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Is the "stolen concept" truly a fallacy?

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"Go ahead, attack the suggestion I gave! Who's stopping you?!" [LauicAcid] [italics added by TomL]

"What suggestions? Where?" [TomL]

Right where they were when I posted them in 95:

X is a deductive argument presentation iff X is a presentation of an argument for evaluation of entailment of the conclusion from the premises.

X is an inductive argument presentation iff X is a presentation of an argument for evaluation of likelihood of the conclusion from the premises.

"Well you're the one that brought it up! Why bother?" [TomL]

Because examples were given that are pretty much standard examples of common uses, but the explanations for the examples do not seem to square with common use, so for me to understand what the poster has in mind, I must be clear whether he intends senses of the terms from common use as part of his use and how his examples work for his use. Also, if you have a definition that departs significantly from ways a term is ordinarily used, then it is good to know that so you can guard against people misunderstanding you. Also, I was challenged on the matter of use, and I responded.

"You have asked how things are contradictory that are self-evidently so. For example:" [Tom L]

"using reason (which depends on validity the senses) to disprove the validity of the senses!" [JMeganSnow]

"Please explain how that uses a contradictory definition as opposed to assuming a proposition to disprove a proposition." [LauricAcic]

I did not just ask how the example is merely self-contradictory, but rather I asked how the example uses contradictory definition and I asked how the example is not an instance of RAA. Your leaving out those things distorts my question.

"The fact that reason depends on the validity of the senses is not a "proposition". Tell me why it is not a "definition"" [TomL]

The word 'that' in my question to JMeganSnow refers to the clause ' using reason (which depends on validity the senses) to disprove the validity of the senses', not to the propositition 'reason depends on the validity of the senses'.

"Who cares how people use it?" [TomL]

You mentioned that common uses for the terms may be incorrect. I just said you're free to show why. If you don't care to show why, then no skin off my nose.

"Then do so, instead of implying that a true definition comes from consensus rather than reality." [TomL]

Hold it right there. You just effectively put words in my mouth.

I have not posted anything that implies that a true definition comes from consensus.

"Oh really?" [TomL]

Yes, really.

"What the heck is that, then?" [TomL]

These are dictionary definitions that I believe reflect common uses:

"1 b : deduction: the deriving of a conclusion of a conclusion by reasoning: specif : inference in which the conclusion necessarily follows from the premises" [emphasis original]

"2 a (1) : inference of a generalized conclusion from particular instances"

But I think, to get closer to common uses, the above definition needs also to mention likelihood or a similar concept.

Note: In my previous post I should have said 'the common definitions are' rather than 'the common definition is'.

"The context is "reason"." [TomL]

How is reason a context in the sense you mentioned that people, using different definitions from yours, do so in contexts?

"Induction: the primary process of reaching knowledge that goes beyond perception through a process of valid generalization. Valid generalization, in turn, requires valid concept formation, and a hierarchy beginning with self-evident first-level generalizations, to which all generalizations must be reducable. It also requires the contextual discovery of causal connections using the methods of difference and agreement." [TomL]

Thank you for that, and it is more than asked for, since it not only defines 'induction' but discusses other concepts as well.

What do you take 'valid' to mean?

"Deduction: a secondary process of reaching knowledge that goes beyond perception by subsuming new instances of known generalizations." [TomL]

And thank you for that.

What form of logic is this:

If P then not-P.

Therefore, not-P.

"It most certainly depends on, at the very least, stating what you think the inconsistentcy is", thereby suggesting possible alternatives." [TomL]

One needs to state the alleged inconsistency, of if just questioning, explain why one thinks there is, or might be, an inconsistency. But doing so does not require one to offer an alternative proposition for the subject matter. For example:

If someone asserts 'A' but one shows how that implies 'not-A', thus a contradiction, then that is not thus required to produce another proposition, say 'B', to elucidate the subject matter, whether the subject matter be the migration of swallows or definitions of terms. And if someone asserts 'A' and it seems to one that it leads to not-A, and one says why one thinks that, then it is reasonable for one to ask why it does not. And if A is enunciated but it's not clear to one, or if others have given contradicting or different enunciations, then it is reasonable for one to ask for clarification.

"All you have done is say "this is inconsistent."" [LauricAcid]

For the record, I have not posted the sentence 'This is inconsistent'.

I've mentioned a few errors, and expressed that I sense inconsistencies (pending the terms being made precise), and I've given reasons for my thinking. If I've not given enough reasons in some cases, it's mainly because my initial questions were not even addressed.

"You have not [stated what you think the consistency is, thereby offering alternatives]." [TomL]

Below is a list of some of the points I've made and questions I've raised. Some of these remain without response:

46: Point about a definition of 'logic' not capturing the idea of 'entailment'.

66: Thoughts about whether FSC contradicts RAA, and contrary to your insinuation of dark motives, I suggested that they might not be in contradiction. However, since then, I've still not seen anything in this thread that resolves the difficulty.

74 and after: (1) Questions about the role of concepts, definitions, and contradiction in FSC, and attempts to clarify whether posters were in agreement on this or disagreement. (2) Remark that the examples seem deductive not inductive.

76: Request for explanation why the examples are inductive and not deductive.

80: Questions on this topic as invited by the poster.

82: (1) Mention that definitions offered are used by but relatively few people. (2) Examples of two arguments, asking why they are or are not deductive or inductive.

83: Question whether two particular sentence commits the fallacy. (If the second one commits the fallacy, then Objectivist philosophy of mathematics is inconsistent.)

86: Question whether there is a hierarchical dictionary. The importance of the question is that if there were conceptual problems with making such a dictionary, then there would be problems with the hierarchical view. (I'm sure you've noticed that common dictionaries are not hierarchical. Among the requirements for a hierarchical dictionary would be: hierarchy (including non-circularity) , (all?) definitions in genus/difference form, and adherence to essentialism. You've noticed that common dictionaries especially suffer from circularity. If this circularity could not be avoided, then there would be fundamental a problem with the hierarchical view.)

