Proto-Logic

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Reconstructo
 
Reply Mon 26 Apr, 2010 12:23 am
@jack phil,
jack;156231 wrote:
Isn't -1 inverted -1?


Doubled-inverted -1, I would say. That's the strange thing about negative one. It's functions in multiplication as a sort of NOT gate, and yet is still a quantity in regards to addition and subtraction. We have the 0 for identity in addition and the one for identity in multiplication.

Imaginary numbers are quite a natural next step after negative numbers, don't you think? Gauss said something like positives were normal, negatives were inverse, and imaginaries were lateral. And we have the negative imaginaries just as we have the negative reals. So the imaginaries are just a perpendicular version of the reals. And 0 is the crux of it all.

It seems these quaternions have been used to model four-dimensional space. The story of their creation is a good read. Hamilton struggled for awhile with it, then suddenly got the flash, carved it into the nearest wood, and dedicated the rest of his life to explaining said quaternions. Also wrote a book calling algebra the science of time.

But I ramble....Smile
 
attano
 
Reply Thu 29 Apr, 2010 04:33 pm
@Reconstructo,
Reconstructo;153804 wrote:
I'm more than a little interested in the structure of human thought. I feel that the TLP is concerned with what I call "proto-logic." An equally good term might be "transcendental logic."

Two little points I'll kick off with. Consider the word "what" (as an instance among other words of this type). "What now?" "What" seems to function like a variable, like an x. This seems related to the existential quantifier in formal logic and the variable in math. Note: I see "proto-logic" as foundational to both language, formal logic, mathematics, algorithms...

Another word is "not." The thought of negation. It seems built in. "He's not here" is the negation of "he's here." A sort of minus sign on a statement. Of course we have this in formal logic, and we have the negative equals sign in math.

For me, this is the core of philosophy, this searching after the proto-logic.
Thoughts?


In a word, NO.
IMO it doesnot work like that.


Of course it is always possible to associate words to logical operators, but this is the outcome of selection/definition out of their possible meanings.
This operation is not finding the core logic that makes our language work. It is a(-n arbitrary) refinement that by limiting the possible meaning of a word, ultimately makes it some other word, a symbol, an operator. To rephrase that, inducing logic in natural language it's an operation ex-post, logic is not the root of language.


This indeed leaves open the question of what is language and what is logic and in which way they relate to each other. (Btw I believe that beforehand some decision is required about the existence of a unique language or if indeed several languages coexist in our words and thoughts (and symbols) - the latter is closer to my hypothesis).
My position is that logic, at least a big part of it, is a cultural byproduct. It represents the need to truthfully process truth, la femme fatale of our Western thought. But does natural language(-s) do really need to process truths so often? Is really language about predicating truth?
Ultimately, logic is religion.


The repeated attempts to try to find deep logical strutures in language are doomed to failure in my hypothesis . They move from the wrong assumption -a white lie, indeed - that language is a lot more crystallised and uniform than it actually is. This is not the case. We might be under this false impression because we focus on an abstract representation of Indoeuropean languages and because the offspring of Indo-europeans has been culturally dominant world-wide since the XVII century (and also for the time before we cannot get rid of a euro-centric perspective). But inferring that any supposed deep structure of Indoeuropean languages (assuming there is such a thing) is the inner working of all possible languages is a leap forward that I don't think it's correct.
 
Reconstructo
 
Reply Thu 29 Apr, 2010 06:33 pm
@attano,
attano;158097 wrote:
In a word, NO.
IMO it doesnot work like that.


Of course it is always possible to associate words to logical operators, but this is the outcome of selection/definition out of their possible meanings.
This operation is not finding the core logic that makes our language work. It is a(-n arbitrary) refinement that by limiting the possible meaning of a word, ultimately makes it some other word, a symbol, an operator. To rephrase that, inducing logic in natural language it's an operation ex-post, logic is not the root of language.


This indeed leaves open the question of what is language and what is logic and in which way they relate to each other. (Btw I believe that beforehand some decision is required about the existence of a unique language or if indeed several languages coexist in our words and thoughts (and symbols) - the latter is closer to my hypothesis).
My position is that logic, at least a big part of it, is a cultural byproduct. It represents the need to truthfully process truth, la femme fatale of our Western thought. But does natural language(-s) do really need to process truths so often? Is really language about predicating truth?
Ultimately, logic is religion.


The repeated attempts to try to find deep logical strutures in language are doomed to failure in my hypothesis . They move from the wrong assumption -a white lie, indeed - that language is a lot more crystallised and uniform than it actually is. This is not the case. We might be under this false impression because we focus on an abstract representation of Indoeuropean languages and because the offspring of Indo-europeans has been culturally dominant world-wide since the XVII century (and also for the time before we cannot get rid of a euro-centric perspective). But inferring that any supposed deep structure of Indoeuropean languages (assuming there is such a thing) is the inner working of all possible languages is a leap forward that I don't think it's correct.



