science is a priori

[John Molineux]

I take that back.  I'm not able to sort out the precise relationship between the following terms: property, type, kind, concept, idea.  

 

They are all pretty closely related.  Sorry for the short and useless response, but my wife would not be too happy if I spend Christmas eve working out the relationship between those terms!  =)

 

Any help would be appreciated.  I do think some of it may have to do with the accidents of the English language, although I am convinced that there is a genuine category in here.  

[dream_weaver]

For my part, there seems to me to be a direct path as follows:

• in any consistent mathematical system rich enough to contain arithmetic, there exist propositions that cannot be proven (or disproven) from the system's axioms.

...to…

• Some mathematical propositions of which we have knowledge do not consist of the mere extrapolation of concepts

...and since…

• Mathematical knowledge cannot come directly from sense experience (which only consists of itself)

...and…

• We have mathematical knowledge

...we can conclude…

• Some of our knowledge does not come from sense experience

I believe I could put that all in syllogisms that would be very difficult to assail (I'll do so if requested).

Merry Christmas everyone!

Fact: Some mathematical knowledge has not been shown to come directly from sense experience.

 

We have mathematical knowledge.

We have mathematical knowledge that has not been reduced hierarchically, to data of sense.

 

"Are Mathematical Truths Discovered or Invented" is a plug for a course that investigates the foundational basis for number: adding, subtracting and multiplication.

 

Corvini goes in depth, from the process of pairing, leading eventually to number as a set of "portable mental pebbles".

She addresses the problem of applying number to magnitude, and goes in depth on the topic of limits.

From there, she puts together the number line.

 

(This is just the first course, "Two, Three, Four and All That")

Edited December 24, 2014 by dream_weaver

[aleph_1]

But if I have misunderstood you then I stand corrected, ....

My statement was qualified, and you stand corrected.

[John Molineux]

I just read McCaskey's work on the problem of induction (http://www.johnmccaskey.com/joomla/images/for-download/PittVolume.pdf).  I stand by what I said earlier--both about his ideas being deeply insightful and important, and about it failing to contain a complete solution to the problem, and I believe subject to the two objections I voiced above.  

[Plasmatic]

Louie said:

I see Plasmatic has many quotes, but for what it's worth I don't usually agree with his understanding when it comes to topics pertaining to epistemology.

For what it's worth, I don't usually agree with most anything Louie post's either. But when I choose to express that disagreement I always show how what he claims is the opposite of what Ms. Rand actually says by quoting her to the contrary.... But lets leave that be...

[Eiuol]

Why a category doesn't also require a category: The thing I think we know is that SOME concepts have to be foundational.

Some concepts do need to be foundational. So how is a category foundational? What makes it valid? And if it really is a priori, it's only waiting to be "activated", so I really don't know what it is. You basically left it as something we "have", but is it an idea? Percept? A platonic Form? If you can't answer that in some way, you can really give any argument for even "science is a priori" since an a priori category is also vague. I need something more substantive.

A sensible way to describe this idea of "activation" is that the human mind has mechanisms sensitive to certain stimuli prior to attaining any experience. You could refer to those stimuli as categories, but they aren't part of the mind, not concepts, and not knowledge - they're referents in the world, not themelves a knowledge foundation. They're implicit knowledge, as in what WOULD be logically implied as knowledge. In this way, a priori fails to apply, a sensitivity to stimuli necessarily involves observation and cognitive mechanisms which aren't a process of reasoning. You can call any "feeling" as intuition here, but yet again, getting the intuition to happen and for any CONTENT of knowledge to be there at all.

 

I wasn't diverging from Rand with implicit knowledge. It's more like an awareness of what can later become a concept without it being knowledge now.

[andie holland]

 

Plasmatic, your claim that we are justified to draw the universal conclusion that 1+1 will ALWAYS = 2 is "answered by knowing what in experience the symbols you are referring to mean," is, in my view, a significant source of our remaining disagreement.  I actually thought the same thing at one time (again, the 1st time I read Kant I write something almost exactly like that in the margin).  But for the following reasons, I now believe this cannot be the case. 

 

1. It has been shown to be impossible to derive all of mathematics from logic.  The 20th-century attempt to do so by deriving all theorems from set theory ended up proving that there are theorems that cannot be proven (and moreover, it is subject to paradox such as Russell's paradox). 
2. Most famously, Godel's theorem proved that in any consistent mathematical system rich enough to contain arithmetic, there exist propositions that cannot be proven (or disproven) from the system's axioms--that is to say, there are propositions that are NOT simply a matter of (as you say) "knowing what the terms mean."