89: (1) Request for explanation of how genus/difference explains a certain definition of deduction and induction. (2) Corrected poster's assertion that I posted a denial of the hierarchical view. (3) Pointed out that poster had committed a non sequitur.

92: (1) Corrected poster by mentioning that conditionals don't imply their antecedents and that questions are not assertions. (2) Corrected poster by pointing out that I had not affirmed the hierarchical view. (3) Answered questions from poster, and refuted example without FSC.

93: (1) Corrected poster who had stated for me, incorrectly, my definitions of 'deductive' and 'inductive'. (2) Denied that usual definitions of 'deduction' and 'induction' harbor dismal philosophy. (3) Mentioned that since I don't hold the definition incorrectly attributed to me, I don't answer for it. (4) Asked poster to cite attribution of Aristotle.

94: (1) Fended suggestion that there's anything remarkable about asking questions but not offering answers. (2) Gave definitions for consideration.

95: (1) Answered poster that his question is irrelevant as to one of his previous statements being a non sequitur. (2) In response to poster, mentioned again point about a hierarchical dictionary. (3) In response to poster, asked again whether a certain sentence commits FSC. (4) Gave an additional example, and asked if it commits FSC, along with explanation of why it would at least appear that it does.

97: In response to poster, addressed again the view that questions and criticisms depend on having an alternative formulation.

99: (1) In response to poster, addressed again the view that questions and criticisms depend on having alternative formulation. (2) Fended posters ad hominem criticism and insinuation.

Edited by LauricAcid
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Free Capitalist

I don't usually form expectations about what people will read. Each person is free to read as much or little as he likes and that's fine with me.

The list of my posts at the bottom of that post is not something I would normally post, but it was motivated by TomL's charge that my posts had not been substantive in certain ways. I now feel that that list probably does not serve the purpose I intended, and, in retrospect, I would not have posted it. Aside from the list, my post is just about twice as many words as the post to which it is in response.

y_feldblum

The post is a point by point reply. It is not intended as an essay nor to offer any attractions of organization or structure other than to make available the on point responses.

I will be using the indigenous quote tag for this forum in future posts, which will make my posts less visually monotonous.

My post 82 in response to you is not onerous and welcomes your reply.

/

Since lack of focus was complained about, I've extracted these questions, which I believe have important bearing on the issues of this thread:

1. What is the meaning of 'valid' in TomL's definitions?

2. What form of logic is this:

If P then not-P.

Therefore, not-P.

3. What conceptual difficulties would there be in making a hierarchical dictionary?

4. Is the fallacy committed here?: "An arithmetical sequence extends into infinity, wihout implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence."

5. If it is a hierarchical fallacy to assert that property is theft, since the definition (or concept?) of theft depends on the definition (or concept?) of property, would it be a hierarchical fallacy to mention criminality in an anarchy, since the definition (concept?) depends on the definition (concept?) of laws of a government?

Edited by LauricAcid
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Marc K. (Post #85):

You asked "... if I said: “you cannot prove that you exist or that you are conscious,” isn’t my inversion of the hierarchy reason enough to dismiss this fallacious statement out of hand?".

If you said "jrs does not exist." or "jrs is not conscious.", then I would dismiss your statement as clearly false. But if I reached it as the conclusion of some chain of reasoning, then I should go back and find my error.

If you said "jrs cannot prove that jrs exists.", then the answer would depend on what standard of proof is required. If I could just manifest myself by posting a message, then I could prove it to you. If you want me to deduce my existence from the axioms of ZFC, then I could not.

I do not think that vague hand-waving about "hierarchical inversion" is going to provide an answer.

Marc K. (Post #88):

You said "Whenever someone uses a concept in an attempt to deny the existence of same concept you can be sure they are employing the Fallacy of the Stolen Concept.".

Please convert this into a precise definition of FSC.

Free Capitalist (Post #91):

Let me give my definitions:

Induction is the aspect of reasoning which takes particular concrete facts and looks for a common (and hopefully essential) pattern and uses it to create a universal proposition.

Deduction is the aspect of reasoning which explores the consequences of those universal propositions by instantiating them and combining them with other facts.

LauricAcid (Post #95):

Regarding "An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence.":

This statement from Objectivist scripture is poorly worded. Let me suggest an alternative:

<<Any actual sequence has an end; but one may speak generally about properties of any sequence which is longer than some lower bound.>>

TomL (Post #100):

In your definition of "Induction", you said "... It also requires the contextual discovery of causal connections using the methods of difference and agreement (which I can explain further if you like).".

Please do explain further.

You said "Thus, any deduction presupposes prior inductions, and thus induction has primacy over deduction.".

I agree that induction must precede deduction. But what do you mean by PRIMACY in this context? Surely deduction is more certain than induction, assuming the truth of the inputs.

LauricAcid (Post #101):

Regarding a hierarchical dictionary, you said "... common dictionaries especially suffer from circularity. If this circularity could not be avoided, then there would be fundamental a problem with the hierarchical view.".

Clearly, it is impossible to write any dictionary without either using undefined words or defining words in circles.

I think that the Objectivist view is that some concepts are so basic that one cannot give formal definitions for them in terms of simpler concepts. They must be defined ostensively (pointing at examples).

However, in such cases one could confirm and clarify the ostensive definition by giving a formal definition in terms of higher level concepts.

This does not detract from the hierarchical nature of concepts, but is merely a limitation on what can be done with formal definitions.