Appreciate your honesty. I still argue for the transcendental. Indeed, if we deny the transcendental, how can we argue the usual happy theme of human solidarity? Also, I'm not one for reduced ambitions.

Still, I don't expect to successfully codify some official proto-logic. It's more an informal quest to root out the structure of thought. Formal logic is like mathematics an invention, and language is presumably prior to both. I suggest that both are built on a few self-evident notions.

Kant was engaged on such a quest, and this is his greatness. If we don't seek the universal, what are we seeking? And if we argue against the possibility of such universal goals, how can we do so if not from the same universal logic we intend to discredit? Sometimes the medium says more than the message.
 
kennethamy
 
Reply Thu 29 Apr, 2010 06:38 pm
@Reconstructo,
Reconstructo;158134 wrote:
. I still argue for the transcendental.


Well, that's must be the refutation. A argues that p is true, but since I argue that p is false, that proves that what A argued is false.
 
Reconstructo
 
Reply Thu 29 Apr, 2010 07:30 pm
@Reconstructo,
I don't think I'm well understood on this, but such is life. I talked to a physics guy today who was almost unaware of non-physics math. He called Hegel "post-modern." Thought "transcendental" meant transcendent. I like this guy. He's no doubt a sharp guy. But he ventured into territory outside his passion, uttered some rubbish. And this is what we A-hole intellectual types tend to do. We half-know one thing, and proceed to speak on anything and everything. And I have done it. Not long ago I decided to speak less about politics, as I have no passion for it. I've thought more than the average joe about it, but so what? It's not my bag. And neither is ethics really. I've got it worked out personally and don't find much joy in arguing for universal ethics.

"Proto-logic" or the "transcendental" or call it what you will is something that amuses me. It's blindingly obvious that such an interest isn't terribly practical, but neither is philosophy in general. More money in math, no doubt, which is fortunately a new obsession for me. For many, the "fact" that we unify perception into objects, and from there derive number....is not so exciting. To seek out the structure of thought is useless, quixotic, blah blah,...sure. Are there are those who are certain that there is no such thing as certainty. Those who know that they can't know, but cannot see the contradiction in this. Those who speak as if for the Wise Incorporated. Group-identified do-rights. No this isn't the thread for this but what does it really matter?

No doubt I've met some excellent folks on this forum, and some of them I would be glad to talk to in person, and the conversation would probably be better than it already has been in its best moments.
 
kennethamy
 
Reply Thu 29 Apr, 2010 07:37 pm
@Reconstructo,
Reconstructo;158162 wrote:
I don't think I'm well understood on this, .


On what, exactly? It is very difficult to know what your point is. Supposing that you have one. After reading your post, I am no wiser. Perhaps you ought to put it more clearly. It might help.
 
attano
 
Reply Fri 30 Apr, 2010 05:26 pm
@Reconstructo,
Reconstructo;158134 wrote:
Indeed, if we deny the transcendental, how can we argue the usual happy theme of human solidarity? Also, I'm not one for reduced ambitions.

That's interesting. I'd be grateful if you write more about this connection (some other thread?).

Reconstructo;158134 wrote:
Formal logic is like mathematics an invention, and language is presumably prior to both.

I agree.
Nevertheless logic (as well as all mathematics), is a very peculiar invention, that is not similar to other human inventions - such as a drug or the diesel engine. (In a sense it's more creative, because it's freed from physical constraints. On the other end, it must comply with a very strict discipline, else it would collapse). I probably lack the knowledge and the skill to grasp the exact nature of this often beautiful ideal artifacts, but I am convinced that they are most peculiar and - although I do not adhere to your proto-logical programme - I share the idea that they are very interesting per se.

Reconstructo;158134 wrote:
I suggest that both are built on a few self-evident notions.

I am reluctant to accept that - I am reluctant to use the idea of self-evidence in general. For the point in case, there is the well known case of non-euclidean geometries against this assumption.

Reconstructo;158134 wrote:
If we don't seek the universal, what are we seeking?

"Seeking", the quest for foundation and principles... No I am not after that - maybe I am not yet past a teenage nihilistic phase.

Reconstructo;158134 wrote:
And if we argue against the possibility of such universal goals, how can we do so if not from the same universal logic we intend to discredit?

If you look after proof and confutation, then it's about the only option.
But if one does not...

Reconstructo;158134 wrote:
Sometimes the medium says more than the message.

Definitely.
 
HexHammer
 
Reply Sun 2 May, 2010 08:47 am
@Reconstructo,
Reconstructo;153804 wrote:
Two little points I'll kick off with. Consider the word "what" (as an instance among other words of this type). "What now?" "What" seems to function like a variable, like an x. This seems related to the existential quantifier in formal logic and the variable in math. Note: I see "proto-logic" as foundational to both language, formal logic, mathematics, algorithms...
I can't agree with the definition of this proto logic, I suck balls at math and language, but are excelent at abstract logic. I know several people who are brilliant at math, but sucks extremely much at language, so in essence it does not rely on same basis.

