A Materialist Account for Abstractions - or - How Theists Misplace the Universe.

todangst's picture

You probably already know how this complaint goes:

"How can you account for axioms in a materialistic universe? What part of your brain are axioms located in? Can you actually point to some neurons and say 'these are what the axioms really are'? Also, since the axioms of math are carried around in people's heads, are there really millions of little axioms of math running around? Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Let's take this apart, piece by piece:

How do you account for the 'laws of logic' in a materialistic universe.

The laws of logic? Which set of laws? For which logic? First-order logic, first-order predicate logic, second-order predicate logic, modal logic, fuzzy logic? Which one? Logic is not a monolithic entity, and there is no one set of 'laws' for all of logic. Not all logical systems even require axioms. The set of axioms for the sentential, or propositional, logic is {} - the empty set:

"The point is that there can be no axioms in this logic (the writer is referring to predicate logic), the most basic of all modern logics (there are other formulations that do have axioms, though): everything in predicate logic is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally." - Gregory Lopez.

Now that we have done away with the blunders attached to that misunderstanding, let's explain the basic metaphysics requires for the creation of an a priori system. The only metaphysic required for the creation of an a priori system is the existence of sentient brains. The basic axioms of existence, identity and consciousness - the so called laws of reason (prior to any logical system and not part of logic itself), are necessary elements of reason; to reason one must first exist, and exist as something. These axioms are therefore implicitly inescapable - an explicit awareness of these axioms is another matter.

We can express this truth thusly:

To exist is to exist as something. And to be aware of this is to be conscious.

The axioms are necessary truths, given the existence of consciousness. They are defended through retortion. But they are not a part of logic, per se. Other rules, such as the other laws of classical logic, can also be gleaned a priori, all of them flow from the axiom of identity (i.e. classical logic, a system of tautologies, can be traced back to the axiom of identity). The specifics of which rules we create do not matter here; what matters is as long as we have sentient brains, we will have the basis for the creation of any a priori system.

Mavaddat, from this site, writes:

(T)o explain the human invention of logical systems as somehow the indirect work of God is to explain precisely nothing at all. It is as good of an explanation as saying "it just happened." Invoking God to explain anything is the very abdication of reason and insight. It is giving up the investigation and search for truth and filling it with some supernatural nonsense (literally). Instead, I think that people like Paul Feyerabend, Karl Popper, and Thomas Kuhn give us a good idea about how science and human knowledge progresses.

"What part of your brain are axioms (or abstractions) located in?"

The cerebral cortex, frontal lobes. http://www.waiting.com/brainanatomy.html#anchor2587568

"Also, since the axioms of math are carried around in people's heads, are there really billions of little axioms of math running around?"

Billions of representations of the same axioms. Billions of sentient brains coming to the same, necessary, analytic, unavoidable, a priori conclusion, just as billions of different bits of falling matter all conform to the same phenomenon of nature that we can summarize in one law: the law of gravity.

If you fail to find it puzzling how 'different pieces of matter' can all conform to the same law of gravity, then you ought to re-examine your supposed puzzlement over axioms. The process is similar. Billions of sentient brains encountering the same, singular reality - the unavoidable basic metaphysics of our universe. If you are looking for a missing 'constant' for the materialistic account, it is this: the universe. You've misplaced the universe. One universe with a basic set of unavoidable, inescapable metaphysics. One universe imprinting itself onto phylogenetically similar sentient beings, who are able to draw the same abstractions from the same stimuli, based on the same rules...

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains is because the same idea can be gleaned, analytically, a priori, by similar brains in the same exact universe. The same idea can be represented in multiple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

"Finally, how come you also call an axiom written on the page the axiom' and the axiom in your head 'the axiom'? After all, paper isn't a bunch of neurons, and you are a materialist after all..."

Ah, but you forget something else: Abstract entities written on a page have no meaning in and of themselves. They are interactive phenomena - a sentient brain is required to interpret them and provide them with 'meaning'. Thus, when we say that the number "eighteen" is written on a page, what materialists are really saying is that this sensory input'18' through some social convention (some rule), yields the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses.

A word written on a page and the same word spoken and traveling as a wave through the air are not 'the same matter'. However, when I read the word, and when I hear the word, my brain eventually interprets them the same way, producing similar electrochemical responses with enough fidelity that slightly different brains can reproduce the same abstraction, based on the same rules.