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jrs:

Stolen Concept

FSC is used to refute objections to the initial set of axioms. But those refutations seem gratuitious. If the axioms are self-evident, then one doesn't need to use FSC to refute objections to them. My response to objections to the axioms would not be FSC but this: "The axioms are self evident. And you couldn't even meaningfully talk about these things (existence, identity, and consciousness) without assuming the axioms."

Earlier you asked about my suggestion that FSC/RAA might be resolved by distinguishing meta-levels. I have only a hunch about this, but the idea is to recast invocations of FSC not as showing contradictions in the "object language" of the criticized argument but as showing that the criticized argument is a meta-argument that uses a method of argumentation in its "meta-language" that it denies as a method of argumentation in it is "object language." For example, "Astrological reasoning proves that you can't tell your future from reading a horoscope." So, 'You can't tell your future from reading a horoscope' is in the "object language", while 'Astrological reasoing shows' is in the "meta-language'. Hence there's no RAA, since the two statements are not direct contradictions within a single theory within a single language. Well, my example probably doesn't work out quite right, but maybe there's something there.

Dictionaries

It's a given that there must be primitives, so that's not the kind of difficulty I wonder about. Granted, an ordinary dictionary must be circular since every term is defined. So a hierarchical dictionary wouldn't suffer that 'from the git-go' limitation. But what happens when we get down to the level of cabbages and kings? We function with a network of concepts. Aside from the complexity of this network, could we truly break the mutual-interdependence of our concepts to codify a hierarchy? (Didn't Rand mention that she envisioned a rigorous codification?)

Infinity

I suspected that the answer to the quote would be the one you gave, pretty much along the lines of the 'potential infinity' explanation. But then how do you (not you personally) say anything about all natural numbers? And what is a line? And how do you do real analysis without infinite sequences? If points, which are "infinitely small", are allowed as concepts of method, then why not just allow infinite sets, which are "infinitely large" as concepts of method too? I don't see what the fuss is about. Granted, you could work with an intuitionist logic - but the semantics are so daunting that I'd think you'd be just as happy allowing infinite sets as concepts of method.

There's no objectivity without effective method. And, at least in classical logic first order logic, as far as I know, you need an infinite set of symbols for the recursive functions that formalize the language. Why would Objectivists forsake effective method when all they have to do is allow that infinite sets are concepts of method?

Deduction and Induction

You mention certainty and degrees of it, but don't include it in your definitions. Why? Or is this provided by your 'consequence' for deduction and 'hopefully' for induction? Why mediate with 'universals'? In other words, why do you prefer your definition over 'deduction - entailment'; 'induction - probability'? Those seem essential to me, while the universal/particular distinction does not. This is seen in the fact that some deductions do move from particular to universal. Also, facts and instantiation seem hardly essential to deduction.

Edited by LauricAcid
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I will be using the indigenous quote tag for this forum in future posts, which will make my posts less visually monotonous.

My post 82 in response to you is not onerous and welcomes your reply.

/

Since lack of focus was complained about, I've extracted these questions, which I believe have important bearing on the issues of this thread:

1. What is the meaning of 'valid' in TomL's definitions?

2. What form of logic is this:

If P then not-P.

Therefore, not-P.

3. What conceptual difficulties would there be in making a hierarchical dictionary?

4. Is the fallacy committed here?: "An arithmetical sequence extends into infinity, wihout implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence."

5. If it is a hierarchical fallacy to assert that property is theft, since the definition (or concept?) of theft depends on the definition (or concept?) of property, would it be a hierarchical fallacy to mention criminality in an anarchy, since the definition (concept?) depends on the definition (concept?) of laws of a government?

Shorter, but not much better.

1. I don't know.

2. I don't know. What form of logic do you think it is?

3. Every dictionary is a hierarchical dictionary, to the extent that it lists genus and differentia in each definition. So, none.

4. I don't know. Why do you think there might be?

5. I don't know. Perhaps. But one stolen concept with anarchy is the expectation that the means of establishing a free market will be bought and sold on the free market.

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I don't usually form expectations about what people will read. Each person is free to read as much or little as he likes and that's fine with me.
But you should form expectations about what people will read. After all, your purpose here, just like mine and everyone else's, should be to foster communication, express your thoughts in a clear and clearly understood manner, and strive together to achieve some sort of resolution. So clarity of communication should be your prime concern, rather than a secondary one. Given this, y_feldblum's comment about your (and presumably jrs') posts being an undifferentiated mass are very valid. The spacing between lines is arbitrary, there is no indentation, no easily visible differentiation between various subjects and sub-headings. You even make almost no differentiation between addressing me and addressing y_feldblum -- just from a simple and quick scanning of your and jrs' posts, it is impossible to tell where they are in their thought process, or whom it is the heck that they are replying to. That is why it is so difficult and tedious to read and reply to you people's posts, and I request that it be more readable before I engage in further discussion with you on the subject.
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y_feldblum

1. I don't think 'valid' is a concept used just by TomL. If I'm not mistaken, it has a role of some importance in Objectivism. If we don't understand the concept, then our understanding of logic is not firm.

2. The example was:

P -> not-P

Therefore, not-P.

That is deduction. If your definition of 'deduction' does not tell you that the above argument is deductive, then either your definition is inadequate or your use of it is.

Aside from that, it seems that FSC is often used this way:

P -> not-P (in some non-Objectivist argument that steals a concept)

Therefore, P. (the Objectivist conclusion that "takes back" the concept that was stolen)

And both that and the first example are valid. But that only means that from a contradiction anything follows. In other words, P is established with no more basis than not-P. RAA reflects that principle. FSC does not invalidate arguments; it just contradicts RAA. Or at least it needs to be explained why that is not the case.

3. Ordinary dictionaries are not hierarchical since they're circular and don't show a hierarchy (it's not true that ordinary dictionaries give all definitions in genus/difference form). Additionally, according to some people who believe concepts are hierarchical, ordinary dictionaries include definitions that are irrational, as was discussed regarding 'deductive' and 'inductive'.