I'v only read very little about intelligences and brain structure, but most intelligences can work independantly of eachother, you can actually lose many areas of the brain, and still have perfectly functional remaining brain functions.

..so no, this proto logic doesn't exist, Imo.
 
Reconstructo
 
Reply Sat 8 May, 2010 05:02 pm
@attano,
attano;158581 wrote:
That's interesting. I'd be grateful if you write more about this connection (some other thread?).

What is the essence of being human? I would argue that humans are essentially essence. Which is to say that humans, as humans and not simply animals, are thinking beings. If thought is the essence of man, what is the essence of thought? Or in other words, the essence of essence. And this took me from Kant to Hegel to mathematics.

It seems to me that we simply do not and cannot live without transcendental assumptions. We can't sincerely question our ability to question. We simply must and do assume that humans have something human in common, which is already implied in the word "humans." For me, the question of essence and accident is itself essential and not accidental to philosophy. The philosopher is on a quest for essence, I think. And there seems to be an eros in man that desires essence.

---------- Post added 05-08-2010 at 06:09 PM ----------

attano;158581 wrote:

I agree.
Nevertheless logic (as well as all mathematics), is a very peculiar invention, that is not similar to other human inventions - such as a drug or the diesel engine. (In a sense it's more creative, because it's freed from physical constraints. On the other end, it must comply with a very strict discipline, else it would collapse). I probably lack the knowledge and the skill to grasp the exact nature of this often beautiful ideal artifacts, but I am convinced that they are most peculiar and - although I do not adhere to your proto-logical programme - I share the idea that they are very interesting per se.


I should make it clear that any "proto-logic" is not an invention. But any formal logic is. I suppose I am studying the inventor by looking at its/his inventions. The essence of any formal logic is the "proto-logic." The rest is accident. It's contingent. It's this little glyph instead of that one.

I like to write computer programs. To make algorithms that have any power at all, one needs a few, but only a few, logical operators. For instance, one needs an "if" statement. There are more complicated versions of "if then" statements like "do while" statements and "repeat until" statements, but these are really just for convenience. A person needs just one logical switch. Of course equally important are variables that store numerical values. (or strings/words).

This may seem like a digression, but I feel that studying several computer languages is good in the same way that studying binary or hexadecimal is good. Exposure to multiplicity can make one aware of the singular essence that lurks apparent plurality.

The world currently runs more on binary than decimal. If we switch all the computers off, we are going to have a mess on our hands. Binary is the simplest possible positional notation system. 2 is a special number. As Eli Maor said, and it effected me, 2 may be a constant more important than pi or e.

---------- Post added 05-08-2010 at 06:15 PM ----------

attano;158581 wrote:

I am reluctant to accept that - I am reluctant to use the idea of self-evidence in general. For the point in case, there is the well known case of non-euclidean geometries against this assumption.

I'm glad you mention that. Non-euclidean geometries are especially dependent upon axioms. I suspect that they are useful for relativity, etc. , and I agree that they are not transcendental. Except perhaps for what is carried over from Euclid. Ideally straight lines, etc.

I too have been reluctant to take self-evidence for granted, and I have trod the road of radical skepticism. But the road is self-refuting. In the end, the skeptic has no grounds for skepticism. Because if he argues against the possibility of knowledge, a more radical skeptic can argue against the assumptions inherent in such an argument. Also, human beings cannot and do not live in accordance with skepticism. Hume wrote well on this. I respect the mental integrity that is associated with skepticism. I suspect you are a sincere thoughtful person. Perhaps you are just on a different piece of the highway.

---------- Post added 05-08-2010 at 06:31 PM ----------

attano;158581 wrote:

"Seeking", the quest for foundation and principles... No I am not after that - maybe I am not yet past a teenage nihilistic phase.

Well, when I was younger, I was much more attracted to questions of ethics, values, etc. And I was skeptical, corrosive, etc. All that was already here was something I had to hack thru to make some room for myself. I had to doubt it all to not be drowned by it all. I feel that as I was exposed, year by year, book by book, to more and more, I could process it better. In the end, I saw how great it all was, all this Western "culture" that preceded my birth.
Also, 13 years of commitment to the same woman clears the mind of all that romantic confusion that might otherwise distract one.

In the end, this "quest" is a blessing. I'm a moth drawn to a flame, and it's only a goal that makes progress possible. I'm a big fan of Spengler's concept of the Faustian man. From Nietzsche and Schopenhauer, in my younger days, to Hegel, Kant, Spengler, Leibniz, these days. Of course math is eating my brain full time. Smile

---------- Post added 05-08-2010 at 06:40 PM ----------

attano;158581 wrote:

If you look after proof and confutation, then it's about the only option.
But if one does not...