 

I believe GrandMinnow (who is apparently seen as the resident Godel-interpretation expert) will attest to both these points, probably adding that "a philosophical argument is needed to draw the latter part of my conclusion on point #2."  =)

 

But I believe the burden of proof is rather light here, and the needed-philosophical arguments have been supplied and reached something like consensus among most experts.  Rather, a philosophical argument is needed to say that our knowledge of mathematics is based on "knowing what the symbols mean," and such an argument has to contend with the whole 20th century, in which many of the world's most brilliant minds tried, and failed, to provide JUST such an argument, and were eventually silenced by Godel's proof. 

 

Yes, the Oist I am referring to is David Harriman. 

 

Thanks for the links on Prof McCaskey's discussions on the problem of induction.  I plan to follow up with that stuff for sure!

 

Minnow, when I mention the defeat of the "empiricist program," I am talking about such writers as Wittgenstein, Carnap, and the logical positivist camp, for whom the attempts to ground mathematics in logic / set theory was part of an attempt to settle one important part of the larger empiricist-rationalist debate.  In order to maintain that all knowledge comes from sense experience, you have to explain mathematics in a way that is consistent with that.  Since obviously sense experience itself can't give you the universal statements of mathematics directly, the ideas that it was simply a matter of the extrapolation of axioms is the only suggerstion I've ever heard argued.  (Granted, I am not an expert in mathematical logic, and I'm confident that, as you say, "there are some informed holdouts.") 

 

For my part, there seems to me to be a direct path as follows:

 

1. in any consistent mathematical system rich enough to contain arithmetic, there exist propositions that cannot be proven (or disproven) from the system's axioms.

...to…

1. Some mathematical propositions of which we have knowledge do not consist of the mere extrapolation of concepts

...and since…

1. Mathematical knowledge cannot come directly from sense experience (which only consists of itself)

...and…

1. We have mathematical knowledge

...we can conclude…

1. Some of our knowledge does not come from sense experience

 

I believe I could put that all in syllogisms that would be very difficult to assail (I'll do so if requested). 

 

Merry Christmas everyone!

 

John.

 

Permit me to expand a bit on your last several sentences. I'll thereby try to draw Godel and your a priori together...

 

Godel's two theorems said that arithmetic was axiomatically inconsistent, therefore, formally incomplete.

This, of course, sent off a red light to those for whom the consequence of 'incomplete' designated something quite serious: there is no longer a formal basis for arithmetic. It's only as viable as its last ad hoc axiom.

 

Therefore, in as much as arithmetic serves as the basis for all maths (that i disagree is beside the point!), Math has no formal basis, either. This cuts to pieces Hilbert's large-scale project, and that of 'Bourbaki (Poincare), too. 

 

Now things get really interesting....

 

Logic can no longer be based upon the certainties of math. Identity therefore becomes an intuition, or an a priori, as it were. The Principia project of Russell and Whitehed is dead in the water.

 

With no consistent logic to guide the formation of personal frames of reference, Wittgenstein's Tractatus is useless. He therefore re-writes philosophy as more modest 'Investigations'.

 

Set theory, as developed by Zermelo-Frankel, becomes incomplete, as well. A 'choice' axiom must be added , hence the much- debated brackets, as in 'ZF©'.. 

 

The practice science, then, is not founded upon any axioms of logic, as they no longer exist as normative rules, but rather only as expressed preferences based upon intuition. Logic is simply following a narrative sequence that makes sense to the community of doers.

 

In other words, i can no more impose my intuitions on you as you might upon me--as if one were to debate the existence of god based upon 'feeling'. 

 

To this end, one might say in passing that a particular group might impose a believed intuition upon others as a qualification for membership. To this end, to say, "I believe in Allah and "I believe in The law of identity" are equally statements of emotive conjecture.

 

Therefore, you stand as absolutely correct in stating that science contains a world of implicit a prioris. 

For example, the experimental method as advocated by Bacon is true to the extent that it produces true-ly verifiable results in terms of its own standards. So, of course, does QM.

 

One cannot hold science accountable to standards set by Philosophy because Philosophy, too, possess standards of logic set and validated only within its own domain. Again, because of Godel, absolute standards such as an immutable A=A do not exist.

 

AH

[John Molineux]

Eiuol, as to what categories are, they are fundamental concepts which are not defined by other concepts, and are not understood by their definitions, but somehow by thought or reason itself.  They are also the things according to which abstraction occurs. 

