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Your thoughts on Hume's case against induction?

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Fred: “But I will say that successful prediction, even a long run of it, may not be enough. Depending on the complexity of the theory - certainly something like Newton's or Einstein's - would require I think successful prediction from a suitable variety of perspectives and under a wide variety of conditions. And there also needs to be no contrary evidence.”

I’m familiar with only the basics of the philosophy of science, but "long-run prediction" would presumably include a variety of perspectives. Even so, this would not be sufficient to establish a theory as immutable, but I'm not claiming that scientific theories are immune from revision.

Fred: “We can never know with certainty what will apply to anything and everything, now or in the future, under any and all conditions known or unknown. Such certainty would presuppose omniscience.”

I would agree with that. I’d also agree that this doesn’t prevent us from achieving all sorts of valuable and useful things using the knowledge we have, nor does it make any difference to what actually is the case.

Fred: “I always gringe when I watch scientific programs on TV and they talk about some phenomenon or another challenging Einstein's theories.”

I put that sort of thing down to media values. The media tends to look for novelty, any apparent departure from the norm (man bites dog), as well as thirsting after the “next big thing”. That said, I enjoy popular expositions of science and other subjects. They tend to be a bit once over lightly, and some are sensationalist, but they’re an easy way of keeping abreast of what’s happening in various fields, especially for the layman.

E

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I really like his example, so I have an uncontrollable urge to defend that deduction. It is a perfectly "valid" (and unsound) formal deduction:

Ax(Dog(x)->Man(x))                       premise

Ax(Man(x)->4-LeggedWalk(x))        premise

----

Ax(Dog(x)->4-LeggedWalk(x))        Law of Transitivity

You can of course also deduce the false statement "Dogs are men and walk on 4 legs"; but you cannot deny that the statement "Dogs walk on 4 legs" is formally deduceable from those two false premises. This a very nice demonstration of why it is essential in doing formal logic that premises be true.

Why is it essential? Formal logic in this context is about studying the STRUCTURE of an argument, not the argument itself. Validity refers to the deductive inference process, not to the truth of the argument, premises, or conclusions. When an argument is said to be valid, no claim is made about the truth of the conclusion, simply about the structure of the argument. Validity is a conditional - it simply means that IF your premises are true THEN your conclusion is true. Your example has a valid structure - the truth of your premises would ensure the truth of your conclusion. However your premises arent true, so nothing can be said about the conclusion simply from analysing the structure of the argument.

You seem to be objecting that a true conclusion can be deduced from false premises, but there is no reason why this should not be the case. Remember the truth table from the material conditional (FF|T, FT|T, TF|F, TT|T) - the premises being false can yield either true or false conclusions if the argument is valid. All that it means to say an argument is valid is that there cannot be a false conclusion as long as the premises is true. Nothing whatsoever is said about the truth of the conclusion if the premises are false - it could be either true or false.

You obviously know all this, so I'm not entirely sure what your problem here is.

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...You seem to be objecting that a true conclusion can be deduced from false premises, but there is no reason why this should not be the case.

The reason is very simple: the truth cannot be deduced from the false. What is the case cannot validly be inferred from what is not the case. Unless perhaps you have discovered some new law of nature?

One can assume, purely as a mental exercise, that some premise is true. And then assuming it, without necessarily acknowledging it is true, see where it leads you. So, if you say, IF such and such is the case, then.... That is hardly the same thing as saying that one can derive true conclusions from false premises.

Not the difference between:

If (i.e. hypothetically) all cats are dogs (which really should be put as: "if all cats were dogs")

vs.

All (i.e. assertively and false) cats are dogs.

Given that what do you say about:

All cats are dogs (false)

This is a cat (true)

This cat is a dog (true?)

Fred Weiss

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...You seem to be objecting that a true conclusion can be deduced from false premises, but there is no reason why this should not be the case.

The reason is very simple: the truth cannot be deduced from the false. What is the case cannot validly be inferred from what is not the case. Unless perhaps you have discovered some new law of nature?