4. The fallacy in that example is assuming an infinity to deny one. This is tempered by explanation that the infinity is not really assumed. But I think the slip of the tongue in the first sentence may still be revealing.

5. If crime is violation of the laws of a state, then there are no criminals in an anarchy. So Rand committed the fallacy. Well, that is, unless we refuse to give her the benefit of the doubt and take her meaning of criminal in that context not to mean 'coercer'. But that suggests that one could give Prodhoun the benefit of the doubt and instead of making a strawman out of a slogan, one would look at his actual arguments to see whether his terms 'property' and 'theft' are left imprecise in the slogan as is Rand's 'criminal'.

What do you mean by 'the means of establishing the free market' and would you give more context of your point and explain more about it?

/

Free Capitalist

In my previous posts, the spacing of my lines was not arbitrary, indentation is not required for block paragraphs, and paragraphs were explicit as to whom I addressed (and where not explicit, to be assumed in general address).

But I expect you've seen that I already posted my intention to accommodate concerns for easier readability and made good on that with my two previous posts and this one.

And while you have problems following jrs's posts, I do not. To whom he's addressing, and the flow of his thoughts is quite clear to me.

Since you've made an issue of this, I will not only keep it in mind for myself, but for the posts of others, and follow your example so that I will be willing to comment upon things that make other posters' messages less communicative, including flow of thoughts, formatting, grammar, and spelling. Thank you for raising the bar.

Edited by LauricAcid
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4. Infinities do not exist in reality. They are concepts of method which one might use in solving problems, and as such are perfectly valid.

5. Crime is often used in a moral sense, as versus in a legal sense. Did you quote Ayn Rand?

The purpose of government is the establishment and support of the free market. The free market does not exist without an objective constitutional representative republic, operating on laissez-faire capitalism, to establish and support it. Anarchists think they have a free market in governments, and so have inverted the relationship between government and free markets, or have stolen the concept of free market, using it where they have no right to use it: its necessary context is that a government has established it and supports it, yet the anarchist has denied the context of a government to establish it and support it.

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4. Whatever the fate of non-existence infinities have in reality, I'm glad you agree that they are at least valid as concepts of method. And unless a set theorist commits to asserting the existence of infinities in reality, then there hasn't been shown anything incorrect with talking about infinity in set theory.

5. The point you just made about the word 'crime; and how Rand may have meant it is exactly the point I just made in my previous post.

If you define 'free market' as ' laissez faire capitalism in a constitutional republic', then of course there is no free market in an anarchy. But that does not entail that laissez faire capitalism is impossible without a constitutional republic.

Edited by LauricAcid
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4. I'm not sure where you're going with that.

5. I think you misunderstand what I said and what a stolen concept is. Remember, concepts have context. I think you're mixing up contexts.

I'm not sure what you're trying to tell me (re: anarchy), and how it's related to what I said.

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4. Some Objectivists seem to think that set theory contradicts Objectivism. I'm wondering why.

5. I don't see what I misunderstood about what you said about the word 'crime'. I believe I agree with what you said. What contexts do you believe I'm confusing and how am I confusing them?

0. Do you agree that your argument does not entail that laissez faire capitalism is impossible without government? If you do, then what is at stake for you other than the definition of the term 'free market'?

Edited by LauricAcid
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Dictionaries ...  could we truly break the mutual-interdependence of our concepts to codify a hierarchy?

Infinity ...  how do you (not you personally) say anything about all natural numbers? ...  you need an infinite set of symbols for the recursive functions that formalize the language.

Deduction and Induction ...  You mention certainty and degrees of it, but don't include it in your definitions. Why? ...  Why mediate with 'universals'? In other words, why do you prefer your definition over 'deduction - entailment'; 'induction - probability'? Those seem essential to me, while the universal/particular distinction does not. This is seen in the fact that some deductions do move from particular to universal. Also, facts and instantiation seem hardly essential to deduction.

Dictionaries: I would suggest that each word in a hierarchical dictionary have a RANK assigned to it and that the rank of a word be given in the dictionary entry for that word. Words of rank 1 would be those which must be defined ostensively with the formal definition as a back-up. Words of rank 2 or higher would have formal definitions which only use words of lower rank than themselves. Would this satisfy you?

Infinity: Personally, I would keep the infinities and quantification over natural numbers or sets or whatever.

I think you are wrong about needing an infinite number of symbols. In particular, one could regard "X127" as four separate symbols to create one variable. And one could have a recursion operator to create expressions for recursive functions.

Induction and Deduction: I think that the introduction or elimination of Universals is the essential difference. The rest of it is just to try to add some context rather than just say:

Induction = Introduction of Universals.

Deduction = Elimination of Universals.

...  Aside from that, it seems that FSC is often used this way:

P -> not-P (in some non-Objectivist argument that steals a concept)

Therefore, P. (the Objectivist conclusion that "takes back" the concept that was stolen)

And both that and the first example are valid. ...

(P => ~P) => ~P is a tautology, but

(P => ~P) => P is not a tautology.

So RAA is valid; but taking back the "stolen concept" is invalid.

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jrs

Stolen Concept

TERMINOLOGY: I'm concerned that people might think that 'FSC' stands for the fallacy (or supposed fallacy) itself. Instead of 'FSC', I'm going to use 'SCW', suggestive of 'stolen concepts are wrong to use' which is close enough to 'there is a fallacy of stolen concepts'.

My view is that If SCW is propositional and its application is within a theory and isn't from a meta-theory to a different theory, then it's invalid.