I think axioms are as inescapable as death and taxes. And I don't mean the formalized axioms, but the built-in hardwired axioms.
 
Arjuna
 
Reply Sat 8 May, 2010 07:15 pm
@GoshisDead,
GoshisDead;155315 wrote:
Wittgenstein's use of "deep grammar" was in reference to psychological causation of the meaning of surface grammar. It was an attempt to internalize the language process and eject the standard object/referent models. It Also suffers the same problems that Chomsky does, it is a series of transformations that lead nowehere. Except in wittgenstein's case the transformation is due to external forces applied, acquired, then transformed. But it still completely skips the actual mechanism of language. It does not address the actual cognitive process underlying language.

Language is part poetry. What gets lost in a translation from decimal to hexidecimal is just that. Ten sounds like tin. "A" is an indefinite article... or better, part of an acronym. I used to deal with hexidecimal error codes... they would become acronyms to me... just like license plate letters do. A german friend speaks english with no german accent. You can only tell it's not her first language when she uses an idiom... that somehow isn't being used correctly... although one can't pin point why not.

Point is: our minds have a fluid character.. moving from one viewpoint to another, finding patterns in clouds and tree leaves. As the mind ponders itself, it finds the primal and eternal. It also finds there can't logically be any vantage point from which to see itself truly. I've been thinking about that lately. Plato has Socrates saying that the philosopher wants to die because his examinations of the ways of the mind lead him to that conclusion: that there is some truth that can't be known from within this life. Logically, it could only be seen from outside. This vantage point is what the philosopher longs for. That was my translation anyway.
 
kennethamy
 
Reply Sat 8 May, 2010 07:42 pm
@Reconstructo,
Reconstructo;161870 wrote:
What is the essence of being human? I would argue that humans are essentially essence. Which is to say that humans, as humans and not simply animals, are thinking beings. If thought is the essence of man, what is the essence of thought? Or in other words, the essence of essence. And this took me from Kant to Hegel to mathematics.




This argument makes no sense at all. Suppose that thought is the essence of a person. And even suppose that people are identical with thought (whatever that is supposed to mean). That would show that a person is identical with the essence of persons (whatever that may mean). But how would that show that humans are essentially essence? (Whatever that might mean)? That would be like arguing that if the essence of being a person was his DNA (which, I suppose has some merit) then the essence of being a person is being an essence, which not only makes very little sense, but doesn't even follow.
 
Reconstructo
 
Reply Sat 8 May, 2010 08:17 pm
@HexHammer,
HexHammer;159309 wrote:
I can't agree with the definition of this proto logic, I suck balls at math and language, but are excelent at abstract logic. I know several people who are brilliant at math, but sucks extremely much at language, so in essence it does not rely on same basis.

I'v only read very little about intelligences and brain structure, but most intelligences can work independantly of eachother, you can actually lose many areas of the brain, and still have perfectly functional remaining brain functions.

..so no, this proto logic doesn't exist, Imo.


What I was driving at is the meeting place of mathematics and word-language. I suggest that number is whitewashed word. That word has a quasi-numerical core. Essence and accident depend upon unification. I suggest that set theory is a more obvious meeting place of mathematical language and metaphorical discourse. The number and the word have a common source. But number has evolved into a complicated system. Quantity is a one-dimensional or scalar concept. Whereas much of what humans talk about is not so simple.

I agree that a person can be quite gifted in one field without expertise in another. I'm sure that many great poets haven't cared much for math. And this probably applies to great kings,ministers,politicians as well.

I still must assert that mathematics is in many ways an ideal universal language. But this comes at a cost. Reduced ambitions of expression but increased efficiency of such expression. e^(pi*i) = -1 is one hell of lot of meaning to squeeze into so few symbols. But one must know the language, and the significance of the "sentence" within this world of shape, quantity, and abstract groups. ....

---------- Post added 05-08-2010 at 09:24 PM ----------

GoshisDead;155240 wrote:
Just one little anecdotal example of why using language to get at proto-logic is so very difficult. But it is correct, I would suppose, to consider that every language as it is processed by the brain has a functional negativizer category that fuzzes out at the edges.


I agree, Gosh, it's quite a task, a bit like battling windmills. But it's a pleasure somehow. For me it was Kant & Hegel that led me to mathematics. The "transcendental analytic." It may be as a Nietzsche might say that it's a lust for the trans-temporal, for treasure that rust and thieves cannot remove.

It seems that if we look at all the classic philosophical problems, we see they are largely a matter of language. So we investigate language. What is its core? I feel that unification is about as close to the core as one can get. Concepts are sets that include "qualia" and/or other concepts. Or so it seems to me. And this takes us to mathematical unity. I suppose we could stay out of math and just talk about Parmenides, but math works both with unity and infinity. And infinity is also quite a fascinating concept, which is also close to philosophy. I find negative theology quite fascinating.