One can assume, purely as a mental exercise, that some premise is true. And then assuming it, without necessarily acknowledging it is true, see where it leads you. So, if you say, IF such and such is the case, then.... That is hardly the same thing as saying that one can derive true conclusions from false premises.

Not the difference between:

If (i.e. hypothetically) all cats are dogs (which really should be put as: "if all cats were dogs")

vs.

All (i.e. assertively and false) cats are dogs.

Given that what do you say about:

All cats are dogs (false)

This is a cat (true)

This cat is a dog (true?)

Fred Weiss

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One can assume, purely as a mental exercise, that some premise is true. And then assuming it, without necessarily acknowledging it is true, see where it leads you. So, if you say, IF such and such is the case, then.... That is hardly the same thing as saying that one can derive true conclusions from false premises.
But this IS whats being said. Saying that an argument is valid simply means that IF the premises is true, THEN the conclusion is also true. No more and no less. If the premises are not true then absolutely nothing is said about the truth of the conclusion. Validity in this context is asserting a conditional statement.

Any argument of the form:

(prem) All A is B

(prem) All B is C

(conclusion) All A is C

is valid in terms of its logical structure regardless of what A, B, or C are. If either of the premises are false, then the truth of the conclusion is not guaranteed. In David's example it was true. It could equally have been false. None of this is important to formal logic, because formal logic is concerned only with the structure of arguments.

Given that what do you say about:

All cats are dogs (false)

This is a cat (true)

This cat is a dog (true?)

This is a valid argument. If all cats are dogs, then this cat certainly would be a dog.

edit: It's perfectly possible to validly infer a true statement from false premises, even outside formal logic. If someone told me that my friend had got a black eye, then I would assume that he has been in fight. If in reality the person was lying and he hadnt got a black eye, but he had actually been involved in a fight at work, then I would have 'accidentally' arrived at the truth from using fairly decent reasoning operating on a false premises (that he had a black eye). My premises would be false and my reasoning from it would be rational but my conclusion would be correct.

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...If either of the premises are false, then the truth of the conclusion is not guaranteed.

Exactly. But then nothing validly follows it from! But this doesn't seem to be the position you are maintaining.

This is a valid argument. If all cats are dogs, then this cat certainly would be a dog.
If... Yes, If

But they are not. You realize what you are saying is, "If anything I might dream up in my wildest imaginings is true, then anything follows from it" That entirely divorces logic from reality.

edit: It's perfectly possible to validly infer a true statement from false premises, even outside formal logic.

<snip a confused example>

No, I don't agree with this. You didn't validly infer anything. You just guessed and happened to be right, accidentally.

Fred Weiss

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Eddie, you'll have to tell me where specifically, if anywhere, we might still be in disagreement and/or if you have any further questions. I could quibble with some of the wording of your most recent reply but largely I agree with it. So, the ball's in your court at this point.

Fred Weiss

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It's been a little while since I looked at formal logic, and I'll grant that "dogs walk on 4 legs" is formally deducible.  But in context, I still think it's wrong, although I'm willing to be shown otherwise.  I don't think it's an incorrect deduction, but a false statement.

That's absolutely right: it is false (my neighbor's dog Nicki is an example of the contexts where it's false).

If I were to say something like "God doesn't exist" you would agree with me.  But if I now say "God is what I call my television" and then say "God doesn't exist", you would disagree with me, assuming that my television exists.  That's what this deduction seems to be doing.
I don't think they are entirely analogous. By naming your TV "God" and then making the claim about the existence of god, you aren't changing the existing definition of the word "god", you are just adding something new, essentially creating a new word that is homophonous with an existing word (compare "foot" refering to the thing you put in your shoe, vs. "foot" which is a verb pertaining to what you can do to a bill). You're playing a word game, which has nothing to do with logic (though word games can be funny if you understand that they are games). Trust me, I would never disagree with your statement about the non-existence of god even if you declare that you've renamed your television.

Suppose I use a classic syllogism and change it:

All dogs are mortal.

Socrates is a dog.

Therefore Socrates is mortal.

When I would then say "Socrates is mortal", what I would mean by Socrates is different from what most people would mean by Socrates.  In fact, since there is nothing in reality that corresponds to this "Socrates", my conclusion is meaningless.

