I was going to follow up the previous post on Rand with a few comments but Triablogue beat me to it. There are also some excellent comments on the post made by Dominic Tennant in the course of a running argument with someone called John Donohue. Tennant leaves me with very little to say on Rand's 'existence exists' axiom. But fortunately it leads me to another thought that had been in the back of my mind, about supporters of Rand. I judge the worth of a writer by reading them. But also instructive to read what their supporters say. Supporters of Rand, in my experience, tend to be shrill, and philosophically and logically illiterate. Perhaps that tells us something about Rand?
Tennant points out the 'Existence exists' is incoherent - existence is commonly regarded as a second-order property. Not by everyone, I should point out, but certainly Frege's view that existence is a second-order predicate is accepted by nearly all those in mainstream analytic philosophy. Nor is Donohue's restatement, "whatever exists exists" in any way useful, because it is either merely tautological and doesn't tell us anything, or it is equally incoherent (for it dubiously assumes that existence is a first-order predicate).
Donohue objects "All truth discovered by Objectivism is through induction, and all induction is consistent with the constraint that all existents named/claimed in the induction must actually exist in objective reality". Tennant immediately objects that if the entire worldview is inductively inferred, there is no certainty in it, for induction is an informal fallacy. Donohue objects that induction is not a fallacy, and that its goal is to deploy reason with greater and greater precision until a given proposition/claim achieves a position of "true" and "certain" within the context of human knowledge. Tennant objects that he cannot be serious. Induction is an informal fallacy—it is a kind of logically invalid inference which may nonetheless yield true results. "In logic, a type of nonvalid inference or argument in which the premises provide some reason for believing that the conclusion is true. Typical forms of inductive argument include reasoning from a part to a whole, from the particular to the general, and from a sample to an entire population. Induction is traditionally contrasted with deduction. Many of the problems of inductive logic, including what is known as the problem of induction, have been treated in studies of the methodology of the natural sciences. (Britannica Concise Encyclopedia, 'induction'.)"
As Tennant correctly points out, what Donohue is describing here —"greater and greater precision"—is characterized by deduction. Induction works in the opposite direction: from greater precision and certainty towards less and less of the same. How can Donohue not be familiar with the problem of induction? How can he not be aware that absolute certainty is not guaranteed by merely inductive inference? Perhaps this is because Donohue has only read Rand, which does seem consistent with his ignorance of basic logical concepts. "Next time, take a Logic 101 course and read some introductory philosophy before you head out into the real world and try to pontificate on a blog published by people who have a clue and can call your bluff."
All very true, and remember that Donohue is one of the more articulate supporters of Rand. This began with problems at the Wikipedia article on Rand. Rand supporters turn up in large numbers to make sure that any 'objective' assessment of Rand's work is impossible, and they wear out the more logically-minded editors with this endless logically illiterate ranting. There is nothing in Wikipedia's policies that prevents this happening. Everything on Wikipedia is done by 'consensus', even if that is a consensus of idiots. This would not have mattered in the days when Wikipedia was a tiny website run by a dedicated band of enthusiasts. Now it really is used by everyone on the planet. If only it really were the sum of all human knowledge. Governments are now forcibly taking over banks. Why can't they forcibly take over Wikipedia?
35 comments:
"Governments are now forcibly taking over banks. Why can't they forcibly take over Wikipedia?"
I looked for irony. Could not see any. If informed it was ironic will retract:
Scratch the witch doctor and you get Attila.
--- [Objectivist inside reference]
John Donohue
Pasadena, CA
Wikipedia has been shown to be edited by a very biased core group. In some cases postings citing data critical of anthropogenic global warming repeatedly removed. Similarly, hypocritical or blatantly incorrect statements by spokespersons of the AGW view have been removed... usually on false grounds of being improperly cited. This was reported in the National Post a few months ago, by a journalist who repeatedly tested the Wikipedia reviewers to see what would happen.
I am reluctant to get into the induction argument, save to say that Donahue is correct. Deductive logic cannot exist without prior inductions, period. The trick is to properly use induction, without overextending — a common error.