But there's still doubt that SCW is propositional. Pro-SCW posters say either that SCW is about hierarchy violation in concept formation or that SCW is about incorrect definition. (Though, these may be equivalent anyway, at least it is so argued, it seems). In either case, if you can't convince people that these are also equivalent to a propositional form, then I don't think you'll get any coconuts to fall from the trees.

Aside from that, I think there is a compelling form of reasoning that is so close to SCW that it can be hard to tell them apart. Here's an example from an article:

"[...] if the notion [of absolute identity] is problematic it is difficult to see how the problems could be resolved. since it is difficult to see how a thinker could have the conceptual resources with which to explain the concept of identity whilst lacking that concept itself." [http://plato.stanford.edu/entries/identity]

This seems to make sense. If one can't argue that there is not absolute identity without using the concept in the argument, then what principles would one use to make any argument? In other words, rationality depends on acceptance of absolute identity. If one doesn't accept absolute identity, then one might as well be irrational, in which case, there's not even a context for an argument either for or against absolute identity. That is to say, if someone assumes that there is absolute identity to disprove that there is, then one has to say to him, "Oookay, let me know when you get back to the world of reason."

Why I think this is not SCW is that the proposition that there is absolute identity is stated in some theory, while using the principle that there is absolute identity is reasoning about the theory. So, suppose the fellow does, within a theory, disprove absolute identity. That is, he proves not-E, where 'E' stands for 'There is absolute identity'. And he used absolute identity as a background assumption in the logistic system he used for the proof. But that background assumption is not the proposition E, since the background assumption is in a meta-theory. So the background assumption is (meta)E. So you get:

meta(E) -> not-E.

But you don't get:

E -> not-E

So this is not the same as RAA.

So axioms that truly do require accepting them at a meta level to deny them at the lower-theory level do have the armor of SCW-like reasoning. But this meta level distinction is stringent. Riffing on a famous example, Let 'S' stand for 'I know that I exist as I am that consciousness that has the experiences that I have, but there is no proof that anything other than me and my experiences exists. And if someone else exists, he would have no proof for himself that he and his experiences are not the only thing that exists.' Someone arguing for anti-S might say, "Then you won't mind if I kick that chair from under you." I think that's invalid SCW. Even if the pro-S guy says (actually, the anti-S guy experiences that the pro-S guy says), "No, don't do that!," it's still not proven that the anti-S guy is not just experiencing that in his own world of experience.

So, if SCW is used within a theory, I think it is invalid, and I think it may be used that way not too infrequently. Moreover, its use can be a kind of cloaked question begging in a way similar to the way the anti-S guy is question begging by assuming that "No, don't do that!" is not just coming out of his own mind.

/

Dictionaries

Such a ranking is fine, but it would be question begging to assume that we could untangle even our everyday concepts out of the tangled mental networks in which we use them. And the mere imposition of a ranking does not ensure that all the definitions would uphold such demands such as defining properties must be essential ones, etc.

/

Infinity

We can't say that the set of symbols is S = {x, 0, 1, 2, 3, 4 , 5, 6, 7, 8, 9} since what we'll apply the recursion theorem to is not S, but rather the set, S', generated by your notation from S. And S' is an infinite set. Also, I'm not don't know what you mean about a recursion operator. What I mentioned was not a concern about creating expressions for recursive functions, but rather the one I just mentioned about applying the recursion theorem. [i am very much interested in your thoughts on this, but perhaps we should continue this particular tangent in the recently active thread about infinity.]

/

Deduction and Induction

I like your revision better since it pares down to a simple contrast: introduction vs. elimination. But it doesn't seem to work. Aristotle's AAA:

All logicians are frogs.

All frogs are stereoscopic.

Therefore, all logicians are stereoscopic.

That's deductive, but just moves from universal to universal.

Our opposing suggestions center on two pairs of contrasts:

Yours: introduction of universal vs. elimination of them.

Mine: entailment vs. likelihood

I think the advantage of your notion of induction is that it better describes everyday inductive thinking (perhaps even to generalize to thought that is so basic that it's even "pre-logical"?). But your notion of deduction has the disadvantage I just mentioned.

I think the disadvantage of my notion of induction is that it leans strongly to more formal or scientific induction and does not do well at capturing everyday induction.. I think the advantage of my notion of deduction is that it is comprehensive to include all inductive arguments and is based on the essential property of deduction, which is entailment, not the inessential, and even often missing, property of moving from universal to individual.

Edited by LauricAcid
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...  people might think that 'FSC' stands for the fallacy (or supposed fallacy) itself. Instead of 'FSC', I'm going to use 'SCW', suggestive of 'stolen concepts are wrong to use' which is close enough to 'there is a fallacy of stolen concepts'.

There is no getting around that fact that this is a very difficult topic to discuss because of the fine distinctions which must be made. But I think that your suggestion will just add to the confusion.

There IS a problem in arguments which contain "stolen concepts" (except for RAA). That is not the issue. The issue is precisely where the fallacy lies. My point is that the fallacy will often lie at a point in the argument before the point where you identify the "stolen concept". Furthermore, the fallacy will be one of the traditional ones, not some new fallacy known only to Objectivists.

But there's still doubt that SCW is propositional. Pro-SCW posters say either that SCW is about hierarchy violation in concept formation or that SCW is about incorrect definition.
I am certain that many important Objectivists believe that FSC is propositional; and they are the ones that I am primarily trying to convince. On the other hand, if FSC is definitional, then it is equivalent to one of the traditional fallacies.

Dictionaries ...  the mere imposition of a ranking does not ensure that all the definitions would uphold such demands such as defining properties must be essential ones, etc.

Of course, there are other requirements; and it remains to be seen whether the dictionary can be constructed. I offer your example of metamath.org as a model of a hierarchical set of definitions.

All logicians are frogs.

All frogs are stereoscopic.

Therefore, all logicians are stereoscopic.