 

By abstraction I mean the consideration of the part.  I believe that it is something like the essence of thought.  But if abstraction is the consideration of the part, then the questions arises, "which part?"--or "which kind of part?"  I believe the answer consists of a category (or a concept itself built upon a category).  But abstraction is only possible if you have something according to which you are abstracting (like extension in space, time, kind, etc.). 

 

I believe they are similar to Ms. Rand's "foundational concepts." 

 

"How is it foundational?"  It is foundational by means of the fact that it cannot be defined with other concepts, but only with synonyms (and obviously when you get down to the tight circle of 3-4 synonyms that all define each other, your ability to understand those concepts cannot lie in having heard the definition--it is presupposed that you already understand it in some other way).  All concepts would be unintelligible if they were not attached to something that was understood directly. 

 

"What makes it valid?"  I guess what makes it valid as a category is the fact that it meets the definition above (with a hat off to the good Prof McCaskey).  

 

"Is it an idea?"  Yes. 

 

As to the "ontological" questions (where does it exist?  What is it made of? Is it a platonic form?), I am agnostic.  I would be lying if I claimed to know the answer to those questions, just as I would be lying if I said I was not certain that there must be categories at the foundation of understanding.  

[Eiuol]

 

Godel's two theorems said that arithmetic was axiomatically inconsistent, therefore, formally incomplete.

This, of course, sent off a red light to those for whom the consequence of 'incomplete' designated something quite serious: there is no longer a formal basis for arithmetic. It's only as viable as its last ad hoc axiom.

No, more like it can't be consistent AND complete. You are rather presenting a logical positivist interpretation here in the Vienna Circle tradition. "Implicit a prioris" doesn't even make sense, as "a priori" is supposed to be used as an adjective. I have nothing else to say other than your post is only going off course to using a totally different style of philosophy. Presumably, JM is looking to see Objectivist criticism or in that style. Besides, this thread isn't -about- Godel.

[Eiuol]

"One does not use any special science to reach backwards to the foundations upon which it can have no say whatever according to Objectivism. "
Plasmatic, let's try to answer the question, not wave away pertinent knowledge. Is science a priori? No, and if I am right than it won't contradict a mathematical theory if we are to take seriously systems of logic or measurement, which science uses. Basic knowledge just doesn't cut it for complex analysis of a system like science. Otherwise, appealing to non-special sciences will mean you lack the means to analyze whether is science a priori. How do we GET the meaning of symbols? You said conclusions like "1+1=2" are justified by "knowing what in experience the symbols you are referring to mean", as though having a referent is granted by experience, and we'll know what it means. This is only another way of stating JM's view - symbols are in some way activated by  experience, so if we know the referent, we acquire the meaning.

You didn't reject that these "symbols" exist a priori, so you're still operating on premises that presuppose content in the head. The important question is how to create meaning, not presume a pre-existing meaning. The error is expressed when you said "1+1 may not always be 2 is a nonsensical missuse of language"; it's only a misuse if there is a priori symbols or that symbols only need to be found because meaning is already in them. It also contradicts your comments on passive process of intuition. So I'm left wondering if these symbols are ALREADY available!

In any case, your quote nukes are good for pointing out a sensible approach. Consider: "The process of measurement is a process of integrating an unlimited scale of knowledge to man's limited perceptual experience—a process of making the universe knowable by bringing it within the range of man's consciousness, by establishing its relationship to man." This doesn't answer the OP though, and Rand didn't provide a total account of how we determine if our integration was valid and justified.

My point being, the quotes are good to get us thinking, but the problem is getting meaning (presuming concept means symbol).

JM, I think I got a good idea of the disagreement now, I think we're not too far apart in terms of our ideas. Largely, it looks like we disagree on the words. Not to suggest it is "merely" a semantic issue of words - precise meaning matters a lot, and it's not an accident that you pick "a priori" or "category" in your writing. I'll post tomorrow maybe.

Edited December 25, 2014 by Eiuol

[Plasmatic]

Oh boy, as usual your response is sloppy, context dropping and irrelevant.

 

Louie said:

 

Plasmatic, let's try to answer the question, not wave away pertinent knowledge.

 

I have not waved away any knowledge pertinent to the question "Is science apriori?". I have spent much time first establishing the different meanings inherent in John and Rand's usages. (the primary obstacle involved in folks who come here to see what Oism has to say about a outside system of thought.) Your typical post attempting to use the language of other philosophers, apart from usually completely getting their systems wrong, only obfuscates the Oist position. (which you usually have misintegrated anyway)

 

Louie said:

 

No, and if I am right than it won't contradict a mathematical theory if we are to take seriously systems of logic or measurement, which science uses. Basic knowledge just doesn't cut it for complex analysis of a system like science. Otherwise, appealing to non-special sciences will mean you lack the means to analyze whether is science a priori.

