The Analytic-Synthetic Dichotomy


Dragonfly

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There comes a point in most of these arguments where one has to defend Rand, or defend (or accept) the truth.

Bob,

That's too broad to be anything but a personal opinion of Rand as a whole. The implication is that Rand's ideas are false about everything.

I know my reaction is not one of intellectual engagement with something like that. I think, "Well, the guy doesn't like Rand." And I stop there.

Michael

I understand, but that's not what I'm trying to say.

I was reacting to what I perceived as an attitude where 'capitulation' was out of the question regardless of the merits of the argument at hand. If this is indeed the case, then truth is not the priority and therefore an honest discussion is not even possible.

Bob

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I asked whether you sought capitulation. I don't expect many people will convert to my knowledge or reasoned positions. I suspect you do, and that you aren't satisfied to state your case without badgering others to give up. True or false, sir?

W.

The original question was not directed at me but to answer the question...

An honest argument can only be argued (properly) in two basic ways.

- fundamental disagreement on a premise of the argument

- possible disagreement in the reasoning process but...

A disagreement on the logic/reasoning is at least theoretically resolvable with only one side being correct of course. So, the final point of an argument should be pinpointing the premise dispute (agree to disagree) or resolution of the logic in which case yes, the honourable thing to is to capitulate. It's an honesty thing.

Of course this rarely happens when someone has a large intellectual investment in some "ism" or other and will go through extraordinary lengths to protect that investment, regardless of the absurdity of their position.

I am not speaking of this line of argument in particular, but in general terms.

Matus for example, used the excuse of me being a big meanie to quit in other arguments rather than face facts.

Bob

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I am not Matus. Capitulation happens in chess, sometimes in tennis, never in philosophy to my knowledge and belief. I think you can be as mean as you like, but I don't expect you or anyone else to capitulate in a discussion forum. The purpose of being here, I imagine, is to discuss matters of mutual interest. If it were a refereed game, I'd blow you away.

:aww:

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I am not Matus. Capitulation happens in chess, sometimes in tennis, never in philosophy to my knowledge and belief. I think you can be as mean as you like, but I don't expect you or anyone else to capitulate in a discussion forum. The purpose of being here, I imagine, is to discuss matters of mutual interest. If it were a refereed game, I'd blow you away.

:aww:

Perhaps you would, but that's not the point. The point is that if I held a viewpoint that you clearly showed was in error, then admitting it would be an indication of honesty and intellectual maturity.

Anything else would be just the opposite. If capitulation is impossible for you to imagine, then I humbly suggest you need some self-reflection.

Damn, I can't think of the name right now, but one philospher in particular totally changed his view on a number of occasions after input and reflection - I was impressed, (and a little embarassed now that I can't remember the name) - crap.

Bob

Edited by Bob_Mac
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It seems to me that the best opportunity to influence someone is at the fringe of their knowledge. Most of us are specialized to a certain extent. Some of us have professional qualifications and a body of work to be continued and defended. Younger people are supposed to explore The Unknown, instead of re-arguing the Scholastic view of universals. My opinion anyway. I would sit up straight and listen carefully if somebody posted a new idea, provided that it's genuinely new.

No hard feelings. We need 21st century creativity to transcend the past and prepare man for the future.

W.

Edited by Wolf DeVoon
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Wolf:

>I asked whether you sought capitulation. I don't expect many people will convert to my knowledge or reasoned positions. I suspect you do, and that you aren't satisfied to state your case without badgering others to give up. True or false, sir?

False, of course. Voluntary capitulation rarely if ever happens in life, let alone internet forums. But there is nothing more rational than a good debate, where we should try to test ideas to the best of our ability. What could be more boring than sitting around chatting with people who already agree with you?

>If it were a refereed game, I'd blow you away.

This was addressed to Bob, but this sounds pretty impressive. Can you provide some examples of these "refereed games" where your interlocutors have been "blown away" by you?

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Wittgenstein? Not sure, but I don't think so - gotta figure that one out - damn.

"Daniel: False, of course. "

Why? Is it too much to ask another to admit a mistake? Not that you'd expect this to happen, but what's wrong with not being 'satisfied' when someone refuses to admit an obvious error?