That's deductive, but just moves from universal to universal.

Eventually, you must go the the particulars or else this is futile.

So you must do something like:

jrs is a logician.

All logicians are stereoscopic.

Therefore, jrs is stereoscopic.

Your syllogism is just a short-cut for:

jrs is a logician.

All logicians are tetrapods. [i changed "frog" to "tetrapod".]

Therefore, jrs is a tetrapod.

All tetrapods are stereoscopic.

Therefore, jrs is stereoscopic.

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There IS a problem in arguments which contain "stolen concepts" (except for RAA).  That is not the issue.  The issue is precisely where the fallacy lies.  My point is that the fallacy will often lie at a point in the argument before the point where you identify the "stolen concept".  Furthermore, the fallacy will be one of the traditional ones, not some new fallacy known only to Objectivists.

Okay, well then we might not be too far off from each other.

Once an FSC is identified, then you know that the argument can't be correct. This can be helpful and important independent of the fact that there are deeper reasons why the individual was led to committing a hierarchy violation. Exploring and analyzing the deeper reasons for the error may be important but that really depends upon one's context. For instance, the average non-philosopher may be justified in simply dismissing an argument once a FSC is identified, while a professional philosopher may have the obligation and interest in pursuing and dissecting the underlying reasons for the error. I object to the hint (if there is one) that under every circumstance we all have some sort of duty to trace the deeper reasons for every error. Like I said, that may very well be warranted and illuminating, but not always.

Here's an interesting stolen concept I was told was made by Albert Ellis in his 1968 debate with Nathaniel Branden. My recollection of the story is that in response to Branden's query whether Ellis would at least concede that "existence exists," Ellis responded that "existence probably exists." (It might have been "possibly exists.")

Now, there can be all sorts of reasons why someone would utter this proposition. Identifying and examining those errors might be useful and interesting. However, in my mind, once the FSC has been identified and you can see that the proposition can't possibly be true, you've performed your epistemological due dilligence and can go on to more important things in life.

Edited by Gabriel_S
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Once an FSC is identified, then you know that the argument can't be correct.

Generally, yes. But there is an important exception.

If the "stolen concept" occurs during an argument which is based on a counter-factual supposition (as might occur during an argument by reductio ad absurdum), then the contradiction may be caused by the false premise of the supposition. In this case, there may not be any fallacy in the argument.

Remember that the conclusions based on such a supposition are not conclusions of the argument as a whole.

I object to the hint (if there is one) that under every circumstance we all have some sort of duty to trace the deeper reasons for every error.
To arrive at a contradiction is to confess an error in one's thinking; to maintain a contradiction is to abdicate one's mind and evict oneself from the realm of reality.

It is often not in your interest to track down the errors in some OTHER PERSON's argument.

But if such an error occurs in YOUR OWN argument, you NEED to track it down for the INTEGRITY of your own mind.

...  in response to Branden's query whether Ellis would at least concede that "existence exists," Ellis responded that "existence probably exists." (It might have been "possibly exists.")

If Ellis means that "Existence might not exist.", then his assertion is clearly false. Since this is merely an assertion and not an argument, there is no issue of whether a fallacy occurred or not.

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jrs

Stolen Concept

Would you give an example of an argument that Objectivists cite as using stolen concept but which you believe the fallacy is in some other step? It would help if you mention the steps of the argument and the step at which you think the actual (not stolen concept) fallacy is committed.

As to definititions, it seems to me that Objectivism ties correct definition to correct concept formation with requirements that go beyond the requirements of mere non-circularity, eliminability and non-creativity, which are the only ultimate requirements of logistic systems. So it seems that with Objectivism one's critique of a definition cannot be isolated from Objectivist philosophy in the way that certain other philosophies might disagree among themelves but at least agree that there is a neutral zone as to what is sufficient and necessary for an acceptable definition. I suspect this demand of Objectivism works against subjecting arguments to stark step by step analysis, since an Objectivist can refute any step that contradicts Objectivism as illogical, since the Objectivist view of logic itself is tied with Objectivist epistemology. If I'm mistaken about this, then, as always, I welcome explanation.

Back to FSC itself, as Hilbert said that taking the law of excluded middle from the mathematician would be like taking the telescope from the astronomer, perhaps so would taking FSC away from Objectivists.

/

Dictionaries

In logistic systems, defintions are sequential and in forms that ensure non-circularity, eliminability, and non-creativity. There's not even a question that a series of mathematical defintions can be non-circular. But an Objectivist hierarchical dictionary of concepts would have requirements beyond those of mathematics and would have to account for concepts that are not as easily put in sequence as are mathematical terms.

/

Deduction

You said, "Eventually, you must go the the particulars or else this is futile." That is just not true as you're imposing a requirement that is simply not required. The syllogism I offered is universal. It doesn't become particular just because you say that it would be "futile" if it weren't. Though, 'tetrapod' is cute and an improvment.

Edited by LauricAcid
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If the "stolen concept" occurs during an argument which is based on a counter-factual supposition (as might occur during an argument by reductio ad absurdum), then the contradiction may be caused by the false premise of the supposition.  In this case, there may not be any fallacy in the argument.

If a counterfactual and a set of premises lead to RAA, then either the counterfactual is self-contradictory or the premises are inconsistent. But I take it that you agree that the mere fact that an assumption is counterfactual doesn't entail that the derived absurdity is not in the other premises. If a counterfactual argument is against a position, then the argument is trying to show that a set of premises is inconsistent. One possible reply to such counterfactual arguments is to say that the counterfactual is self-contradictory. But that would be question begging unless a self-contradiction in demonstratd in the counterfactual. But what is the Objectivist view of necessary truth as opposed to contingent truth? If there is no distinction (is there?), then aren't counterfactual arguments refuted simply for being counterfactual arguments? If that is so, one can't try to derive an inconsistency from premises by using counterfactual argument anyway.