 

The above is confused nonsense. This is a perfect example of you rushing to appear friendly and knowledgeable to non-Oist philosophy and while doing so misrepresenting Oism by your half understood take on it.

 

 In order to attempt to claim that I have "waved off" pertinent info, you equivocate between using science as a category apart from Philosophy and then in the same paragraph call the "basic knowledge" acquired by philosophy a species of "non-special science"......

 

For anyone who is reading this post, Oism regards Philosophy as a science:

 

But philosophy is a science that deals with the broadest abstractions and, therefore, many people do not know how to observe its influence in practice or how to grasp the process by which it affects the conditions of their daily life.[..]

 

 What about the fifth branch of philosophy, the basic one, the fundamental of the science of fundamentals: metaphysics? [...]

 

They have never discovered the fact that the trouble comes from the three unanswered questions—and that there is only one science that can answer them: philosophy. 

PWNI

 

It's hard to be more of a "basic" question than wondering whether axiomatic concepts are "apriori" and grasped by "intuition". You don't even understand what the question is. That question cannot be added to one bit by "taking seriously" any concept stealing inversion of hierarchy that claims that Gödel's proof using a special science system (that rests upon and presupposes these "basic" axioms) somehow has a say in general knowledge that can be grasped in any context of awareness.

 

What's more is that we cant even get to that question without knowing what "apriori" is, historically and in John's usage.

 

This is first grade Oism and even though I have provided quotes numerous times of Ms. Rand saying this about the science of philosophy in several ways, you just don't get it.....

 

Louie said:

 How do we GET the meaning of symbols? You said conclusions like "1+1=2" are justified by "knowing what in experience the symbols you are referring to mean", as though having a referent is granted by experience, and we'll know what it means.

 

Let me educate you on what meaning is in Oism:

 

 

A definition is a statement that identifies the nature of the units subsumed under a concept.

 

It is often said that definitions state the meaning of words. This is true, but it is not exact. A word is merely a visual-auditory symbol used to represent a concept; a word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of its units. It is not words, but concepts that man defines—by specifying their referents.

ITOE

 

The statement " as though having a referent is granted by experience" shows complete lack of understanding of the above.

 

Louie said:

 

This is only another way of stating JM's view - symbols are in some way activated by  experience, so if we know the referent, we acquire the meaning.

 

First, you have it backwards. Symbols are chosen after experiencing the generative context of differentiation as a means of unit economy.

 

Second, I have spoken in detail on meaning and its relation to symbols:

 

The whole discussion is about concepts and what the cognitive use of them is. We use words-language to convey and preserve meaning. The symbols are a means of achieving referential economy and integration. Context, hierarchy and integration are all methods of connecting extrospective and introspective experiences into a cognitive whole. The whole need of the general science of epistemology is to teach men how to do this explicitly precisely because man is capable of contradiction. [...]

Justification, proof, reference and definition are all matters of meaning. That is, they all are devices for conveying, recalling and integrating the content of perceptual experience (introspection included) for the purpose of survival. We reduce a concept back to its origins in experience-reality because it is perceptual experience that we are trying to recall and convey so as to situate ourselves in relation to reality in a life preserving manner. The connection to existence for man starts with perception. All philosophic primaries are implicit in perception at any moment of awareness.

 

 

Third, I have pointed out that John has equivocated on this by saying both:

"Neither logic alone, nor experience alone, nor the two working together can get you there! "

 

and :

"Sense experience does cause it to arise, but it goes beyond what sense experience could provide"

[...]

the scientific method relies on a number of concepts which can (in my mind) never be justified or taken from sense experience, and out of which actual universal knowledge (such as that of mathematics) can be extrapolated (I'm thinking things like math, logic, cause-and-effect, etc.). That's what I mean by a priori. ----

 

His protestations notwithstanding...

 

 

Louie said:

 

You didn't reject that these "symbols" exist a priori, so you're still operating on premises that presuppose content in the head.

 

 

 

This is completely nonsensical reasoning. The absence of a statement about another persons claim is not itself a claim about my premises. I don't recognize the concept "apriori" historically or in Johns idiosyncratic usage...

 

Louie said:

The important question is how to create meaning, not presume a pre-existing meaning. The error is expressed when you said "1+1 may not always be 2 is a nonsensical missuse of language"; it's only a misuse if there is a priori symbols or that symbols only need to be found because meaning is already in them. It also contradicts your comments on passive process of intuition. So I'm left wondering if these symbols are ALREADY available!