Of course, the mapping itself is completely arbitrary. Our written alphabet needn't be what it is, and we could choose totally different symbols to represent the same thing as the spoken word.

Common Responses:

The Identity of Indiscernibles is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.

This formula can be used to demonstrate that if x shares the same properties of y, then x and y are the same entity.

The argument continues:

A material entity cannot be in more than one spatio-temporal location at the same time.

Response: This claim confuses fails to consider that abstractions are tokens or representations - formed in neurons by the same set of rules. However, the claim is doubly false, for even if we presume that abstractions are in fact the same identical entity, quantum physics tells us that there is no contradiction in having the same material entity in more than one spatio-temporal location:

http://www.fizyka.umk.pl/~jkob/physnews/node30.html

For more in the principle of Identity of indiscernibles and Liebnitz' transposition of the principle, the law of Indiscernability of Identicals, see here:

http://plato.stanford.edu/entries/identity-indiscernible/#Rec

Greetings Mr. Todangst!

Greetings Mr. Todangst! I've been in this forum for about 3 days now, and i've got to say that i've learned alot of very, very interesting theories and ideas here.

I've posted this a few times now and so far with negative results. I was hoping to ask for your help in finding the answer to my question.

Lately, i've been learning from posts of deludedgod and your post about axioms and how its formed in the brain by chemical reactions and are therefore material.

The definition above, though satisfactory, leaves me with a question hanging. Its been nagging me for quite a while now, and i couldn't place it or articulate it until now. Here goes:

The definition of thoughts being material (electric impulses in the brain) serves to define it only at the point of its creation.

I just realized, i want to be able to define it at the point after its creation.

So to illustrate, when i decide to write a thank you note to a friend for a gift, thoughts are created as follows:

1) Brain fires up, creates thoughts. (material)

2) I write my thoughts down on a hallmark card (material)

3) card is mailed to my friend (??????)

4) friend reads card, understands my message/thought (material)

Or another way of illustrating my story is below:

 

 

    ME              LETTER IN TRANSIT     MY FRIEND

   Brain                   | No Brain |                 Brain

electrical impulses | no electrical impulses |elec. imp.

        |                            |                         | 

   material           |???????????????? |          material

thoughts ---------------------------------------------------

 

At certain points in time (when there is a brain), thoughts are material because of the electrical impulses it generates. But at other points (when there is no brain) no electrical impulses are generated at all, which is why i put a question mark on it.

True, the thoughts or symbols on the hallmark card are useless and meaningless without a brain to interpret it, but it still exhists even when there is no brain. Proof of such is when a brain is again introduced, the symbols on the card elicit the same electrical reactions in the brain.

What i therefore need to know is how to define thoughts in a material way when the brain is not present. The thoughts are still there. Albeit in a different form, since no electrical impulses can be detected it at that point. If i say that the thoughts are the card, it doesn't really sound satisfactory as an explanation. (to me)

The Patrician's picture

Jorge, I'm not sure I

Jorge, I'm not sure I understand.  Without anyone to view the card it is simply a piece of decorative cardboard with writing on it.  It is only when someone who can understand the message and internally translate it picks it up and reads it that thought comes into play.

Freedom of religious belief is an inalienable right. Stuffing that belief down other people's throats is not.

Hambydammit's picture

Yeah, this seems pretty

Yeah, this seems pretty simple.  When you mail it, it's a piece of matter being transported using energy.  When it gets to its recipient, it is the catalyst for a thought which creates an idea which brings you right back to point A.

When a concept exists in a brain, it is inexorably linked to that brain.  If two brains use matter and energy to communicate, it's still matter and energy and concepts created by and intrinsically bound to matter and energy.  What's the problem?

 

Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin

http://hambydammit.wordpress.com/
Books about atheism

todangst's picture

It sounds to me that the

It sounds to me that the problem is that he is mistaking the representation of the thought (the card) for the thought itself.

The card carries a representation of the information you wish to present to your friend. It is not your thought, but instead a set of symbols that can be interpreted by others with similar brains, so as to produce the same thought in their brain.

The original thought is material.

The thought can be represented in words, or in written form on a card. 

The card is material.

The card will be interpreted by your friend's material brain.

There is no time where your 'idea' or its representation is non material.

Think of a printing stamp. The printing stamp is used to stamp ink onto paper to produce copies of an image. The printing stamp goes nowhere, ever... it remains where it is, but is produces copies of itself.

The thoughts are not 'the card', they are merely represented there. 

