“Though I can tell you approach your philosophical warbling with some
integrity I'm afraid that your loyalty to Binswanker and your dismissal of
the 20th centuries greatest mathematician Godel reveals far more than any
amount of well written and well formed arguments ever could.”
Actually, my philosophical loyalty is not to Binswanger (please note the
spelling here) or any other personality. My loyalty is to reason. I simply
think you might want to investigate matters where obviously you have not.
Don’t do so for my sake. Whether or not one wants to say that Godel was one
of the greatest 20th mathematicians or not is in the end irrelevant. Being
great doesn’t mean that you’re always right or infallible. Keep in mind,
later thinkers like Binswanger and others have the advantage of reviewing
Godel’s conclusions in the light of more recent discoveries and advances,
some of which may in fact bring those conclusions into question. And that's
assuming they're relevant to begin with. You tout on about Godel’s
conclusions, but what were his premises? How do you know that they were
sound? It’s possible that Godel’s entire theorem was built on shaky footing.
Nothing you have stated in your post indicates that you are willing to
accept this possibility, let alone show why that is not the case.
Furthermore, you yourself seem quite unfamiliar with the philosophy of
Objectivism (you didn’t even know what the fallacy of the stolen concept is;
who knows what else you do not know about Objectivism), and thus most likely
completely unfamiliar with the nature of Binswanger’s criticisms of Godel’s
theorem. You seem to think that one’s loyalty to a personality speaks louder
than arguments. Fair enough; as I stated in my last response to you, without
more substance to your position, it is impossible to debate it. And with
your latest secretion, there’s still quite a bit lacking, and what is
present in your statements is sufficient for me to determine that your
ignorance of Objectivism’s structure and content may indeed be the source of
your misunderstandings and disconnects. So, why not investigate the
arguments and their philosophical basis for yourself in order to determine
their quality? You might learn something after all.
“Godel's theorem is as important in maths and logic as relativity theory is
Then I would say, in addition to investigating what Binswanger has to say on
the matter, investigate also what David Harriman has to say on these matters
as well. (That is, unless you do not want to question your loyalties.) Both
have quite a bit to say about science and mathematics (Harriman himself is a
physicist). There are others, as well, which I could recommend, but I don't
see the point if you're not willing to examine your own premises.
“There are plenty of books and websites: go find one read, understand and
maybe you would wish to re-evaluate your certainty on some matters.”
I’m always open to re-evaluating my certainty. I don’t think that is the
problem here. I think the problem is that you’re arguing against something
you do not fully understand. You might want to re-evaluate your own approach
“Godels proof is not in question. It is a mathematical proof not a
Then what relevance do you think it has to philosophy?
“So most of your posting demonstrates only ignorance.”
That’s odd, I think the same thing about your post. I guess we’re even.
“The fallacy from disbelief. Or the Victor Meldrew fallacy. "I don't believe
it, therefore it can't be true."”
Are you saying this about yourself? You have not established that this
applies to anyone else. I have merely pointed out that at least one scholar
has provided some criticisms of Godel’s views, and you seem unwilling to
research it yourself. Seems you’re guilty of what you’re accusing others of.
“If you can't be bothered to look it up I shall scan the formal mathematical
proof onto the site for you, just ask.”
Feel free to do so. But while you’re at it, think critically on these
matters, and see if you can determine what Godel’s fundamental philosophical
premises were. Any approach to mathematics has philosophical implications,
like it or not. How, for instance, did Godel deal with the issue of
metaphysical primacy? His ideas will indicate his position(s) on this issue
implicitly if he did not identify them explicitly (and Binswanger brings
this out). How did Godel define his terms? Did he identify those definitions
and remain consistent to them throughout his theorem, or did he, like many
philosophers and theists we know, continually shape-shift their definitions,
or leave them unstated so that any shape-shifting is not easily detected?
I’m not saying that Godel did one or the other; these are simply questions I
think you might want to keep in mind as you investigate his or anyone else’s
work. It’s easy to argue for certain illicit conclusions when you play games
with definitions. But if one is serious and his conclusions are rational,
there would be no need for this, don’t you agree?
“Never mind the quantity, slow down and hunt the quality.”
Are we to trust you as a source for quality?
"Specifically, which axiomatic systems did Godel review?"
“Godel's proof applies to all axiomatic systems.”
Really? How do you know? Where does Godel investigate Objectivism? If Godel
did not investigate Objectivism, then how can one say his proof applies?
Just because you say so? And if you yourself are unfamiliar with Objectivism
(which your own statements indicate), how can you know anything for certain
about this matter? If you say “It doesn’t matter!” then it’s obvious you’re
on the ropes here. Perhaps you just want Godel to be right, and anyone who
disagrees with him to be wrong. From what you’ve provided in your post,
there’s nothing I see by which I can eliminate this possibility from serious
Notice also that lordbyron did not address the question above. My question
was "which axiomatic systems did Godel review?" and his answer is simply
that “Godel's proof applies to all axiomatic systems.” From what lordbyron
provides, it's possible to conclude that Godel did not investigate any
axiomatic systems at all, for lordbyron does not say which ones he examined
when specifically asked to identify which ones he investigated. Gee, such
“The few points worth responding to prior to you reading Godel are thus:
“Universally accepted axiom.