Edited by LauricAcid
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Stolen Concept

Would you give an example of an argument that Objectivists cite as using stolen concept but which you believe the fallacy is in some other step? It would help if you mention the steps of the argument and the step at which you think the actual (not stolen concept) fallacy is committed.

You are asking me to argue their case for them. Since they are asserting the existence of this alleged fallacy, I think the burden is on them to provide an example.

This example must meet these requirements:

(1) it must appear as a step in an argument where all the other steps are valid;

(2) it must not be an example of another fallacy, so it must appear to be a valid step to non-Objectivists;

(3) all the premises of the argument must be true; and

(4) the conclusion must be false.

I have yet to see anything from them which even comes close to satisfying these requirements.

...  Objectivism ties correct definition to correct concept formation with requirements that go beyond ...  the only ultimate requirements of logistic systems.
The only extra requirement of which I am aware is that the the concept be an important (rather than arbitrary) grouping of units. And reflecting that, the definition must be by the essential characteristics which the units share. For example, "grue" (green before Bush took office and blue afterward) is not a valid concept.

The reason for this requirement is that Objectivism regards reason as a tool for living in the real world, not as game played in some imaginary parallel "universe".

Back to FSC itself, as Hilbert said that taking the law of excluded middle from the mathematician would be like taking the telescope from the astronomer, perhaps so would taking FSC away from Objectivists.

Taking FSC away would force them to face the fact that some of their ideas are false. Now, they are able to evade that by shooting down any argument against them as a "stolen concept".

The syllogism I offered is universal. It doesn't become particular just because you say that it would be "futile" if it weren't.
There is no reason to do a AAA syllogism, unless you are going to follow it up with an instantiation. My point was that AAA is not an end-in-itself, it is a short-cut to help you do instantiations in fewer steps.

If a counterfactual and a set of premises lead to RAA, then either the counterfactual is self-contradictory or the premises are inconsistent.

Wrong. The premises might be {X=3; Y=1; Z=X-Y} and the supposition might be Z=4. {X=3; Y=1; Z=X-Y} is consistent; and {Z=4} is consistent; but {X=3; Y=1; Z=X-Y; Z=4} is inconsistent.

But what is the Objectivist view of necessary truth as opposed to contingent truth? If there is no distinction (is there?), then aren't counterfactual arguments refuted simply for being counterfactual arguments?

In the Objectivist view, truth is truth. "necessary" and "contingent" are meaningless.

The supposition may be false without the argument being invalid.

Even though Z=2, it is still true that (Z=4 => Z=4) and

also (Z=4 => Z+Y=5).

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FSC

I agree with you that if one asserts FSC, then the ball is one's court to give an example, and I agree with the criteria you listed. So, I'm not asking you to show a valid application of FSC, since you're not asserting FSC. On the other hand, you say that often Objectivists invoke FSC against an argument that can be shown invalid at a different step from the one cited as a violation of FSC. For me to get a picture of what you mean, an example would help.

What are some of the Objectivist ideas that you think are false but whose falsehood is masked by FSC?

About counterfactuals, I stand corrected by your correction. I misstated what I meant to say. Earlier in this discussion, you said, "If the "stolen concept" occurs during an argument which is based on a counter-factual supposition (as might occur during an argument by reductio ad absurdum), then the contradiction may be caused by the false premise of the supposition. In this case, there may not be any fallacy in the argument."

But a contradiction wouldn't come from the counterfactual just being false. As I meant to say previously (but misstated then): a contradiction can only come from the false counterfactual being self-contradictory or from contradicting some other premises or from the premises being inconsistent by themselves (in which case the counterfactual premise would be superfluous). Would you say what you're driving at with the above quote?

One way RAA by way of counterfactual often works is by adding the counterfactual to a set of premises, then deriving not an inconsistency with those premises alone but with some other unstated background premise.

Argument:

(1) All crimes should be punished by execution.

(2) Kidnapping is a crime.

(3) Mr. Jones is convicted of kidnapping.

(4) Therefore, Mr. Jones should be executed.

An RAA by way of counterfactual might be:

(1) [RAA premise:] All crimes should be punished by execution.

(2) Kidnapping is a crime.

(3a) [Counterfactual:] Mr. Jones is convicted of stealing a fountain pen, but not of kidnapping.

(4a) Therefore, Mr. Jones should be executed for stealing a fountain pen.

(5) [unstated background premise:] People should not be executed for stealing a fountain pen.

(6) (4a) contradicts (5).

(7) So if one is not willing to let go of any premise other than (1), then the only thing to do is let go of (1).

But one might say, "No, I'm kicking out (3a) since I never agreed to using counterfactuals to begin with." If an Objectivist does not allow a distinction between contingent falsehood and self-contradiction, then an Objectivist likely would not countenance RAA by way of counterfactual (and hypothetical?), since such arguments that depended on a counterfactual premise would have only trivial import. Couldn't an Objectivist say to someone making a counterfactual argument, "You derived a contradiction from a set of premises, one of them (the counterfactual) being manifestly false. Well, duh, with a false premise, of course you were able to derive a contradiction."

If there is no distinction between necessary and contingent truth, then what are the semantics of propositions? Structures and models depend on the distinction between necessary and contingent. And the method of counterfactual comes from the method of counterexample, which is a common sense way of thinking that is formalized by structures and models, which depend on the distinction between necessary and contingent, as does the very notion of entailment. It makes sense that an Objectivist would want to define logic without referring to entailment. How do you define entailment without the distinction between necessity and contingency?

I had said, "But what is the Objectivist view of necessary truth as opposed to contingent truth? If there is no distinction (is there?), then aren't counterfactual arguments refuted simply for being counterfactual arguments?"