You seem to agree with me loosely on some sort of ur-negativity that must be part of any language. I admit this is more of a hunch, on my part, as I obviously have not been exposed to all human language.

I also suggest that "if" is related to "not," as another example as a necessary proto-logical operator. Smile

---------- Post added 05-08-2010 at 09:29 PM ----------

Arjuna;161900 wrote:
Language is part poetry. What gets lost in a translation from decimal to hexidecimal is just that.


Well, I think we should note that no information gets lost from hexadecimal to decimal, or the reverse. (Possible minor exceptions if dealing with transcendental numbers.)

This for me is exactly the difference between poetry (metaphorical language in general, which is most language) and mathematics (which is language stripped as much as possible of its metaphorical imprecision.)

But then perhaps you mean that the digits themselves, as glyphs, have a poetic value.

---------- Post added 05-08-2010 at 09:31 PM ----------

Arjuna;161900 wrote:

Point is: our minds have a fluid character.. moving from one viewpoint to another, finding patterns in clouds and tree leaves. As the mind ponders itself, it finds the primal and eternal. It also finds there can't logically be any vantage point from which to see itself truly. I've been thinking about that lately. Plato has Socrates saying that the philosopher wants to die because his examinations of the ways of the mind lead him to that conclusion: that there is some truth that can't be known from within this life. Logically, it could only be seen from outside. This vantage point is what the philosopher longs for. That was my translation anyway.


Very nice! I agree, the primal and the eternal. And I also agree that there are limits perhaps to what we can acheive this way, from this side, from the inside....(or are we Moebius strips?)

Anyway, nice paragraph!

---------- Post added 05-08-2010 at 09:33 PM ----------

GoshisDead;155315 wrote:
It does not address the actual cognitive process underlying language.


How tricky it is that we must use language to understand language...

Self-conscious logos. Smile
 
HexHammer
 
Reply Sun 9 May, 2010 09:02 am
@Reconstructo,
Reconstructo;161925 wrote:
I still must assert that mathematics is in many ways an ideal universal language. But this comes at a cost. Reduced ambitions of expression but increased efficiency of such expression. e^(pi*i) = -1 is one hell of lot of meaning to squeeze into so few symbols. But one must know the language, and the significance of the "sentence" within this world of shape, quantity, and abstract groups. ....
I am so lost.

1) in what way do you think math is an universal language? At no point do I see tribal behaviour having any knowledge of math, they have other values for communicating.

Vikings rules most of Europa back in the days, yet didn't have any greater knowledge of math.

2) last part of your quote are beyond my understanding, I understand nothing.
 
kennethamy
 
Reply Sun 9 May, 2010 12:19 pm
@HexHammer,
HexHammer;162147 wrote:
I am so lost.



Vikings rules most of Europa back in the days, yet didn't have any greater knowledge of math.



Even more striking is that Obama is attempting to extract the United States from deep economic chaos, without any knowledge of basic economics, not to mention ignorance of math. For instance, like the Greek politicians, he seems to be oblivious to the fact that if you continue to spend more than you have coming in, and if you try to conceal this by massive borrowing, you will inevitably go bankrupt. The Greeks are learning this now; I suppose the United States will learn it, but after Obama leaves office (which I hope will be fairly soon).
 
HexHammer
 
Reply Sun 9 May, 2010 03:12 pm
@kennethamy,
kennethamy;162177 wrote:
Even more striking is that Obama is attempting to extract the United States from deep economic chaos, without any knowledge of basic economics, not to mention ignorance of math. For instance, like the Greek politicians, he seems to be oblivious to the fact that if you continue to spend more than you have coming in, and if you try to conceal this by massive borrowing, you will inevitably go bankrupt. The Greeks are learning this now; I suppose the United States will learn it, but after Obama leaves office (which I hope will be fairly soon).
What amazes me, is the basic concept of moderd civilizations. We have very modern and advanced educational institutions, yet some idiot leader nullify thousand years of educational evolution in a few pen strokes, and bring their country into chaos, as he had monkeys as staff, govenors ..etc.

There is just something wrong.
 
Reconstructo
 
Reply Mon 10 May, 2010 03:59 pm
@HexHammer,
HexHammer;162147 wrote:
I am so lost.

1) in what way do you think math is an universal language? At no point do I see tribal behaviour having any knowledge of math, they have other values for communicating.


I see your objection, and I respect that. It's a good point. Still, I think it's a relatively universal language. If a German comes up with some equation to find the primes, this equation can be written precisely in a way that someone who does not understand German can understand. Apparently, the decimal system is quite the standard these days, to dwell on the mere foundation of modern number.

I suppose the only truly universal languages are music, facial expression, dance. There are still enriched by context, but they can be largely understood with a minimum of social experience.