Why can't deductive logic cannot exist without prior inductions?
"The trick is to properly use induction, without overextending — a common error."
Eh?
Response to Ocham:
Induction is the procedure of observing a related set of things, attributes, actions or relationships. Repeated instances of the same phenomenon suggest, a certain commonality may indicate a reliable principle or rule about Reality.
Only once that induction and others are clearly reliable can they be used deductively. As one example consider this deductive syllogism:
All men are mortal;
Socrates is a man;
Socrates is mortal.
The syllogism could not have been generated with the inductive inference of the first premise.
Induction certainly has its challenges.
To use a very common example:
I have seen twenty crows.
Every crow I've seen is black.
At this point I will tentatively conclude that "all crows are black".
After a number of repetitions of this process, we may assert, with certainty that "all crows are black". Epistemically, this is the procedure most children use as they learn thousands of first words. They may initially think all dogs look like Golden Retrievers, the family pet; a step akin to the first one, above, that is based on a very small sample. However, they soon grasp that there are other animals that have definite similarities to the family dog, but they are not Golden Retrievers. Their grasp of the concept "dog" expands as they grasp that their initial induction was insufficient.
The difficult question becomes, for each phenomenon of interest, how many instances are needed before certainty becomes possible.
E.g. yes, there are albino crows. That fact does not eradicate the epistemic value & epistemic certainty of the initial inference. One simply retains the biological (& metaphysical) exception to the rule. The same applies to "all swans are white." Australian black swans are a color anomaly.
In reasoning (epistemically) the inference remains valid, & even certain, when properly retained!
Many inferences are without such exceptions (e.g. "all men are mortal"). Consequently, the process of induction is THE primary, and absolutely inescapably necessary, method of grasping Reality.
There are procedures to form inductive inferences properly, that involve identifying what is essential and what things are derivative. The Black Swans are still Swans, and their color with respect to the induction is, in practice, derivative. There is no such derivative feature in "all men are mortal" etc.
...because all concepts are derived through induction. (unless you believe in some form of divine revelation). The existents available to a deduction can only be identified by the human consciousness through induction.
John Donohue
...and Richard is correct that (contrary to claims posted elsewhere) induction itself is completely sound and more than sound. However, the execution of your induction to identify truth must be free from fallacious argument and free from existents not previously proven true through other induction.
John Donohue
Yes I know all that stuff. I was questioning the claim that deductive logic cannot exist without prior inductions. Why not?
"All concepts are derived through induction. " Discuss.
Richard said,
Induction is the procedure of observing a related set of things, attributes, actions or relationships. Repeated instances of the same phenomenon suggest, a certain commonality may indicate a reliable principle or rule about Reality.
Why do they suggest this? You're presupposing the uniformity of nature without justifying it. Or are you just using induction again? Begging the question?
All men are mortal;
Socrates is a man;
Socrates is mortal.
The syllogism could not have been generated with the inductive inference of the first premise.
False. As a Christian foundationalist, I can know that all men are mortal without requiring inductive inference (cf Romans 5:12).
The trick is to properly use induction, without overextending — a common error.
Interesting. I'd love to know how one can tell when one is overextending and when one is not. Wait, don't tell me! Is it by induction? Should we bake a question-begging cake with petitio principii icing and a delicious assuming the consequent center?
John said,
...and Richard is correct that (contrary to claims posted elsewhere) induction itself is completely sound and more than sound. However, the execution of your induction to identify truth must be free from fallacious argument and free from existents not previously proven true through other induction.
There's that philosophical illiteracy again John. Did you know that "sound" in logic means "valid and true"? Since induction is an informal fallacy (ie, a form of nonvalid inference), as I've pointed out to you a couple of times now, it's simply inappropriate to use the term "sound" in reference to it—let alone "more than sound". That is quite an astounding claim. I would be fascinated to hear your justification for it.
Regards,
Bnonn
ask yourself, "If I disavow revelation and I disavow induction, how do I identify any and all existents with which to perform deduction?"