“An axiom which everyone is prepared to accept. OK. Just because everyone
accepts an axiom as valid does not guarantee its validity, nor just because
everyone rejects an axiom does it guarantee its falsity. The only genuine
arbiter is the truth or otherwise of whatever axiom is being proposed.
However, we have to look to others to some degree to confirm our own beliefs
otherwise debate turns to pantomime. Its true, oh no its not. oh yes it is
Look at what I stated in my last post. I wrote:
“An axiom does not gain validity simply because it is universally accepted.
So I don't know why the criterion of universal acceptance is even relevant.
lordbyron does not say.”
So again, universal acceptance is hardly a criterion to consider here.
Objectivism’s fundamental axiom is ‘existence exists’ and indeed, I’ve
encountered many theists who have disputed the truth of this statement
(which IMO only shows how dishonest those individuals are).
“I cannot understand your desire for complete reducibility of an axiom.”
If you cannot or do not understand this, then you have no understanding of
how axioms function in Objectivism, nor do you understand the Objectivist
view of knowledge or concept-formation. Thus any criticism you might want to
launch on the basis of your own lack of understanding for these matters as
they apply to Objectivism, can only falter on their own lack of
understanding. Again, lordbyron, there are so many issues of which you seem
quite ignorant here. That’s not bad in and of itself; after all, you would
have to learn somehow if you’re going to learn at all. But this matter is
crucial here, and unless you begin to understand the need for
irreducibility, your criticisms are contentless, or at best miss the point.
You might as well bark like a dog from here on forward.
“Any argument is only capable of discussing whatever is contained in the
At the axiomatic level, arguments are irrelevant. In order to construct an
argument, one must have terms and thus have concepts. In other words, the
issue of axioms has already been decided, one way or another, by the time
one gets to evaluating arguments. True axioms are not the product of
arguments or proofs (to suggest otherwise only leads to stolen concepts).
Besides, I’ve already discussed how the concept ‘existence’ (Objectivism’s
fundamental axiomatic concept) is the widest of all concepts. So there is no
problem for Objectivism here. The problem is that someone doesn't understand
what he's talking about, and that someone is not me.
“Some concepts are complex concepts, but this needn't be a barrier to their
appearing in axioms.”
Check your premises here. You might be able to critique some philosophies
with this approach, but until you learn a little more about what you’re
talking about, your criticisms (and quite possibly Godel’s as well) are
inapplicable to Objectivism.
“The concept mind for example couldn't be discussed under your terms, as it
wouldn't be sufficiently simple to appear in an axiom.”
See, here you’re again showing your own lack of understanding of
Objectivism. What have I stated in past posts? I identified the fundamental
axiomatic concepts of Objectivism: existence, identity and consciousness. I
have argued (and successfully so) that one must accept the validity of these
concepts and their applicability as foundational concepts even to dispute
them. Just by questioning them, you are affirming them. I think you need to
learn how to integrate what you read. I can’t hold everyone’s hand on these
“Of course, as an atheist I suspect that you would ultimately consider the
mind to be reducible to biochemistry, chemistry and physics and that axioms
should be constructed to reflect this reducibility.”
I am not a reductionist in this sense. When Objectivism speaks of the
irreducibility of the axioms, it refers to conceptual irreducibility, not
the supposed metaphysical reducibility of consciousness to brain activity or
chemical interactions. Objectivists do not hold to this view. These are two
different matters completely. Again, there’s a lot here you are trying to
speak about, but of which you have little understanding. So far, you may
have arguments with some philosophies out there, but so far, none of it
applies to Objectivism yet.
“As a Platonist I would reject these assumptions yet would not consider this
to be a problem should we decide to have some discussion of the mind
See! What did I say? Good grief! I don’t think you’re even aware of what
you’re saying here.
“A brief example should give you some indication of Godel's theorem.
This example is to prove the existence of the natural numbers.
“1 is defined and the qualifiers + and = are defined, as axioms. Using these
three axioms we are then able to generate the sequence of natural numbers.
Using these axioms it is possible to generate any natural number we care to
name, thus proving its existence in the set of natural numbers. However,
what we cannot do is generate all of the natural numbers using this system.
NB we can generate any individual number we care to name, yet we are unable
to generate all of the natural numbers together! This is because to prove
the existence of very large numbers takes a very large amount of time, and,
as the list of natural numbers are neverending we come to the problem of
requiring a period of time that is neverending.”
This does not resemble the Objectivist approach to mathematics or the
formation of the concept ‘number’ in any way, shape or form. Again, if you
think this example is relevant to a criticism of Objectivism, I’m sorry to
break the news, it just isn’t. I’m saying this whether or not I am an
Objectivist. Numbers in Objectivism are not axiomatic concepts. See Rand,
_Introduction to Objectivist Epistemology_ where she discusses the formation
of the concept ‘unit’ and the role of measurement-omission in the formation
of concepts as fundamental issues in the development of a number system. If
you do not have a good understanding of this, then I do not see how you are
qualified to comment on these matters.