 

 

This whole fixation on "symbols" is nothing but context dropping.

 

1). WTF is an "apriori symbol"?

2). Nowhere did I say anything like "meaning is in symbols" which is nonsense. In fact I sad the opposite:

 

The whole discussion is about concepts and what the cognitive use of them is. We use words-language to convey and preserve meaning. The symbols are a means of achieving referential economy and integration. Context, hierarchy and integration are all methods of connecting extrospective and introspective experiences into a cognitive whole. The whole need of the general science of epistemology is to teach men how to do this explicitly precisely because man is capable of contradiction. [...]

Justification, proof, reference and definition are all matters of meaning. That is, they all are devices for conveying, recalling and integrating the content of perceptual experience (introspection included) for the purpose of survival. We reduce a concept back to its origins in experience-reality because it is perceptual experience that we are trying to recall and convey so as to situate ourselves in relation to reality in a life preserving manner. The connection to existence for man starts with perception. All philosophic primaries are implicit in perception at any moment of awareness.

 

3). Nothing I've actually said contradicts what I said about a "passive process of intuition".

 

4). In my statement "1+1=2" are justified by "knowing what in experience the symbols you are referring to mean", "symbols" is just referring to words used to express meaning. Not an equivocation between symbols and Johns "apriori". Its a general statement about any use of the various auditory-visual-tactile tools used for the purposes I explained in detail above! (But that requires one to integrate context properly.)

 

Louie said:

 

In any case, your quote nukes are good for pointing out a sensible approach. Consider: "The process of measurement is a process of integrating an unlimited scale of knowledge to man's limited perceptual experience—a process of making the universe knowable by bringing it within the range of man's consciousness, by establishing its relationship to man." This doesn't answer the OP though, and Rand didn't provide a total account of how we determine if our integration was valid and justified.

My point being, the quotes are good to get us thinking, but the problem is getting meaning (presuming concept and symbol).
 

 

 

As I pointed out your confused about what the OP is even asking and I even said that I have more to add in my last response to John. This basically makes your entire post a waste of time due to context dropping....

 

 Feel free to lay out somewhere what you think the account Ms. Rand actually gave is lacking....

Edited December 25, 2014 by Plasmatic

[Eiuol]

"1). WTF is an "apriori symbol"?"
A symbol created and justified without experience. Identical to JM's "a priori categories".

"First, you have it backwards. Symbols are chosen after experiencing the generative context of differentiation as a means of unit economy."
Of course it was wrong, I was presenting a view I oppose!

Look, I was questioning an important sentence you used. That's all.

[New Buddha]

Minnow said:

For the same reason that I do not consider your comments to me to be a wiping of anything, I'll point out that the entire discussion of technical mathematics and Godel is misguided by Oist standards. One does not use any special science to reach backwards to the foundations upon which it can have no say whatever according to Objectivism.

Math is a language and follows all the same epistemic prescriptions of a valid epistemology. My statement about Godel was actually a question about John's associating it with philosophical foundations-axioms.

+1

 

Back in high school, I hated math.  This was the early '80's, and math was taught entirely by rote memorization.  It wasn't until I began studying architecture in college that it made any sense.  All the algebra, trig, analytical geometry and calculus only began to make sense once I was studying physics and engineering.

 

Draw a beam diagram with a uniform load of X lbs/sf and a point load 1/3 from the left bearing point.  Determine the shear (and number of bolts required to resist the shear) and the moment-of-inertia and size of the beam required to resist the loads....  Establish allowable deflection by the material used, and account for thermal expansion.  Solve the area under the triangle for shear, and the area under the curve for moment.  Oh, so that's what the quadratic equation is used for....

 

Math is not an end within itself... it is a means to an end.  It is a tool.  Just like language.

 

Mathematicians (some but not all) like to make math seem other-worldly in the same way that the Pope reads his sermons in Latin.

 

Ooooohhh... look what I know and you don't....  I'm so much smarter than you stupid materialistic engineers with your petty bourgeoisie concerns.  Math is concerned with the Transfinite!  Math reveals to us the way that that the Universe is, independent of our biased perception!  Math is Pure Knowledge!

Edited December 25, 2014 by New Buddha

[John Molineux]

Easy guys!  =)

 

Plastmatic, I'm not aware of ways that my usage of a priori is different than the typical use.  I just mean proceeding from something other than sense experience--which, as I understand it, is the standard meaning.  When you type "a priori" on google, the following definition comes up:

1. The terms a priori ("from the earlier") and a posteriori ("from the later") are used in philosophy (epistemology) to distinguish two types of knowledge, justification, or argument: A priori knowledge or justification is independent of experience (for example "All bachelors are unmarried").