John Donohue
Ocham, the point was that at least one premise of a deductive syllogism entails a conclusion arrived at by induction. Further, many of the words used in the process of generating a syllogism arise from the inductive aspect of concept formation.
I don't think I said *all* concepts arise by induction, but the great majority do. The notion that Science is based on deductive logic (K. Popper) is, thereby, substantially flawed. One must observe Reality, and form concepts about things, actions, attributes and relationships, before any science is even possible. I can see that certain scientific ideas may become concepts as a result of deduction.
Perhaps Donahue can correct me, but miles per gallon (mpg) is a concept achieved by the integration of two abstractions: distance traveled and liquid volume of fuel consumed in doing so.
What would be an example of a concept obtained solely by deduction? At the moment I am drawing a blank... which always means "time to stop".
I noticed Maverick Philosopher has smeared Rand in a post that presents no rational argument whatsoever; and he has disabled comments. There is something rationalistic and bluntly craven about both actions, not to mention unprofessional.
There is no need for correction Richard; I too am awaiting some indication how any cognition can start from deduction. If induction is fallacious in toto, how does one validate the identity of the existents involved in a deduction? Those slamming induction will hopefully respond.
Note, however, that one poster has already done so and the answer is "divine revelation" complete with chapter and verse citation.
I am open to hearing alternatives to the revelation method of validating truth.
Also, I indeed saw that despicable smear job by Maverick Philosopher. Mix that with the fuss over the Wikipedia article, complete with a wish by Ocham to confiscate Wikipedia(!), and you have to sense that panic is afoot.
John Donohue
Pasadena, CA
Bnonn
Induction per se is only a fallacy in your world view. I'll thank you to stop calling me philosophically illiterate and when you do I'll stop pointing out your parochialism in this respect.
John Donohue
I suggest induction as being as I explain it because that procedure is the means of identifying commonalities in nature, wherever they may be found. It precedes all other forms of objective knowledge.
If nature did not have commonalities it would be a 'place' of constant violation of all natural laws, of constant arbitrary flux. No entity could exist, let alone one that could question "the uniformity of nature". You, Dominic, are all the evidence you need.
The rest of that question set is puerile baiting.
***
As a Christian foundationalist you accept arbitrary revelation, however you wish it to might 'appear' to you. Your revelation, to you, is absolute & inarguable, but independent of any objective reality or justification. It is no more verifiable than the revelations of a Buddhist monk or Osama bin Laden. You have no case for discussing 'reality' with anyone on such subjective terms, because such terms have no referents in Reality.
Romans 5 (for those not familiar):
12 "Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned."
So, Men are mortal because Adam sinned by eating of the fruit of.... wait for it.... the Tree of Knowledge of Good and Evil (Genesis 2:17). God wanted human beings to be ignorant animals. Then, demonstrating His Almighty sense of justice, he made all innocent descendants of Adam and Eve suffer for their 'sin'. How dare Dominic challenge any reasoning skills? By demanding more 'reasonable' answers, regardless of how unreasonable his own may be, he is personally furthering the sin Adam and Eve committed against Dominic's professed God.
***
In some respects, the means of grasping when an induction is approaching certainty, is similar to ascertaining a suitable sample size for statistical analysis: the greater the variation in the sample the larger the sample population must be. However, and this is crucial, the process must focus on essential characteristics pertinent to the commonality observed.
Each case of induction necessarily has its own 'N' number of observations before an inductive evaluation can justify further consideration. In some cases N may be quite small, even N=1, whereupon the principle being inferred is absolute. E.g. slamming one's finger in a car door allows for a pretty clear inductive inference.
Again you stoop to puerile baiting.
***
Induction itself is not a fallacy, though there are fallacies OF induction such as slothful induction, hasty generation etc. Discarding induction because some inductions can be faulty is equivalent to discarding language because some people lie.
More puerile baiting.
I'd like to acknowledge Ocham for keeping comments open, even if moderated. Other blogs opposed to Objectivism who have recently initiated disagreement are either closed to comment or are not posting every submission.