---------- Post added 05-10-2010 at 05:03 PM ----------

HexHammer;162147 wrote:

2) last part of your quote are beyond my understanding, I understand nothing.


Well, math is about shape and groups as well as numbers. Numbers are just one part of math. That's my experience, at least. There are some who try to think of numbers as sets, as abstract groups, and not as quantities. It gets pretty wild. And the concept of functions is something special. You have to dive in, I guess, to see what I mean. I study constantly, and I feel that I am merely an enthusiastic beginner. But it's all relative.
 
HexHammer
 
Reply Tue 11 May, 2010 01:42 am
@Reconstructo,
Reconstructo;162519 wrote:
I see your objection, and I respect that. It's a good point. Still, I think it's a relatively universal language. If a German comes up with some equation to find the primes, this equation can be written precisely in a way that someone who does not understand German can understand. Apparently, the decimal system is quite the standard these days, to dwell on the mere foundation of modern number.

I suppose the only truly universal languages are music, facial expression, dance. There are still enriched by context, but they can be largely understood with a minimum of social experience.
Small children can understand very very simple math, that 1 is more than nothing, it scales very low if math is not taught. However the understanding of mass is better understood by tribal people than modern people, often herders can tell if just 1 creature is missing from the herd of 200 animals.

And I do fully agree with your reasoning of the truly universal languages.

Reconstructo;162519 wrote:
Well, math is about shape and groups as well as numbers. Numbers are just one part of math. That's my experience, at least. There are some who try to think of numbers as sets, as abstract groups, and not as quantities. It gets pretty wild. And the concept of functions is something special. You have to dive in, I guess, to see what I mean. I study constantly, and I feel that I am merely an enthusiastic beginner. But it's all relative.
Official math often differs from personal math understanding, some number/math savants think in very unique patterns.
 
Reconstructo
 
Reply Tue 11 May, 2010 01:58 am
@HexHammer,
HexHammer;162798 wrote:
Small children can understand very very simple math, that 1 is more than nothing, it scales very low if math is not taught.

I was just reading about that. They have tested newborns by measuring the attention they pay in the changing of quantities. Indeed, we are born numerical. Of course it takes time to get the words and symbols right.

---------- Post added 05-11-2010 at 02:58 AM ----------

HexHammer;162798 wrote:

And I do fully agree with your reasoning of the truly universal languages.

It's nice that we agree sometimes. Smile

---------- Post added 05-11-2010 at 03:03 AM ----------

HexHammer;162798 wrote:

Official math often differs from personal math understanding, some number/math savants think in very unique patterns.


I completely agree. And even the famous math guys are famous precisely for thinking in a different way, and adding to the language. If the notation of math is somewhat universal, math thinking isn't. I agree. Some like to think in terms of geometry and others in terms of arithmetic. Personally, I find spatial representations radically speed my comprehension. I think the coordinate plane is one of man's best inventions. It's an obvious invention, once it's invented, but it still took us awhile. Just like positional notation took us awhile. Cartesian coordinate system - Wikipedia, the free encyclopedia
Positional notation - Wikipedia, the free encyclopedia

I think we take the positional notation system for granted. It was a huge leap, I think.
 
attano
 
Reply Thu 13 May, 2010 05:55 pm
@Reconstructo,
Reconstructo;161870 wrote:
What is the essence of being human? I would argue that humans are essentially essence. Which is to say that humans, as humans and not simply animals, are thinking beings. If thought is the essence of man, what is the essence of thought? Or in other words, the essence of essence. And this took me from Kant to Hegel to mathematics.


I have no such concept of man. Human is just a class of animals. (And it seems quite possible that other animals think - and use a language).
What makes men special is their history. Probably men are the only animals with a History - but that does not make us intrinsically special.


Reconstructo;161870 wrote:
It seems to me that we simply do not and cannot live without transcendental assumptions. We can't sincerely question our ability to question. We simply must and do assume that humans have something human in common, which is already implied in the word "humans." For me, the question of essence and accident is itself essential and not accidental to philosophy. The philosopher is on a quest for essence, I think. And there seems to be an eros in man that desires essence.


A definition of "transcendental" would be required here.
It is quite agreed that our senses do not represent the completeness of things.
Whether this distortion in our perception extends to such a thing (category) as Causality, is more problematic to many.
One more level it's represented by the reality of the subject - that Kant never questioned, but that Fichte, Schelling, Hegel, Schopenhauer and Nietzsche (and others) did. (And I side with this third group).

Taking into account the distortions in our perception - that we would be able to control/unmask in many instances - I do not see the transcendental assumptions as compulsory, although one may make them.
The naive(?) assumption that objects exist outside and independently of us - the tempered belief that our senses are a way to know all these things to a degree that let us infer that they are (somehow) such as we perceive them - has been rife for centuries and it still is. So far, it does comply with the Occam's razor a lot more than any explanation trying to deny this and seeking to explain patterns in our perception.