That is exactly how I'm defining it--basically as what does not come from sense experience.  In addition to the science-based arguments I have given, I could add the following arguments that seem to me to literally prove with certainty that empiricism is false and self-defeating:

• the only knowledge that comes from sense experience is the knowledge of that sense experience itself. 
• some of our knowledge is of things besides the objects of our sense experience (for instance, math, but also pretty much everything except for knowledge in the form "I am having the experience of seeing yellow," etc.)
• therefore, not all knowledge comes from sense experience (which, with the definition above, is exactly tantamount to saying that "we have a priori knowledge")

Or this one:

• the statement "all knowledge comes from sense experience" does not (and cannot possibly) come from sense experience, and it is therefore self-defeating (this does mean that it cannot be TRUE, but that it cannot be KNOWN)

Given the clarity and prevalence of arguments like this, it has been amazing to me how common empiricism is.  So much harm has been done in philosophy (and by extension, science), by the fear of the "metaphysical" nature of the a priori.  I understand that the enlightenment was largely about getting superstitious drivel out of philosophy, which is admirable and important.  But (it seems to me) the over-extension of this idea resulted in "empiricism," for fear of "vague metaphysical superstitionism."  And I think the idea is that a priori means something mystical is unfounded.  I think it could very easily simply be a feature of our brains (which contain enough mystery to easily swallow up all the mystery contained in the question, "what is it?") and the way that we must conceptualize things based on the way our brains evolved.  

 

But the aprioriphobia of the enlightenment ran so deep that empiricism reached something like a consensus among the scientific and much of the philosophical community--not by argument (I am not aware of any argument FOR empiricism, and it wouldn't matter since from the two arguments above constitute a logically-tight proof that empiricism is self-defeating)--but simply (it has seemed to me) by riding a wave of popular anti-superstitious sentiment.  And this empiricism has literally (in my view) destroyed philosophy.  It has lead to the triumph of skepticism in philosophy, and has created in science its own form of the very mysticism that it set out to eliminate (I mean the current situation in Quantum Mechanics, which is a direct descendant of the dogma of the elightenment, empiricism).  

 

Now one of the few remaining schools (as I see it) where neither the new mysticism of quantum mechanics, nor the irrationalism of postmodern philosophy prevails, is Ojbectivism.  But Oists seem to me to be largely isolated (and unfortunately, not taken too seriously) by mainstream philosophy (partly because that philosophy has itself become insane after embracing the consequences of the irrationalism that proceeded from the skepticism that resulted when near-consensus was reached about the impossibility of solving the problem of induction from an empiricist framework).  Oism is one of the few schools (maybe the only) that is still actually trying to solve the problem of induction.  Thanks God for that, but it seems plain to me that it will never be solved by sense experience (which can't even solve a schoolboy's math problem, much less the philosophical problem that brought down the Western intellectual tradition).  

 

In Godel you have a rigorous mathematical proof (close to the highest-possible certainty) with a half century of philosophical debate about its meaning, and something like consensus.  In the above two arguments, you have two of the simplest, tightest arguments possible.  Simple, old fashion syllogisms, with none of the meanings really in dispute.  And what stands against that?  Is there an argument of equal strength and clarity somewhere?  I have read dozens of books by empiricists and I can't recall a single argument for it--all the authors took it for granted, and then proceeded to fail to solve the great problems of modern philosophy (and by extension, destroyed the western intellectual tradition).  There is certainly nothing like the simple syllogisms above, which seem to me to be unassailable.  

 

Nevermind....I'm just ranting, which may or may not be helpful.  But I genuinely don't understand why people cling to empiricism or refuse to allow in the a priori.  Anyone who would be willing: what is at the core of the reason that you believe that all knowledge must come from sense experience?  And how do you escape the above two arguments?

 

By the way, does Ms. Rand's "implicit knowledge" come from sense experience?  If so, how?  If not, it's a priori under the definition above (which is the standard definition).

[Plasmatic]

Only time for this :

By the way, does Ms. Rand's "implicit knowledge" come from sense experience? If so, how? If not, it's a priori under the definition above (which is the standard definition).

I planned to explain this in my next substantive post.

Yes, implicit knowledge is knowledge of similarities and differences in experience which one is aware of in a preconceptual-verbal-linguistic form. Ill respond to your comments about apriori definitions in detail later.

By the way, if you listen to Harriman's lecture you will find ample refutation of your belief that empiricism led to the current nonsense in physics.