Naturally when moderating if the comment is abusive it would need to be rejected. I have made some sharp statements on this thread and yet they have been accepted.
For the record, none of my submissions to Ocham have been refused. So even though we apparently are true antagonists, credit is due. Thanks.
John Donohue
Pasadena, CA
>> For the record, none of my submissions to Ocham have been refused.
Indeed not but to be honest this is because I like to see people dig large pits for themselves :-)
I accept that motive, if that's what you think is happening!
Okay, here is my first admission of philosophical naivete:
While long aware of Hume et al being un-fans of induction, and radical skeptics believing knowledge is a matter of arbitrary construction but bragging about that as if it is an absolute truth, I have never encountered a belief system that validates definitions based on revelation, and/or believes deduction can establish concepts, and I mean actually believes it and contends it is a modern, rational philosophy. This is new to me.
I can't specifically attribute that position to you Ockam; it is being explicitly forwarded by another poster, Bnonn. So I'll just say if you subscribe to that view, then this applies:
That is a huge pit the likes of which takes my breath away.
As for deduction, it can only succeed in identifying an existent if the concept that subsumes it has been rationally and universally -- universally in the context of validated knowledge -- proven. By induction.
John Donohue
Pasadena, CA
John said,
Induction per se is only a fallacy in your world view. I'll thank you to stop calling me philosophically illiterate and when you do I'll stop pointing out your parochialism in this respect.
Oh dear John. Oh dear, oh dear, oh dear. Truly, I'll be happy to stop calling you philosophically illiterate when you evidence a clue. But continuing to deny what any philosophically literate person knows isn't the way towards that goal. For example, someone who weighs in on philosophical debates, and who doesn't know that induction is an informally invalid form of inference, can justly be accused of philosophical illiteracy. But such a person might, having been presented with evidence such as a definition from Britannica, admit his mistake and stop repeating it. That sort of person would at least be considered reasonable and worthy of further debate despite his ignorance. But a person who refuses to admit his error is plainly not qualified to be in such a debate at all.
Look John, I'll say this once so you can no longer claim any ignorance, and if you continue to deny it that's your choice; it's no skin off my nose if you are so unreasonable you cannot admit a simple mistake. In fact, it serves pretty well to demonstrate the attitude and learning of Randian Objectivists for others: namely, not merely philosophical illiteracy but also willful stupidity, and the inability to interact with even the most basic criticisms, or correct themselves on the most simple errors.
There are two kinds of inference: valid, and invalid. A valid inference is one where the conclusion is necessarily true if the premises are true; ie, a deductive inference such as modus ponens. And an invalid inference is one where the conclusion is not necessarily true if the premises are true. There are, of course, many kinds of such inference, but they are again broadly divided into two categories: formal and informal. Formally invalid inferences are deductive arguments which, due to some fault of reasoning, fail to establish their conclusions necessarily. And informally invalid inferences are—wait for it—inductive arguments, which by definition cannot establish their conclusions necessarily. A person who does not know this is philosophically illiterate. Incidentally, I'd point out that calling you this didn't originate with me. I simply agreed with the observation. People better trained in philosophy than I have called you out for your patent and willful ineptness.
Richard said,
If nature did not have commonalities it would be a 'place' of constant violation of all natural laws, of constant arbitrary flux. No entity could exist, let alone one that could question "the uniformity of nature". You, Dominic, are all the evidence you need.
Of course, I never said that nature didn't have commonalities. I questioned your basis for presupposing the uniformity of nature. It's possible to have commonalities without uniformity. Reading comprehension fail.
The rest of that question set is puerile baiting.
It's interesting that you characterize a critique of your view which points out all of its question-begging, unjustified metaphysical baggage as "puerile baiting". Is this the psycho-analyzing I've heard about, by which Randians effectively dismiss refutations of their view by refusing to interact with them?
Your revelation, to you, is absolute & inarguable, but independent of any objective reality or justification.
False: strawman (also ambiguous, but I'll let that slide since it's false either way).