Well, assuming that you mean that Socrates is the name of a dog, there almost certainly is a dog named Socrates (there's a bitch in our namorhood named Plato: in fact, look here for pictures of basenjis named Socrates and Plato the conclusion is quite true -- keeping context. This can be dealt with formally, and essentially it amounts to requiring that context be maintained, and not dropped by treating proper names as predicates translated as "has the name Socrates".

I understand that, and that's what I'm unsure about.  Is there much use for this type of logic (outside of, say, math) if it divorces it from words and real-word referents?  Isn't the conclusion therefore also divorced from reality?

None. What I'm pushing is not an abandonment of formal logic, but a reform of it, where such considerations of reality are part of the system. Of course, the question of how to integrate word-meaning into the system is the big problem. There is an immense need for a formalization of actual logic, not the broken subset that they teach in Logic 101.

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Why is it essential? Formal logic in this context is about studying the STRUCTURE of an argument, not the argument itself.

Because there is nothing intrinsically of value in the form of an argument. And because while some people practice formal logic with total disregard for reality, that is not a necessary feature of logic. A formal logic which unifies form and function is superior to one which focuses on form alone and which has no means of self-validating.

Validity refers to the deductive inference process, not to the truth of the argument, premises, or conclusions.
That's not true for two reasons. First, "valid" has a general meaning, referring to whether the action produces a result which is of value (is something you want to keep), and the ability to detach reasoning from reality is not of value (so a method that does so is not valid, i.e. invalid). Second, you are referring to a specialised redefinition of "valid" as contrasted with "sound" that logicians have invented, which distinguishes arguments that at least play by the rules, vs. ones that don't play by the rules. The rules are not just fixed at the standard Logic 101 subset modus tollens, modus ponens etc. So whether or not an argument is valid depends on how you define valid, which in our case depends on whether you include the rule of inductive generalization or not; whether you allow arbitrary or false statements to be included as premises, and so on. Thus the original dog argument is invalid because it is false that men walk on 4 legs: the premise is inadmissible in the first place.

The form of an argument tells you nothing at all, if the rules for well-formed arguments are wrong.

You seem to be objecting that a true conclusion can be deduced from false premises, but there is no reason why this should not be the case. Remember the truth table from the material conditional (FF|T, FT|T, TF|F, TT|T) - the premises being false can yield either true or false conclusions if the argument is valid.

Well, I have a special place in hell for the conditional, since it isn't a valid logical concept (it represents different things under one umbrella, including both 'causation' which is the valid usage that I'd like to preserve, and context restriction for universal quantifiers -- Generalised Quantifier Theory has apparently developed a better account of expressions ike "all men" which avoids this). That would be a case where there would, in The Better System, be no false antecedent.

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Spearmint: “Why are the rules of classical logic better than any other arbitrary set of rules, assuming that the system is consistent? Simply because classical logic is better suited to describing reality during our day to day experiences.”

I substantially agree, except I would say that certain rules of this type are accepted because they can be applied to reality with better results than other sets of rules, rather than because they better describe reality. In that case, our decision to use one set of rules rather than another is determined by what proves most useful for us.

Spearmint: “…it is perfectly possible to talk about one geometry being 'true' within a given context while another isnt, assuming that the first one is better suited to describing reality.

In the same sense I would agree with your analogy with geometry, although again I don’t think that geometry actually “describes” the external world, in that here’s nothing in nature that corresponds to the geometrical notion of, say, a triangle.

E

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Betsy: “That would be news to Aristotle who first identified the laws of classical, formal logic and established the validity of a deductive syllogism by appealing to "being qua being," i.e., things that ARE, i.e., reality.”

Aristotle believed that logic was about analysing thought as it thinks about reality. He also appeared to assume that the categories of correct human thought are found in reality. But nowadays we would draw a distinction that Aristotle did not: that one may derive the laws of logic without appeal to the external world, although these laws can be applied to guide our actions in the external world.