The fact that we must assume a common character in humans is generally undisputed (by realists and all sorts of transcendentalists). It seems to me that your consideration on this common character has more a moral value, but I do not exactly understand what is your point.
Btw, I believe that a philosopher is basically a would-be ruler, a potential tyrant (even analytic philosophers). Pol Pot or Ceauşescu were a lot more philosophers than Mother Teresa. (And I guess that this means there is gulf between us)


Reconstructo;161870 wrote:
I should make it clear that any "proto-logic" is not an invention. But any formal logic is. I suppose I am studying the inventor by looking at its/his inventions. The essence of any formal logic is the "proto-logic." The rest is accident. It's contingent. It's this little glyph instead of that one.


This is clear to me, and I guess that you may have a point.
I mean that it is possible that there are forms of our perception that morph into forms of our thought and then are reflected in language. Whether these forms really structure our though, that there would be no thought or that it would be impossible to have a meaningful thought by ignoring these forms, it is something that I don't believe.
I am reluctant to accept this thesis because I am not persuaded that thought precedes language, I do not believe that language is just a tool - and even then the tool modifies its user. Language aside, I guess that our thought is governed by factors/players that have a predominant role even on perception - I think that perception is constantly modified by thought. (And conscience does not master thought).


Reconstructo;161870 wrote:
I'm glad you mention that. Non-euclidean geometries are especially dependent upon axioms. I suspect that they are useful for relativity, etc. , and I agree that they are not transcendental. Except perhaps for what is carried over from Euclid. Ideally straight lines, etc.

I too have been reluctant to take self-evidence for granted, and I have trod the road of radical skepticism. But the road is self-refuting. In the end, the skeptic has no grounds for skepticism. Because if he argues against the possibility of knowledge, a more radical skeptic can argue against the assumptions inherent in such an argument. Also, human beings cannot and do not live in accordance with skepticism. Hume wrote well on this. I respect the mental integrity that is associated with skepticism. I suspect you are a sincere thoughtful person. Perhaps you are just on a different piece of the highway.


Actually... I agree with you. But you just presented my argument: we value our knowledge before testing it. In the process of knowing we apply values. Knowing is a form of valuing. And this has a lot of consequences and implications... (BG&E I, 1-4)
There is no such a thing as pure perception and there's no such a thing as pure (scientific) knowledge - they both have moral values before, between and after them.


Reconstructo;161870 wrote:
Well, when I was younger, I was much more attracted to questions of ethics, values, etc. And I was skeptical, corrosive, etc. All that was already here was something I had to hack thru to make some room for myself. I had to doubt it all to not be drowned by it all. I feel that as I was exposed, year by year, book by book, to more and more, I could process it better. In the end, I saw how great it all was, all this Western "culture" that preceded my birth.


So do I, and one thing I retained (well... not the only one): God is dead...


Reconstructo;161870 wrote:
In the end, this "quest" is a blessing. I'm a moth drawn to a flame, and it's only a goal that makes progress possible. I'm a big fan of Spengler's concept of the Faustian man. From Nietzsche and Schopenhauer, in my younger days, to Hegel, Kant, Spengler, Leibniz, these days. Of course math is eating my brain full time. Smile


And that's probably why I am always keen on reading your posts Smile
 
Reconstructo
 
Reply Thu 13 May, 2010 07:33 pm
@attano,
attano;164021 wrote:
I have no such concept of man. Human is just a class of animals. (And it seems quite possible that other animals think - and use a language).
What makes men special is their history. Probably men are the only animals with a History - but that does not make us intrinsically special.


Well, the viewpoint I enjoy "arguing" for (because I'm really not a fanatical type, just a person who likes to work a theme thoroughly) is difficult to express exactly because I see all essences as contingent.

You say man is a class of animals. I would counter by saying that "man" is the imposer of classes. I see "man" "animal" and "class" as abstractions, as inventions. They are real because we live in them.

I can't offer any proof that we are intrinsically special. I do feel that humans are the salt of the earth. I love this Planet Earth documentary. I wonder if a lion could enjoy it? I am forced to use the same abstractions I have called contingent, but I think that human consciousness gives the Earth much of its meaning and beauty. If the world were devoid of thought, would it not be mostly eating, mating, and excretion in the relative dark?
attano;164021 wrote:

A definition of "transcendental" would be required here.
It is quite agreed that our senses do not represent the completeness of things.
Whether this distortion in our perception extends to such a thing (category) as Causality, is more problematic to many.
One more level it's represented by the reality of the subject - that Kant never questioned, but that Fichte, Schelling, Hegel, Schopenhauer and Nietzsche (and others) did. (And I side with this third group).