It is no more verifiable than the revelations of a Buddhist monk or Osama bin Laden.
False: strawman. Also, verificationalism actually died about fifty years ago because it's a self-refuting idea. You should probably familiarize yourself with philosophy written in the past few decades; this objection just reveals your ignorance. I take Scripture as properly basic.
You have no case for discussing 'reality' with anyone on such subjective terms, because such terms have no referents in Reality.
False: question-begging.
God wanted human beings to be ignorant animals.
False: strawman.
Then, demonstrating His Almighty sense of justice, he made all innocent descendants of Adam and Eve suffer for their 'sin'.
False: strawman.
How dare Dominic challenge any reasoning skills?
On the basis of their merits?
By demanding more 'reasonable' answers, regardless of how unreasonable his own may be, he is personally furthering the sin Adam and Eve committed against Dominic's professed God.
Interesting. Under your own view, isn't "sin" just an internal psychological event without any extrinsic value in the "real" world? I'm left wondering what you're so uptight about.
In some respects, the means of grasping when an induction is approaching certainty, is similar to ascertaining a suitable sample size for statistical analysis: the greater the variation in the sample the larger the sample population must be. However, and this is crucial, the process must focus on essential characteristics pertinent to the commonality observed.
Even if I accept all your unjustified premises, it's still question-begging to assume the uniformity of nature. You aren't engaging with the actual problem of your worldview, which is that it is entirely built on unjustified metaphysical assumptions. You just take them on faith.
Induction itself is not a fallacy, though there are fallacies OF induction such as slothful induction, hasty generation etc. Discarding induction because some inductions can be faulty is equivalent to discarding language because some people lie.
You're confused, but maybe not as confused as John. Induction is a fallacy in the sense that it is a form of nonvalid inference. That doesn't mean that induction is necessarily fallacious. It just means that it's an informally invalid form of reasoning.
Regards,
Bnonn
"Ocham, the point was that at least one premise of a deductive syllogism entails a conclusion arrived at by induction."
[1] Laws of logic are necessary
[2] LNC is a law of logic
[3] LNC is necessary.
Care to show which premise is arrived at via induction.
>>the point was that at least one premise of a deductive syllogism entails a conclusion arrived at by induction
Whether or not that is true, the claim I was questioning was "that deductive logic cannot exist without prior inductions" Thus
the moon is made of cheese
cheese is made of metal
entails
the moon is made of metal
That is 'deductive logic' and it is clear that it can exist whether or not any of the premisses are arrived at by induction (because I made the premisses up). Similarly this
A batchelor is an unmarried man
A an unmarried man is a man
ergo, A batchelor is a man
does not require any induction. The premisses are true because of the meaning of the terms.
As for this new claim that 'at least one premise of a deductive syllogism entails a conclusion arrived at by induction'. Do you mean 'requires' when you say 'entails'? What exactly do you mean?
To Ocham, correct.
I'd also add that there seems to be some confusions. The Objectivists seems to be conflating epistemology and ontology. That is, "how we know a premise" with "the structure of the argument." (Of course, the above two posts disprove even the epistemological point.)
re: Bnonn
will not be responding except to say i have already answered sufficiently.
John Donohue
Pasadena, CA
Dom, introduced the phrase "uniformity of nature". Uniform has several meanings. In context. I was using it as (via dictionary.com)
2. Conforming to one principle, standard, or rule; consistent.
3. [natural laws within Reality, as per #2] Being the same as or consonant with another or others.
Without such consistency there is nothing justifying his very existence. He would be more interesting if he dropped the slurs & baiting remarks, & properly identified "Straw Man" arguments since he has misapplied the term repeatedly.
Induction is a valid form of reasoning/inference, as explained, Dom's unsupported claim to the contrary notwithstanding.
The rest of his 'critique' is a ridiculous exercise in context dropping, or simple failures to grasp the full meaning of the premises he so readily ignores.
I see no reason to debate such a congeries of snide remarks & unreason.