Betsy: “Then what gives the rules of logic their status -- if not reality?… If appeals to reality do not justify the rules of logic, WHAT DOES??… Without appealing to reality, WHAT IS the value of understanding the rules of logic? Is it just a neat little word game not based on and inapplicable to reality?

I’ve already dealt with these issues in previous posts.

Betsy: “If inductive arguments don't refer to the real world validly, truthfully, and usefully, why bother with them?”

I‘ve never claimed that generalisations about the world may not be truthful and useful. Some are, some are not. The issue has been the logical validity of induction.

E

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That would be news to Aristotle who first identified the laws of classical, formal logic and established the validity of a deductive syllogism by appealing to "being qua being," i.e., things that ARE, i.e., reality.

Aristotle believed that logic was about analysing thought as it thinks about reality. He also appeared to assume that the categories of correct human thought are found in reality.

So do Objectivists.

But nowadays we would draw a distinction that Aristotle did not: that one may derive the laws of logic without appeal to the external world, although these laws can be applied to guide our actions in the external world.

Who is this "we?" Certainly not Objectivists who define logic as the art of non-contradictory identification of reality. Since we live in reality, logic is one of the most useful arts since it aids in our understanding and knowledge of reality. As for non-Objectivist modern "logicians" who so blithely dispense with the "external world," of what use or value is logic at all?

Then what gives the rules of logic their status -- if not reality?… If appeals to reality do not justify the rules of logic, WHAT DOES??… Without appealing to reality, WHAT IS the value of understanding the rules of logic? Is it just a neat little word game not based on and inapplicable to reality?

I’ve already dealt with these issues in previous posts.

But you haven't answered my question. If logic is not used for the identification of facts of reality, what use is it? Why care? Why bother?

If inductive arguments don't refer to the real world validly, truthfully, and usefully, why bother with them?”

I‘ve never claimed that generalisations about the world may not be truthful and useful. Some are, some are not. The issue has been the logical validity of induction.

If "logical validity" does not necessarily refer to the truth of an argument or its usefulness in reality, what DOES it refer to? An arbitrary convention? A game? Or what?

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... I would say that certain rules of this type are accepted because they can be applied to reality with better results than other sets of rules, rather than because they better describe reality. In that case, our decision to use one set of rules rather than another is determined by what proves most useful for us.

How do you determine what proves useful...except by reference to reality?

Fred Weiss

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Betsy: “If logic is not used for the identification of facts of reality, what use is it? Why care? Why bother?”

Off the top of my head here is a list of real-world uses for logic, both formal and informal: clarity in thinking and correct reasoning, for everyday problems as well as more specialised areas, including economics, politics etc; analysing concepts, definitions; organising ideas and issues; developing persuasive techniques; extracting essential information from a mass of detail; identification of fallacies in reasoning; analysis of beliefs and values. More specialised applications include computers and science. All of these activities help us in our everyday lives, and are therefore useful.

E

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Fred: “How do you determine what proves useful...except by reference to reality?”

I’ll use an analogy here. For everyday and other numerical calculations, we use the decimal arithmetic system. There’s nothing in the external world that leads up to conclude that the decimal system is more in accord with reality than, say, a binary system. We use whichever system is best suited to the purpose at hand.

That purpose may well be dealing with the external world, so in that sense usefulness can be determined by reference to reality, but that hasn’t been the issue under debate. What has been a matter of debate is the derivation of logical systems of thought, not their application.

E

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...We use whichever system is best suited to the purpose at hand.

How, except by reference to reality, do you determine which is the best suited to the purpose? And how do you decide the purpose - and whether it is a valid or useful one, again, except by reference to reality?

That purpose may well be dealing with the external world, so in that sense usefulness can be determined by reference to reality, but that hasn’t been the issue under debate. What has been a matter of debate is the derivation of logical systems of thought, not their application.

I don't know what you mean by "derivation" or its significance. A logical system of thought should be...well...logical, which means it should make sense, which means it should have some connection to reality. Otherwise what's the point?

Fred Weiss

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Betsy: “If logic is not used for the identification of facts of reality, what use is it? Why care? Why bother?”

