence. I thank you for calling me to account for being unclear. Smile (In my little triangle, the minus sign is concept-in-itself, inferred but never experienced. And the infinity is qualia not organized by concept, inferred (conceptually) but never experienced, or at least unspeakable/thinkable. Thanks for engaging me on the issue. Smile

---------- Post added 04-15-2010 at 08:34 PM ----------

jeeprs;152556 wrote:

Actually I have been reading up on Descartes, Newton and Galileo again. It was the latter who said the book of nature was written in mathematics. This is such a profound observation although nowadays I am sure many people take it for granted.


Kojeve's teacher, , made a big deal out of this, and I entirely agree that it's profound. However, as I am discovering, there are some strangenesses involved. Consider the numbers pi and e, both of which show up everywhere in our math applied to nature. Well, both are transcendental, cannot be represented in closed form, but only by means of an infinite series. And both are related by that strange and beautiful equation, the one in my profile picture. Our numbers don't mesh with nature perfectly? Or is it that they don't mesh with themselves? Also, I have been studying calc lately, and the limit concept is a sort of dodge of Zeno's paradox, which I still find relevant. Of course none of this can take away from Galileo. These computers we use are proof. And yet computer programs are based on discrete math. Logic gates. Ones and zeros. Closed forms.

---------- Post added 04-15-2010 at 08:37 PM ----------

jeeprs;152556 wrote:
. I suppose, moving down the track a little, these in turn give rise to the possibility of algorithms. But to take a step back, the fact that these mathematical insights do have such universal applicability, and reveal things about the workings of nature that could never be ascertained by mere observation, is still amazing.


Ah yes, and thus my obsession. Math, questionable foundations or not, offers ideal precise form. An algorithm is a machine made out of thought. And these same thought machines, which lives like spirits in our hardware, are obviously going to be a big part of the future of mankind, from here on. (I'm going back to my left-brain roots, after a long and rewarding right-brain detour...)
 
jeeprs
 
Reply Thu 15 Apr, 2010 07:40 pm
@spiltteeth,
It's interesting writing and I guess suited to this medium (which is after all kind of a universal interactive whiteboard). I think you're in the process of defining your own approach to many of the big questions, put it that way, and I am OK with it, but I can see that many people would take it completely the wrong way. (AND I have a rule never to engage in a conversation that involves the use of 'qualia'...). But my instinct is that you're running up against the edge of what can be meaningfully spoken or expressed discursively, as it were.

---------- Post added 04-16-2010 at 11:44 AM ----------

I don't know if you have read any abstracts of Roger Penrose's The Emporer's New Mind, yet another monster volume of densely packed arguments that i will never have the remotest chance of reading or absorbing...
Quote:
Penrose presents the argument that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer. Penrose hypothesizes that quantum mechanics plays an essential role in the understanding of human consciousness. The collapse of the quantum wavefunction is seen as playing an important role in brain function.
...not enough time in the world for all this stuff....
 
Reconstructo
 
Reply Thu 15 Apr, 2010 09:32 pm
@jeeprs,
jeeprs;152569 wrote:
It's interesting writing and I guess suited to this medium (which is after all kind of a universal interactive whiteboard). I think you're in the process of defining your own approach to many of the big questions, put it that way, and I am OK with it, but I can see that many people would take it completely the wrong way.


Perhaps a better expression would be RE-fining. As, believe it or not, the notion is quite clear to me. In my opinion it is logical, exciting, and perhaps insignificant for practical purposes. I must say that I don't yet feel completely understood on this by anyone, although I could be wrong.

---------- Post added 04-15-2010 at 10:34 PM ----------

jeeprs;152569 wrote:
(AND I have a rule never to engage in a conversation that involves the use of 'qualia'...).


Well, I suppose I could use "sensation"...but "qualia" is a nice complement to quantity, and I feel that number is just word washed of its quality, leaving its discrete quantifying core. Quantum =discrete, right? Logos/discourse is made of words that have, in my mind, a discrete core. The de-fin-ition of a word...because words are essentially finite. Except that they refer to feeling and sensation, and how does one communicate redness? Except by pointing? Or how about "justice"? Numbers are washed off such imprecision. For me, the TLP shows the difficult relationship between the two. We all agree that P = P, but as soon as we leave this realm of perfect abstraction, we don't agree on much, not even on the meaning of a word like "reality."
 
jeeprs
 
Reply Thu 15 Apr, 2010 09:37 pm
@spiltteeth,
No, I think you're pretty right, on the first point, although I think i see where you're going with it.

Needs to be road tested, though.