Ocham, I mistakenly took it as a given that valid logical deductions require that"the premises are valid in Reality". Yes, one can create proper *syllogisms* that use invalid premises, but a valid conclusion requires valid premises, at least one being a product of inductive inference.
Another reason deduction depends on induction is that most words (sensu concepts) arise from inductive inference, or by some form of integration from other inductively formulated concepts.
>>>Ocham, I mistakenly took it as a given that valid logical deductions require that"the premises are valid in Reality". Yes, one can create proper *syllogisms* that use invalid premises, but a valid conclusion requires valid premises, at least one being a product of inductive inference.
You need to get the terminology right. We speak of ‘true’ or ‘false’ premises, but ‘valid’ or ‘invalid’ argument forms. A valid argument form is such that its premises cannot be true if its conclusion false. The conclusion is said to ‘follow’ from the premises.
If you mean that a true conclusion requires true premises, this is also not true.
Everything made of cheese is made of rock
The moon is made of cheese
The moon is made of rock
The argument form is valid. The premises are false. The conclusion true. If you mean that in a valid argument, the truth of the premises requires the truth of the conclusion, then this is correct. But I’m not sure you meant that
>>Another reason deduction depends on induction is that most words (sensu concepts) arise from inductive inference, or by some form of integration from other inductively formulated concepts.
No. Read a book on logic or philosophy, and avoid Rand.
"""All men are mortal;
Socrates is a man;
Socrates is mortal."""
The syllogism could not have been generated with the inductive inference of the first premise.""""
Actually you are correct: deductive reasoning via propositional logic applied to the 'real world" only works assuming the truth (or at least plausibility) of premises--(unless one wants to use only numbers and functions, perhaps). It's a point even many pro philosophers overlook: you can't really do much with formal logic, except show that given conclusions follow from premises (many of which cannot be proven). Paraphrasing the madman Wittgenstein, it's pretty much just tautologies and contradictions--forms, more akin to chess moves than to claims about empirical reality.
....well it works if you prove the truth of the premises.
1) i would not say 'plausibility' but stick to "truth." Yes, that carries a high burden since the definitions of the existents in the syllogism then have to be proven. The tool for that is induction.
2) if instead the premises, or indeed any existent named in them, are either known to be false, are arbitrary, or (here is my new-found one:) from revelation, then even if the logic is valid, the proof is indeed not a claim about reality. ['empirical' dropped']
In Objectivism we sometimes call proofs with arbitrary existents in them parlor games.
NOTE: there is a special case, in which everyone is non-controversially aware that the claim is about something imaginary from the get-go. That is okay, one can sort of 'get to the truth' with such a syllogism. I usually give the example of an argument from Middle Earth.
All hobbits have hair on their feet.
Bilbo is a hobbit.
Bilbo has hair on his feet.
I must 'prove' that hobbits exist, as well as 'hair' and 'feet' and validate the definition of all three.
Since we all accept this is an imaginary case, I stipulate Professor Tolkien's definition and identification of hobbits and their essential characteristics as true.
In claims that are not meant to be imaginary, however, the existents cannot be so stipulated; their definition and essential characteristics must be proven through induction.
John Donohue
Pasadena, CA
>>> if the premises are either known to be false, are arbitrary, or from revelation, then even if the logic is valid, the proof is indeed not a claim about reality.
Therefore
1. If God reveals to me the truth of a mathematical theorem, perhaps one whose truth is presently unknown, then this is not a claim about reality, even though it is true?
2. If someone states an 'arbitrary' proposition that happens to be true, this is not a claim about reality?
3. If the premisses are false but the conclusion true (see my example above), the not a claim about reality?
I have not had much contact with Randians before, but my impression so far is that they tend to make claims about truth and logic and metaphysics as though they were experts on the subject, which turn out to be nonsensical or silly, or ill-thought out.
Can any of the Randians here explain why that is?
Rand defined reason as “the faculty that identifies and integrates the material provided by man’s senses.”