Off the top of my head here is a list of real-world uses for logic, both formal and informal: clarity in thinking and correct reasoning, for everyday problems as well as more specialised areas, including economics, politics etc; analysing concepts, definitions; organising ideas and issues; developing persuasive techniques; extracting essential information from a mass of detail; identification of fallacies in reasoning; analysis of beliefs and values. More specialised applications include computers and science. All of these activities help us in our everyday lives, and are therefore useful.

Oh, I see.

Logic provides clarity in thinking and correct reasoning about reality, for real everyday problems as well as more specialised areasof reality, including economics, politics etc; analysing concepts derived from reality, definitions; organising ideas about reality and issues in reality; developing persuasive techniques which will persuade real people; extracting essential information about reality from a mass of detail from reality; identification of fallacies in reasoning about reality; analysis of beliefs to see if they are justified in reality and values to see if they really are of value. More specialised applications include real computers and real science. All of these activities really help us in our everyday lives, and are therefore really useful.

But to repeat my question. If logic is not used for the identification of facts of reality, what use is it?

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For everyday and other numerical calculations, we use the decimal arithmetic system. There’s nothing in the external world that leads up to conclude that the decimal system is more in accord with reality than, say, a binary system.

Yes there is. The decimal system is based on two facts:

1) Human beings first counted on their fingers.

2) They have ten fingers.

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Fred: “I don't know what you mean by "derivation" or its significance. A logical system of thought should be...well...logical, which means it should make sense, which means it should have some connection to reality. Otherwise what's the point?”

By derivation I mean whether this type of knowledge is derived by appeal to experience, or independently of experience. Its connection to the external world is via application.

E

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Betsy: “Logic provides clarity in thinking and correct reasoning about reality, for real everyday problems as well as more specialised areasof reality, including economics, politics etc;…”

You asked me whether logic had any point. I gave some examples of real-world applications. You are now agreeing with me that logic can be applied to reality, so I guess we’ve made some progress.

Betsy: “The decimal system is based on two facts: 1) Human beings first counted on their fingers. 2) They have ten fingers.

There is a general and probably accurate assumption that human beings first counted on their fingers. But that doesn’t necessarily account for why human beings adopted the decimal system, nor does the mere possession of digits account for the wider phenomenon of arithmetic.

The question is whether or not arithmetical statements are known by reference to our experience of the external world. I believe they are known independently of such experience, because among other things they cannot be falsified. 1+1=2 is true under any real-world conditions, whereas “all swans are white” can theoretically be falsified by discovering swans of other colours. Therefore, it seems that arithmetic is understood independently of the way the world works

Nor does the possession of ten digits explain the coincidental fact that for human beings, the decimal system is the most useful and efficient for everyday purposes. This would hold true whatever the number of digits human beings possessed. And this raises another fact about arithmetic. The number “11” in a binary system has quite a different meaning to “11” in a decimal system, because their meaning is determined by their relationships to other symbols within their respective systems.

E

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Betsy: “Logic provides clarity in thinking and correct reasoning about reality, for real everyday problems as well as more specialised areas of reality, including economics, politics etc;…”

You asked me whether logic had any point. I gave some examples of real-world applications. You are now agreeing with me that logic can be applied to reality, so I guess we’ve made some progress.

My actual question was "If logic is not used for the identification of facts of reality, what use is it?"

Are you now saying that the only proper use of logic is for the identification of facts of reality? If not, what are those other uses and what use are they?

Betsy: “The decimal system is based on two facts: 1) Human beings first counted on their fingers. 2) They have ten fingers.

There is a general and probably accurate assumption that human beings first counted on their fingers. But that doesn’t necessarily account for why human beings adopted the decimal system, nor does the mere possession of digits account for the wider phenomenon of arithmetic.

Perhaps people have a real need to count real things?

The question is whether or not arithmetical statements are known by reference to our experience of the external world.

Then how are they known.

I believe they are known independently of such experience, because among other things they cannot be falsified. 1+1=2 is true under any real-world conditions, whereas “all swans are white” can theoretically be falsified by discovering swans of other colours. Therefore, it seems that arithmetic is understood independently of the way the world works
HOW?? Are we born with arithmetic as an innate idea?