I can tell you what I mean by it. I think there are certain ways that human experience is always structured. I can't prove this. But to give you an example, I can't truly imagine four spatial dimensions, and I don't think any human can. I don't think we can imagine a round square, or a spot that is simultaneously red and blue. Number is an ideal example. Whence the number one, the concept of unity? I don't see that as an invention. Experiments have been done on babies, who before they speak react to changes in quantity.

I too side with the 3rd group. I think the subject is an abstraction. The "self" is learned. Of course survival may demand this sort of learning, and the adoption of that which is not strictly logical. In a way, absolute idealism (which is just as much an absolute realism) is art made of logic. Of course I have been equally passionate about the pragmatism of Nietzsche, especially when presented in the sunnier style of Rorty, for instance. I don't know if Nietzsche would have liked the term pragmatism, but I feel he can be included in the group. I think of Nietzsche as a partisan of dynamic "truth." Truth is whatever makes us thrive. That sort of thing. I may be arguing the Kojeve / Hegel angle because I spent so much of my earlier forum days arguing the Nietzsche/Rorty angle. Smile

attano;164021 wrote:

Taking into account the distortions in our perception - that we would be able to control/unmask in many instances - I do not see the transcendental assumptions as compulsory, although one may make them.
The naive(?) assumption that objects exist outside and independently of us - the tempered belief that our senses are a way to know all these things to a degree that let us infer that they are (somehow) such as we perceive them - has been rife for centuries and it still is. So far, it does comply with the Occam's razor a lot more than any explanation trying to deny this and seeking to explain patterns in our perception.

But what about physics? What about electrons? F = ma? I can't help but see physics as implicitly transcendental. We have science which, apparently, exists only as equations who meaning cannot be intuited. What is a wave-particle? With respect...
attano;164021 wrote:


Btw, I believe that a philosopher is basically a would-be ruler, a potential tyrant (even analytic philosophers). Pol Pot or Ceauşescu were a lot more philosophers than Mother Teresa. (And I guess that this means there is gulf between us)

I agree with this completely. Even if I am amused by the absolute approach (because the transcendental for me is only a ladder to the absolute approach) the comedian/cynic has not stopped working in me. Diogenes was one of my first philosophic heroes. I also love Bukowski. This is why I think the sort of politeness we have going on says more than a person's current views. And this ties in with Schopenhauer's distinction between character and intellect. A person's manners are perhaps as better window into their soul than their current intellectual position. I wish I could claim to have never had bad manners on this forum, but maybe it's good to "sin" a little and realize it.

attano;164021 wrote:


I am reluctant to accept this thesis because I am not persuaded that thought precedes language, I do not believe that language is just a tool - and even then the tool modifies its user.


I agree. I can't see the difference between language and thought. Not really. The "transcendental" must be inferred from language and still can only exist as language. Let's look at words like "concept" and "trope." This sort of linguistic self-consciousness seems like a central part of philosophy to me. Kojeve (blending Hegel, Heidegger, and Marx) presents the dialectical progression of philosophy as an advance of "self"-"consciousness." "He" realizes that "his world" is made of his "language." I know all those quotes are a bit thick, but that's sort of the way I experience abstractions, at least when I think about Kojeve/Hegel. For me, a sublime notion is that the "real is rational" and rational in the sense of intelligible. If we say the world is not intelligible, this is still the application of concept. Just as I also think that infinity the concept is itself finite, or simply a negated concept that is somewhat paradoxical.

I don't think that language is just a tool, either. I would say that we are language, but that leaves out what is difficult to speak of --qualia, emotion, value. I like the Gospel of John. In the beginning was the Logos. I think the incarnation myth represents the overcoming of man's alienation from his creation "God."
attano;164021 wrote:

Actually... I agree with you. But you just presented my argument: we value our knowledge before testing it. In the process of knowing we apply values. Knowing is a form of valuing. And this has a lot of consequences and implications... (BG&E I, 1-4)
There is no such a thing as pure perception and there's no such a thing as pure (scientific) knowledge - they both have moral values before, between and after them.

I agree. Epistemology cannot be separated from motive. So my quest for the absolute or the transcendental cannot be neutral. It's an idiosyncratic painting that strives toward my idiosyncratic notion of the universal.
attano;164021 wrote:

So do I, and one thing I retained (well... not the only one): God is dead...

For me as well. I expect no afterlife, no justice from the sky. For me "God" is a great piece of conceptual art, or a word applied to the totality, to the "nature of things." I think the word still has valuable uses, but ultimately I live as if "God is dead" if God is understood in the usual crude sense as some invisible person in the sky. I will admit that atheism isn't obvious or provable in my book. It's theoretically possible that God is up there. But that's not my conscious position. In fact, I think and feel as if we are on our own "down here" --unless Hawking's aliens show up.

attano;164021 wrote:

And that's probably why I am always keen on reading your posts Smile

Thank you. I enjoy yours as well. I have only respect for you, and look forward to continuing our conversation. :Glasses:
 
 

 
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