[skip irrelevant material]
“1.Even in the most certain of mans intellectual endeavours, mathematics,
there is dispute at the most fundamental level.”
This “dispute at the most fundamental level” is avoided when mathematics is
built on the basis of a rational philosophy. Even mathematics cannot get
away without philosophical foundations. If you or Godel or others disagree,
then it’s no surprise that you’re encountering disputes at the most
fundamental level! In philosophy as well as in reality, you get what you
[skip irrelevant material]
“2.The second important issue, and the one that is fundamental to the
atheism/theism debate is the matter of top-down or bottom up. Atheists tend
to begin with basic principles and construct the universe from small units.
For example, understand logic, we can do maths. Understand maths we can do
physics. Understand physics we can do chemistry. Understand chemistry we can
do biology, then psychology then sociology etc.”
I think this whole section is a little confused (for one, I think you grant
more sophistication of structure to theists than is warranted), but a
fundamental point can be salvaged. Overall you seem here to affirm that
knowledge has a hierarchical structure. If you are willing to affirm this,
then it seems you should be able to grasp the need for knowledge to have a
foundation. Otherwise, without a foundation, you leave yourself at the mercy
of an infinite regress. Don’t you have a starting point? Without a starting
point, then how do you achieve certainty at all? (I think this guy has been
so confused by some of the philosophers he’s read that perhaps it’s useless
to even engage him.)
“Theists tend to start at the top end, ie assume that God exists as a given
and then deconstruct. To preempt the attack of "what is your definition of
God?" I could draw attention to the above Godelian proof and point out that
such a being is similarly indefinable, and that to attempt such a definition
would necessarily lead to contradiction.”
You don’t need Godel to show this.
“However, my favoured approach is far more basic. My only axiom is that I
want to consider the existence of the universe as a single entity and to
discuss the universe as a whole. This "the universe is one" approach is
quite legitimate and considers the universe as a single entity, the things
in the universe being attributes of the universe. All things; matter,
artifacts, thoughts, actions, racehorses are all attributes of the one same
thing- the universe, or nature, or God.”
According to Objectivism, this is wrong. The universe is not an entity, but
the sum total of all existence. Entities are objects which we perceive as
indivisible units, such as a glass, a car, or a person. The entities have
attributes, such as shape, color, weight, measurement, etc. But we cannot
perceive the universe as a single entity. Furthermore, you claim that
Godel’s theorem proves all axiomatic systems to be problematic, and yet here
you seem to be endorsing an axiom. And the fact that your only axiom amounts
simply to your wants and desires also says a lot.
“Now given these two clearly different approaches to an understanding of the
nature of the universe it should be no surprise that there are two different
If you think these are the only two approaches, then I suggest you’re locked
between two horns of a false dichotomy. Indeed, nowhere do you even address
the issue of metaphysical primacy, a matter which is unavoidable, even for
Platonists (and just by your own statements, we can infer what your position
is on this issue, even though it seems to have eluded your understanding).
Failure to deal with this issue is a sure sign of uncertain footing.
“The final word however should come down to scientific fact. Scientific fact
cannot however provide any evidence as to which approach, if either, is
correct. In all areas of philosophy the same two basic problems surface,
nominalist and platonic, depending on ones approach to the problem in
But even our evaluation of scientific facts is not exempt from the need for
sound philosophical foundations. So until you deal with your foundations,
you’re trying to reason in mid-stream.
“And the problem of God is a genuine problem.”
Only for those who confuse the arbitrary with reality. And without a
rational philosophy to enable one to distinguish between the two, such
confusion is inevitable.
“It is inadequate (and pathetic) for someone to point at the bible and say
so-and-so is true because the bible says so.”
Agreed. But even though it’s both inadequate and pathetic (not to mention
naïve), I still encounter Christians who practice this habit all the time,
even among highly educated apologists.
“Any decent Theist would have to agree that the bible is a not a document
which has anything to offer to serious scientific/philosophical debate.”
Good luck finding one.
“It is equally as pathetic and inadequate for an atheist to point at the
bible and say its crap, therefore God doesn't exist.”
Not if the god in question is the Christian god, the believer in question
holds that the Bible is the “inerrant word of God” and “saying it’s crap”
consists of pointing out fatal flaws in the Bible. That’s perfectly
“The issues are far more finely balanced than you atheists seem to be
I don’t think so, not in all cases anyway. How can one say there is balance,
for instance, between those who embrace reason consistently, and those who
“Now that term time is almost finished, I shall be content to engage in
serious debate with any atheist who is genuinely willing to tease out the
problems and arguments in a rational, scientific and non-point scoring
fashion. If all out abuse is what you would prefer, I am game for that too.”
As a Platonist, you naturally reject reason as well. So why should one