Edited December 25, 2014 by Plasmatic

[New Buddha]

@John #65

 

John,

Empericism can mostly be attributed to Hume and Locke - both of which PRE-DATED any notion of a priori and a posterior arguments.  Perhaps what you mean is Pragmatism, and not Empiricism?

 

Roughly stated:

 

Plato believed that prototypes exist in the mind - obtained from another realm, prior to birth.

Aristotle believed that essence is a physical attribute, perceived by the senses.

Hume believed that essence is grasped by habit (a psychological argument).

Kant believed that there is an inseparable gulf between what is 'out there" and what is "in the mind" (and this is the birth of most, if not all modern philosophy since).

Hegel/Marx developed a dialectic argument between "out there" and what is "in the mind".

Pragmatism didn't care what was out there, so long as it "works".

Sartre was bored of the entire discussion.

 

Objectivism holds that OBJECTIVE knowledge can be obtained by an INDIVIDUAL, but that essence is epistemic.

Edited December 25, 2014 by New Buddha

[Plasmatic]

I said:

Yes, implicit knowledge is knowledge of similarities and differences in experience which one is aware of in a preconceptual-verbal-linguistic form. Ill respond to your comments about apriori definitions in detail later.

I should have said:

"Yes, implicit knowledge is a type of awareness of similarities and differences in experience which one grasps in a preconceptual-verbal-linguistic form. "

Edited December 25, 2014 by Plasmatic

[Eiuol]

Math is not an end within itself... it is a means to an end.  It is a tool.  Just like language.

True, but if we accept that all knowledge is connected, all knowledge can inform all domains of knowledge. As related to the OP, there is no separated "pure" or ontological foundation upon which reality is -built-. There is only a logical foundation of what I -already know-. That was my point, and why Plasmatic's phrase "knowing what in experience the symbols you are referring to mean" made no sense to me. Looking at the Rand quote:

 

It is often said that definitions state the meaning of words. This is true, but it is not exact. A word is merely a visual-auditory symbol used to represent a concept; a word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of its units. It is not words, but concepts that man defines—by specifying their referents.

 

The idea is not the same. Meaning of a concept consists of its units. The meaning of a word is the concept it symbolizes. A unit, or even the "what" of experience (entities), doesn't have a meaning. A concept has meaning. The meaning consists of units, but it doesn't suggest the units reveal their meaning. That's why 1+1=not 2 is valid. It depends on your context. Knowing what the units are won't tell you what '1' means on its own.

[Eiuol]

But I genuinely don't understand why people cling to empiricism or refuse to allow in the a priori.  Anyone who would be willing: what is at the core of the reason that you believe that all knowledge must come from sense experience?  And how do you escape the above two arguments?

Let's be clear: Objectivism, as in Rand's system of philosophy, is neither empiricism nor rationalism. It is not a Hegelian synthesis of empiricism and rationalism, either. I see it as validating knowledge to correspond with reality which perception allows us to be in contact with. If we (people on this forum) say "knowledge comes from experience" we would mean all knowledge is connected to or rooted on experiences. The process of concept formation is a fallible, active process that can fail to connect to experiences. How can a connection be made? Rand gives key factors: differentiation and similarity, then integration from there.  How does differentiation work prior to a first experience, or for first-level concepts? Rand doesn't answer how it happens. There has to be something attuned to the world, lest everything is a mass of colors. So one answer is "a priori" categories or knowledge. A better answer is that some mechanisms in the mind are already attuned to the world, but they are not ideas or conscious mechanisms.

Edited December 25, 2014 by Eiuol

[Plasmatic]

Louie, dropping context again, said:
 

"1). WTF is an "apriori symbol"?"
A symbol created and justified without experience. Identical to JM's "a priori categories".

"First, you have it backwards. Symbols are chosen after experiencing the generative context of differentiation as a means of unit economy."
Of course it was wrong, I was presenting a view I oppose!

Look, I was questioning an important sentence you used. That's all.

1. No one, not even John called his apriori concepts "symbols". In fact he even showed understanding that symbols are not concepts by his "by any name" comment and his "switching of symbols" comment about clocks...

2. You were presenting a view no no one holds in this thread, which resulted from your failure to integrate all that I said in context.

Louie said:
 

The meaning consists of units, but it doesn't suggest the units reveal their meaning.

Some virulent rationalism you have there. When I point to a referent-unit I immediately identify what I mean and that is always done in a context that involves prior use of symbols. The meaning of a concept, expressed using symbols, is the referents that are being concretized by said symbols.