The only reason I hate 'qualia' is because it crops up in so many conversations with uber materialist Dennett.
 
Reconstructo
 
Reply Thu 15 Apr, 2010 09:39 pm
@jeeprs,
jeeprs;152569 wrote:

I don't know if you have read any abstracts of Roger Penrose's The Emporer's New Mind, yet another monster volume of densely packed arguments that i will never have the remotest chance of reading or absorbing......not enough time in the world for all this stuff....


It sounds good. In my mind, it's all still within the range of concept. We relate quantum mechanical concepts to concepts of the brain. Abstractions wired to abstractions. And of course I love this sort of thing. And yes, not enough time. The human lifespan needs an adjustment.

---------- Post added 04-15-2010 at 10:47 PM ----------

jeeprs;152615 wrote:
No, I think you're pretty right, on the first point, although I think i see where you're going with it.

Needs to be road tested, though.


Ah, but that's just it. The dichotomies it dissolves are the ones we live by. I don't expect it to survive a road test. Here's a parallel. It's impossible to construct a perfect circle in the real world, as pi cannot be expressed in a closed form. Pi is something like a fractal. You can zoom in all you like. There's always more. It's quite strange really, the very idea of a perfect circle. Transcendental. We work with approximations. Life is messy.

---------- Post added 04-15-2010 at 10:48 PM ----------

jeeprs;152615 wrote:

The only reason I hate 'qualia' is because it crops up in so many conversations with uber materialist Dennett.


Ah, well that makes sense. Perhaps my theory walks the line between two camps, a questionable attempt at synthesis...

---------- Post added 04-15-2010 at 10:50 PM ----------

Marx accused Hegel of being one more theology, and he was, in a way, quite right. Perhaps Hegel is just a poet, and Marx wanted action.
 
jeeprs
 
Reply Thu 15 Apr, 2010 10:14 pm
@spiltteeth,
A meta-comment. You are smart enough to read Hegel via Kojeve and extract a lot of meaning from it. But you have to realize that Hegel almost singlehandedly brought The Grand Tradition to a complete halt through his immense complexities. I was reflecting the other day that after Kant, Hegel and Schopenhauer, brilliant though they were, there was a tremendous reaction against that kind of ornate intellectualism and philosophical idealism generally. The rejection of all this was one of the things which drove the movement to science and secularism.
 
Reconstructo
 
Reply Thu 15 Apr, 2010 10:38 pm
@jeeprs,
jeeprs;152634 wrote:
A meta-comment. You are smart enough to read Hegel via Kojeve and extract a lot of meaning from it. But you have to realize that Hegel almost singlehandedly brought The Grand Tradition to a complete halt through his immense complexities. I was reflecting the other day that after Kant, Hegel and Schopenhauer, brilliant though they were, there was a tremendous reaction against that kind of ornate intellectualism and philosophical idealism generally. The rejection of all this was one of the things which drove the movement to science and secularism.


I agree. And like I say, Kojeve has the clarity of a Witt, and he was my bridge. And from there I toyed around with my influences. I should stress that I only drop Hegel's name to honor my influences. It would probably be easier for me to present such thoughts w/o dragging in his bad reputation. But I would feel like a cheat.
Spengler writes about this shift. In his eyes, a culture has a life span like any other organism. Yes, H is complex, but perhaps because he is indeed at the end of the grand tradition, and is therefore, in his own jargon, for dialectical reasons, going to be the most complex pile of "determinate negations." Error becomes closer to mirroring being by just such an accumulation of qualifications. The Begriff (system of concepts) must penetrate itself, ingest its own substance (negate/synthesize the syntheses it is made of). In other words, a man has to bite off the entire tradition, and sort it out. Spengler likes to draw parallels to Greece, Rome, China. Let's look at the Greeks. Movements like Stoicism, Skepticism, Epicureanism. And these follow Pythagoras, Parmenides, Plato, who were apparently concerned with something grander. Plato griped about the sophists, of course. We see a movement from grand abstractions to lifestyle, to the equivalent of existentialism.

Another point. Where could metaphysics go after Hegel? Do we not see in painting, drama, mathematics, poetry a certain exhaustion of possibilities? Classical music exhausted its tonal possibilities, according to some views, and therefore the invention of twelve tone, the invasion of Cage and finally process music, minimalism. Kundera calls this the midnight hour. After the midnight hour, there is only essentially repetition.

I'm not saying the reaction to ornate intellectualism was wrong. Pragmatism is just Hegel digging ditches. It's the same dialectical theory of truth, but with the poetic resolution ignored as moonshine.

Smile
 
 

 
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