 

Those who know the good, do the good. - Socrates

Books on atheism.

lpetrich's picture

 I like to call this the

 I like to call this the Argument from Platonism, the idea that there must be some special mind-stuff or thought-stuff.

The main argument I've seen for that, to the extent that its advocates make any argument at all, is some sort of "nothing but" hyper-reductionism. Those advocates often ignore the possibility of emergent properties -- and sometimes seem to deny them outright.

Consider a grain of sand vs. a sandpile. Those two entities have several important differences in their properties, differences that result from sand grains getting arranged in a sandpile. However, a hyper-reductionist would maintain that there is no such thing as a sandpile -- only grains of sand -- and may also apply that analysis to those grains of sand themselves.

I remember arguing at length with a gentleman named "Ed" at IIDB about such things; he claimed that a river is not really a persistent entity because its water continually changes. He failed to accept that riverness could be an emergent property, and not some special "stuff". He also claimed that we have absolutely fixed souls, which is absurd, no matter what one believes about the metaphysical status of our consciousnesses.

Such people might have a cogent argument if they attempted to demonstrate that mind cannot possibly be an emergent property of nonmental entities, but I mainly see bare assertion of its impossibility. And Ed is no exception.

todangst's picture

lpetrich wrote: I like to

lpetrich wrote:

 I like to call this the Argument from Platonism, the idea that there must be some special mind-stuff or thought-stuff.

Nice name for it. Although it predates Plato - he got it from the Orphic religious tradition that ran rampant in Greece. In the end, it's a religious idea, so to say it's irrational is practically redundant.

Quote:

The main argument I've seen for that, to the extent that its advocates make any argument at all, is some sort of "nothing but" hyper-reductionism. Those advocates often ignore the possibility of emergent properties -- and sometimes seem to deny them outright.

Agreed.  Emergentism kills their argument, ergo they must ignore it.

Quote:

Consider a grain of sand vs. a sandpile. Those two entities have several important differences in their properties, differences that result from sand grains getting arranged in a sandpile. However, a hyper-reductionist would maintain that there is no such thing as a sandpile -- only grains of sand -- and may also apply that analysis to those grains of sand themselves.

I do wonder if there really is a 'hyper reductionist' error.... whatever emergent property that is produced by a grouping of sand must exist, in some humbler form, in the individual grains... I believe that a proper reductionist approach would not be contradictory to the emergentist/holistic approach... in fact, I really see reductionism and holism as not competing, but complimentary....

But I see your view too.

Quote:

I remember arguing at length with a gentleman named "Ed" at IIDB about such things; he claimed that a river is not really a persistent entity because its water continually changes.

His error is old: he assumes that the word "river' is static, a platonic real... in reality, when we say 'river' we don't really indicate a completely static, unchanging ideal, but in reality, 'a bunch of moving water'

 His error is as old as the hills, and it comes from not having a clue concerning the last 300 years of philosophy.

 

Betrand russell corrects the error in a paragraph.

 

In short, there are two major errors in Plato's view:

 

1) his idea that heraclitus' changing world lead to chaos was a parody of heraclitus.... the fact that our world changes does not imply that it changes to the level of radical uncertainty!

 

2)  he presumes that while the world changes, words remain the same. Nonsense, words change along with the world, ergo there's no problem.

 

changing world, and changing, varied meanings to words... and in both cases, the changes are not so great as to lead to chaos.

But to listen to a theist, you'd think that birds turn into bicycles in midflight.

Quote:

He failed to accept that riverness could be an emergent property, and not some special "stuff".

Probably... I think his presumption is that the word 'river' actually intends to point to some ideal of a river, he probably believes that a word must be precise to be useful at all. Old error.

 

Quote:

He also claimed that we have absolutely fixed souls, which is absurd, no matter what one believes about the metaphysical status of our consciousnesses.

"absolutely fixed'.... yep, that's his error... he's hanging from Plato's nutsack.

Quote:

Such people might have a cogent argument if they attempted to demonstrate that mind cannot possibly be an emergent property of nonmental entities, but I mainly see bare assertion of its impossibility. And Ed is no exception.

 

Ed should be informed that there was a period of time called the '20th century' and that it produced philosophy. He might then read some it, and find out how error riddled Plato's ideas are....

Those who know the good, do the good. - Socrates

Books on atheism.

  all I say is slang .....

  all I say is slang ..... as is all changing language .....