That's actually superior to her "axioms," and shows a fairly common-sensical empiricism. Any bright college boy should identify the first somewhat Lockean issue: where does Reason itself derive from? One reason for all those metaphysical games that the naive empiricists (including Randians) reject was to show that Reason could not derive from the senses, or experience--any more than a baboon could play chess or do calculus (that said, I think a Frege and Russell better guides than say Kant in regards to these issues)
Randianism really becomes a type of relativism, tho' the RandBots would deny that. They might insist on the commonality of experience, but that itself is not logic: you can't prove for one that everyone perceives the same world--One can posit it, insist on it, but proof another matter.
Integrals don't hang on trees. At best, the empiricist or naturalist can ala JS Mills suggest chains of association and so forth, but until cognitivist work out the exact workings of mind, metaphysical issues will remain in force: tho' I will grant (unlike some of those associated with the Mav-P posse) that what appear to be "a priori truths" of logic and mathematics may have a physicalist and neurological basis.
A. Please stop using the word "Randians." The correct word is "Objectivists." The return courtesy is easily done: what do you prefer for yourself, if anything?
1) if you can suddenly prove a mathematical theorem, which can be validated to all fair rationals in the world, you are within your rights to say you got it from God if you wish. The rest of the world will validate it without referring to God inside the proof.
2) arbitrary existent, not arbitrary proposition. what is meant by arbitrary existent is one that has not been proven to exist prior to use in the premise.
3) no. but you will have won the parlor game.
John Donohue
Pasadena, CA
"J", Thanks for your very sensible expansion of the point!
John D, I love your use of the Hobbit logic example. It's fun and accurate.
Ocham,
On 1.
You began with an unreal premise, so what follows cannot stand. Let's suppose, for "Parlour Game" value, that the mathematical theorem is true. Your (hypothetical) revelation from God is no demonstration of its truth. If the content of the revelation, once examined in real world terms, is found to be true, then logic prevails from the latter reasoning, not from the former.
Even if metaphysically factual, the mathematical revelation is not epistemically true. "Truth" is an epistemic evaluation of facts about reality, not a revelation. A "fact" refers to a metaphysical existent (including actions, attributes and relationships).
Thus, epistemically, the revelation may be a 'claim' about reality, but as a claim it remains arbitrary until facts demonstrate its truth.
Unfortunately, you use the term "claim", which is rather a loose term. It can refer to the arbitrary or to an inference based on considerable evidence. These two senses of the term leave much room for equivocation. I am using it here to mean "a reference to certain Truth".
For the sake of clarity I must also distinguish mystical revelation from those subconscious integrations that provide sudden insight, which are also called 'revelations'. If the latter integrations are based in fact, then the insight has a greater chance of being a truth. Nonetheless, at first blush it is a postulate at best. That is, epistemically, it is not a certainty.
Consider a gambler claiming he knows the next toss of the dice will turn up 'boxcars' (double 6), and boxcars do indeed occur. He still cannot claim he 'knew' it would be boxcars, because he had no means to know. His initial claim was neither knowledge nor "truth". His claim was not even a postulate, it was a purely arbitrary assertion. His assertion has the same *status* as the mystical revelation, but without invoking another, prior, arbitrary assertion (God).
I do not know if the gambler's position has a name as an informal fallacy, but it is clearly irrational/illogical.
The Greeks postulated that everything consisted of minute particles (atoms), but had no proof. The notion was retained as a postulate, until modern research with radiation (beginning with Rutherford) began to elucidate the true existence of those particles. The Greeks were more honest than the gambler and the man whose mystical revelation provided him with the 'truth' of a mathematical theorem.
On 2.
Exactly, it is not a justified claim about reality, it is an arbitrary assertion. Any truth it holds about reality is coincidental in the same manner as the gambler's 'boxcars' claim.
On 3.
This is a variation of the same statement in number 2.
cont'd
Ocham you asked,
"...my impression so far is that they tend to make claims about truth and logic and metaphysics as though they were experts on the subject, which turn out to be nonsensical or silly, or ill-thought out.
Can any of the Randians here explain why that is?"
I'll try, perhaps another Randian can do better.