You replied, "The [counterfactual] supposition may be false without the argument being invalid." But your examples show conclusions that are only trivially true. I don't think those are the kinds of conclusions that Objectivists want to deny as being implied by RAA by way of counterfactuals. I don't think that's what's at stake here. If one denies a distinction between necessary and contingent, then I don't see how counterfactuals can be persuasive. As I mentioned, an Objectivist just has to say, "False premise, false conclusion. Garbage in, garbage out." But that reply doesn't work if there is a distinction between necessary and contingent.

/

HIERARCHY

Is the only requirement that of importance? Or of essentialness? Are these the same? Important to whom? What is a non-arbitrary definition of 'essential'? To assume that it's easy to sort out what is essential is question begging. Doesn't defining 'essential' goes past mere 'necessary' and/or 'sufficient', and involve a more complex theory of properties and modality? Anyway, if there is no difference between necessity and contingency, then it would make no sense to even use 'necessary' in a definition of 'essential'. But then how does one define 'essential'?

You brought up the Goodman paradox! Please, not that can of worms! But one related point: What is not arbitrary in marking all history as B.C. or A.D., based on the life of a certain human being? To some people, the marking is very much not arbitrary, but to others it is, since other historical events would be just as good, or better, markers. In general, a theory of non-arbitrariness of the concepts of a natural language needs to include clear methods by which we can determine which properties are essential and which are not.

You say, "The reason for this requirement is that Objectivism regards reason as a tool for living in the real world, not as game played in some imaginary parallel "universe"." So concepts are non-arbitrary according to their usefulness? Useful to whom? People have different purposes. Mr. A's purpose is to sell automobiles, so his concept of an automobile is year, make, and model. Mr. B's purpose is to fix automobiles, so his basic concept is of what makes automobiles run, or their engine types. Mr. A and Mr. B have differing hierachies. Of course, this is allowed. But there could be many many Mr. A, B, C, and Ds with many different hierarchies. At some point it may be arbitrary to say that, say Mr. Y's hierarchy is arbitrary, since it may be just as useful to Mr. Y and his friends as is Mr. A's to a wide population. And hierarchy is not determined by a consensus vote. One could devise even better examples than automobiles; I'm just pointing to the general idea. Moreover, mathematical concepts can be arbitrary. Any arbitrary finite collection of known existents is a set. And mathematics does not demand that definitions not be arbitrary or that definitions capture essentials (whatever that means) or that definitions even be intuitive.

/

DEDUCTION

You say, "There is no reason to do a AAA syllogism, unless you are going to follow it up with an instantiation." One may want to know relations among predicates. That's a reason. And deduction does not depend on individual instantiation. One asks if there are an infinite number of primes, then deductively proves that there are. It's purely a general question.

Edited by LauricAcid
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LauricAcid: Please try to make your messages shorter and more to the point.

...  you say that often Objectivists invoke FSC against an argument that can be shown invalid at a different step from the one cited as a violation of FSC. ...  an example would help.

X=3; Y=1 premises

X=3Y calculate both sides

XX=3XY multiply both sides by X

XX-9YY=3XY-9YY subtract 9XX from both sides

(X+3Y)(X-3Y)=3Y(X-3Y) factoring

X+3Y=3Y actual fallacy -- division by (X-3Y) i.e. zero

X+X=3Y replace 3Y by X

X+X=X replace 3Y by X again

X=0 subtract X from both sides;

this contradicts premise X=3, thus it is a "stolen concept fallacy".

This is so contrived that it probably would not impress them;

but let them provide a better example.

What are some of the Objectivist ideas that you think are false but whose falsehood is masked by FSC?
Many Objectivist hold these false ideas:

<<Empty space (vacuum) does not exist.>>

<<Space-time is not curved.>>

<<Relativity is at best an illusion.>>

<<The Universe is not expanding.>>

<<Volition is an uncaused cause [like God].>>

<<Infinite numbers are meaningless.>>

<<Neutrality is worse than overt evil.>>

<<A person can be introspectively aware of all his thoughts.>>

(1) [RAA premise:] All crimes should be punished by execution.

....

(3a) [Counterfactual:] Mr. Jones is convicted of stealing a fountain pen, but not of kidnapping.

I think you missed the point -- the premise of the reductio ad absurdum would itself be the counter-factual,

i.e. (1) and (3a) should be the same step.

If there is no distinction between necessary and contingent truth, then what are the semantics of propositions? Structures and models depend on the distinction between necessary and contingent.
I have not studied this issue, so I do not know whether to agree with the Objectivist position or not. Why would models depend on analytic versus synthetic truth?

HIERARCHY ...  importance ...  essentialness? Are these the same? Important to whom? What is a non-arbitrary definition of 'essential'?

Important to the person who holds the concept. This depends on causality as below.

The answer to the Goodman paradox (grue and bleen) lies in the Law of Causality:

The same causes produce the same probability distribution over possible effects regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving.

Green is green because it is always caused by the same things and always has the same effects. This is not true of "grue".

Moreover, mathematical concepts can be arbitrary. Any arbitrary finite collection of known existents is a set. And mathematics does not demand that definitions not be arbitrary or that definitions capture essentials (whatever that means) or that definitions even be intuitive.
Arbitrary sets are not concepts as understood by Objectivism.

You argue with them. I do not want to bother.

One asks if there are an infinite number of primes, then deductively proves that there are.

Actually one proves that there is a prime between N+1 and

lcm (1,2,...,N-1,N)+1 inclusive, for any N. So this can be instantiated.

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The answer to the Goodman paradox (grue and bleen) lies in the Law of Causality:

The same causes produce the same probability distribution over possible effects regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving.

Indeed. The emeralds are grue at all times, regardless of when, where or why.

Edited by Hal
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