Nor does the possession of ten digits explain the coincidental fact that for human beings, the decimal system is the most useful and efficient for everyday purposes.

A "coincidence," huh? In fact, it is not nearly as efficient as either a base 2 system or a base 12 system in terms of even divisions by more factors, repeating decimals, irrational numbers, etc.

This would hold true whatever the number of digits human beings possessed. And this raises another fact about arithmetic. The number “11” in a binary system has quite a different meaning to “11” in a decimal system, because their meaning is determined by their relationships to other symbols within their respective systems.

Do you mean they have a different meaning in reality?

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Betsy: “My actual question was "If logic is not used for the identification of facts of reality, what use is it? Are you now saying that the only proper use of logic is for the identification of facts of reality?”

Logic, as I said, is used for clarity in thinking, correct reasoning, analysis, organization of information etc. These activities can be applied to what we discover about reality, but logic per se will not identify the facts of reality. Such facts are identified by empirical means, observation, testing etc, although logic certainly plays a part in this process.

Betsy: “Then how are they [arithmetical statements] known.”

They are known a priori, that is, independently of experience.

Betsy: “A "coincidence," huh? In fact, it is not nearly as efficient as either a base 2 system or a base 12 system in terms of even divisions by more factors, repeating decimals, irrational numbers, etc.”

I said for “everyday purposes”. On the other hand, if the decimal system is less efficient than other systems, this would support my contention that it was adopted for its pragmatic utility.

Betsy: “Do you mean they [“11” in a binary system, “11” in a decimal system] have a different meaning in reality?

No. They have different meanings because they are components of different numbering systems.

E

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Betsy: “Then how are they [arithmetical statements] known.”

They are known a priori, that is, independently of experience.

Knowledge without any contact with reality?

How does THAT happen? Innate ideas? Kantian categories? Or??

If this "knowledge" isn't knowledge of reality, what is it knowledge OF? What do you really "know?"

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Logic, as I said, is used for clarity in thinking, correct reasoning, analysis, organization of information etc. These activities can be applied to what we discover about reality, but logic per se will not identify the facts of reality. Such facts are identified by empirical means, observation, testing etc, although logic certainly plays a part in this process.

Do you think it is a coincedence that "clarity in thinking, correct reasoning, analysis, organization of information" helps us in dealing with reality? And how would it be possible to discover anything in reality if we didn't think logically? It is in fact logical thinking which enables us to make these dicoveries. It is not something separate and distinct from the "empirical means", the observations. The observations are, on the most raw, basic level, simply isolated facts. You can't do anything with them without logic.

There's a certain equivocation in the way you are approaching this. Yes, there is an innate aspect to human cognition, namely, our capacity for rational thought. But that doesn't make actual rational thought innate or "a priori" or distinct from experience. There is nothing that requires us to think rationally. It is a choice.

But in fact it is reality which demands that we do if we are to survive and prosper. It is out of that demand, in effect the nature of reality, from which the necessity of rational thought arises. To divorce it from reality is to sever it from its basis and purpose.

There is something else which confuses this issue which is our capacity for imagination. We can create ideas which bear little or no relationship to reality (e.g. we can imagine a cow jumping over the moon) and we can create elaborate and complicated systems of ideas which are in fact mere "constructs" of our imagination (arguably that's all that String Theory is). But this is not the fundamental basis for logic or rational thinking. If all we did was construct elaborate castles in the sky we wouldn't survive for long.

Incidentally, we also know the difference between flights of imagination and actual objective facts. Your entire argument in fact presupposes that and wouldn't make any sense unless you did. But what enables you to tell the difference and what grounds you in reality is in fact....logic. So far from being "a priori" and divorced from reality it is the very means by which we ground ourselves in it.

This all by the way is axiomatic in Objectivism. I point that out to you because as you study it more, you will want to try and grasp why that it is the case. But the key is that you cannot deny any of this without in fact presupposing it. It is implicit even in your very attempt to deny it - and must be. There is no way around it. This in her own words is also what Betsy has been conveying.

Fred Weiss

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