 

 

ITOE said:

 

 

In order to be used as a single unit, the enormous sum integrated by a concept has to be given the form of a single, specific, perceptual concrete, which will differentiate it from all other concretes and from all other concepts. This is the function performed by language. Language is a code of visual-auditory symbols that serves the psycho-epistemological function of convening concepts into the mental equivalent of concretes. Language is the exclusive domain and tool of concepts. Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e., that stands for an unlimited number of concretes of a certain kind.

 

Edited December 25, 2014 by Plasmatic

[Eiuol]

ITOE said:

Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e., that stands for an unlimited number of concretes of a certain kind.

Yup, that quote is what I'm saying. Either explain what you meant ("knowing what in experience the symbols you are referring to mean"), or I still won't understand what you were talking about. Quoting Rand isn't helping. The "what in experience" doesn't have meaning, a symbol does. Unless you forgot a comma as "...what, in experience, the...", which changes what you said quite a lot.

[John Molineux]

Eiuol, if we take empiricism to mean the belief that all knowledge comes from sense experience, and rationalism to be the belief that not all of it does, it is impossible to be "neither empiricist nor rationalist" as per the law of the excluded middle.  Either all knowledge comes from sense experience, or it doesn't.  

[New Buddha]

Eiuol, if we take empiricism to mean the belief that all knowledge comes from sense experience, and rationalism to be the belief that not all of it does, it is impossible to be "neither empiricist nor rationalist" as per the law of the excluded middle.  Either all knowledge comes from sense experience, or it doesn't.

Pardon my jumping in,  but how does this square with your point from post #64

 

• the only knowledge that comes from sense experience is the knowledge of that sense experience itself. 
• some of our knowledge is of things besides the objects of our sense experience (for instance, math, but also pretty much everything except for knowledge in the form "I am having the experience of seeing yellow," etc.)
• therefore, not all knowledge comes from sense experience (which, with the definition above, is exactly tantamount to saying that "we have a priori knowledge")

You seem to be arguing for some type of "synthesis".

Edited December 27, 2014 by New Buddha

[Plasmatic]

John consider these words from OPAR on what reason is:

 

 

Ayn Rand defines "knowledge" as "a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation."(11) This definition, which the discussion so far has validated, can serve as a summary of the Objectivist epistemology. It also indicates our rejection of two widespread viewpoints. Contrary to skepticism, the definition affirms that man can "grasp reality." Contrary to mysticism, it affirms that such grasp is achieved only by observation and/or reason.

 

 

But Objectivism holds that all knowledge in the hierarchy begins with sense experience...

 

Likewise objectivity is a relation between subject and object:

 

 

The concept of "objective," which applies as a norm to all rational cognition, has its roots in the theory of concepts. "Objectivity" arises because concepts are formed by a specific process and, as a result, bear a specific kind of relationship to reality.

 

The conceptual faculty is an instrument that reduces units by omitting measurements. Or: concepts are a human method—of integrating perceptual data. Or: concepts are a device of our consciousness—to deal with existents. All these formulations point to a crucial fact. Concepts do not pertain to consciousness alone or to existence alone; they are products of a specific kind of relationship between the two. Abstractions are products of man's faculty of cognition and would not exist without it. But a faculty of cognition is concerned to grasp reality and must, therefore, adhere to reality.

OPAR

Edited December 27, 2014 by Plasmatic

[Eiuol]

Eiuol, if we take empiricism to mean the belief that all knowledge comes from sense experience, and rationalism to be the belief that not all of it does, it is impossible to be "neither empiricist nor rationalist" as per the law of the excluded middle.  Either all knowledge comes from sense experience, or it doesn't.  

If that's all empiricism meant was, then sure. But empiricism generally is not merely that "all knowledge comes from experience" but also along the lines of how knowledge is built from perceptual "simples" as Locke believed. Or some other additional thesis that is skeptical of abstraction or representations. Logical positivists are similar, but really do find abstraction as something that is problematic to justifying our contact with reality and the knowledge we have. It's no accident that Godel was closely associated with the Vienna circle. He saw that, at least with regard to his theorems, we're not going to get completeness by some axiomatic foundation alone. The thing about either empiricism or rationalism is that there is a "gap" between experiences and abstractions, and the gap is a major problem to fix. It's an issue for Objectivism to answer, but I think it really eliminates any gap at all leaving the "gap" more like a question for philosophy of cognitive science and in-depth epistemology beyond what Rand wrote. My previous post is kind of why I think the gap isn't real.

 

I read about one philosopher that I think gives a lot of good ideas for a view I find useful to build on. http://www.susannaschellenberg.org/file/Papers.html