First, Randians vary in their understanding and expertise; e.g. I detect greater understanding in Donahue than I can claim for myself.
As a Randian learns principles and fallacies of various types, they become very confident of the truth of their knowledge. The abstract ideas connect to reality and to each other with such dramatic reliability that they become as apparent as observing a physical action. Their veracity becomes unassailable. This can be extremely grating to people who
a) consider academic honesty to include unending doubt, uncertainty, &/or rejection of absolutes;
b) use concepts loosely, even within their own profession, which causes them to accept faulty connections, unaware of their own equivocations and subsequent misapplication of concepts in their reasoning.
b) is the reason why non-Randians conclude that the Randian arguments are "turn out to be nonsensical or silly, or ill-thought out" —of course, Objectivism does not guarantee that any given Randian will:
*- express a point correctly,
*- grasp what the person, with whom he is debating actually needs to understand, or
*- have the time or space to explain in sufficient detail.
The more abstract a concept is the more of a conceptual hierarchy it hinges upon, and the extent of explanation needed might require a textbook. E.g. Fully grasping the two word summation of Objectivist metaphysics, "Existence Exists", requires a lot of integration between certain inescapable metaphysical and epistemic requirements. Every attempt to deny those requirements necessarily depends on their validity! Consider the absurdity of "How can I be sure I exist?" Who or what is making such a proclamation, to whom and where?? Yet, philosophers often seek to deny the inescapable fundamental that Existence exists, and/or that the laws of Identity and Causality cannot be escaped. Were those fundamentals untrue, it would be impossible to raise any subsequent philosophical or scientific ideas whatsoever. As Rand puts it, it becomes "anything goes".
On the use of concepts, to hit on a very narrow example, it is a common claim that "Objectivism is a false philosophy because it holds that its fundamentals are absolutes". That claim, that Objectivism is a false philosophy, IS an absolute statement: "Objectivism IS false"! The claimant has failed to keep to the meaning of the very words he uses (see b), wanting his [intellectual] cake and to eat it too. It is usually when caught in such contradictions that, rather than think things through for themselves, people resort to sneers, smears and insults. I have seen variations of this one conceptual confusion made by plenty of professional(!) academics and philosophers.
Actually I think Mav P dealt with Rand's "axioms" fairly effectively. For that matter, so have many philosophers with a somewhat skeptical bent, whether Hume or Popper. Rand's rather primitive "law of identity" may work for most common-sensical empiricism: yes a right triangle is a right triangle, and table is a table (well, at least for a few decades, or unless destroyed in a fire, etc.0). It doesn't work for say measuring the random decay of radioactive isotopes--the isotope decays at one rate for a few thousand years, and then at another for a few other thousand---, or many other concepts from Einsteinian physics or quantum mechanics. It doesn't really suffice for say atmospheric physics, and many other fields which depend on statistical inference--even say the so-called laws of economics (rules of thumb proven wrong all the time).
Russell wrote on this issue: yes common sense, naive empiricism, more or less suffices for the everyday world of main street, usually: tho' even then there are issues (say different languages). It doesn't suffice for philosophy or science.
That said, I think Miss Rand's "epistemology" was meant to be secondary to the Randian Heroics: fortunate favors the brave, or is it the few, or just the inheritors of large estates. (Rumors there are that Miss rand did not hate her bolshevik enemies that much either, once she realized that they understood some are more equal than others....and I suspect Ayn enjoyed a few wild nights in old Pasadena, eh: maybe hush hush with L Ron Hubbard and palsies. :-) )
I would like to second Donahue's rejection of the term Randians, as it is chosen to presume a faith in a leader. In contrast, "Objectivist" presumes someone who is pursuing a properly and purposeful objective understanding of the Universe, the people within it it, and of oneself.
J, not one of your examples contradicts the Law of Identity which has remained an absolute (as Truth) since Aristotle first grasped it.
The rest of your comment has nothing to do with Ayn Rand... you've been reading too many authors, who are ignorant of Rand, copying authors commenting on Rand, who are ignorant of Rand, copying...
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