Bob

P.S. - I was once a physics teacher. Sometimes students would ask a question that I didn't know. I would say I didn't know. Sometimes I would be unsure and I would say I was unsure. Sometimes I would return the next day and start the lecture with "I was wrong yesterday". Upon reflection, I think it was the probably the single most important factor of what I considered my to be my strengths as an educator. It is NOT too much to expect in my book.

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I was once a physics teacher. Sometimes students would ask a question that I didn't know. I would say I didn't know. Sometimes I would be unsure and I would say I was unsure. Sometimes I would return the next day and start the lecture with "I was wrong yesterday". Upon reflection, I think it was the probably the single most important factor of what I considered my to be my strengths as an educator. It is NOT too much to expect in my book.

Very likeable statement. I've had to answer questions, too. Very often I had to admit 'I don't know.' And it's always admirable to admit a mistake. Never fun. Ideas, policies, decisions have consequences.

I'll give more thought to the gap between set theory and fuzzy natural language predicates.

W.

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Bob:

>It is NOT too much to expect in my book.

Well, one lives in hope, but this is not the same as what I expect...;-) Unlike our hopes, our expectations are tempered by experience. Plus people generally need time to change their minds on a major issue. Conversion experiences, while powerful, are rare. So I am generally satisfied by simply a good debate.

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Greg, concerning #446,

I was too hasty and overstepping when I said that Rand’s position on metaphysics and logic commends ways of developing modal logic different from what Bostock would or should commend given their divergence on the following: Rand’s conception of logic as resting on the axiom existence exists entails, I maintain, that it is not logically possible that existence might not have been. Whereas Professor Bostock maintains that it is a logical possibility that nothing should have existed at all.

Perhaps the two perspectives should indeed lead to different developments of modal logic, but I have not followed that through to see if it is so. Here is what difference is evident from Bostock's Chapter 8, "Existence and Identity."

Sticking to Rand’s idea that logic rests on the axiom that existence exists, I would say that all logically possible worlds are relatable to the actual world and that all logically possible worlds are relatable to each other via the actual world. That is, the appropriate modal logic for broadly logical necessity is some variety of S5, which is a normal modal logic.

Bostock uses his contention that it is a logical possibility that nothing should have existed at all to motivate a dilemma: Either one must plunk for a non-normal modal logic as the logic appropriate for logical necessity or one must adopt a certain sort of non-orthodox classical logic (where classical here means non-modal). He favors the latter alternative, and for all I know, it may be that that is a classical logic square with Rand’s conception of metaphysics and logic. But from an Objectivist perspective, neither the dilemma nor the non-orthodox classical logic can be motivated by an alleged logical possibility that nothing should have existed at all.

Leaving now comparison with Bostock, let me add a bit more on Rand. In view of the implications I wrought from Rand’s further metaphysics and epistemology in my “Universals and Measurement” (JARS V5N2), we should readily notice also that although metaphysical possibilities are wider than physical possibilities, they are not wider than logical possibilities. For in Rand’s metaphysics, all concretes stand in some measurement relations to some other concretes in at least the ordinal-scale (or ordered-geometry) levels of measurement relations. And mathematical possibility will not extend further than logical possibility.

Edited by Stephen Boydstun
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Greg, concerning #446,

....Rand’s conception of logic as resting on the axiom existence exists entails, I maintain, that it is not logically possible that existence might not have been. Whereas Professor Bostock maintains that it is a logical possibility that nothing should have existed at all.

....

Sticking to Rand’s idea that logic rests on the axiom that existence exists, I would say that all logically possible worlds are relatable to the actual world and that all logically possible worlds are relatable to each other via the actual world. That is, the appropriate modal logic for broadly logical necessity is some variety of S5, which is a normal modal logic.

Bostock uses his contention that it is a logical possibility that nothing should have existed at all to motivate a dilemma: Either one must plunk for a non-normal modal logic as the logic appropriate for logical necessity or one must adopt a certain sort of non-orthodox classical logic (where classical here means non-modal). He favors the latter alternative, and for all I know, it may be that that is a classical logic square with Rand’s conception of metaphysics and logic. But from an Objectivist perspective, neither the dilemma nor the non-orthodox classical logic can be motivated by an alleged logical possibility that nothing should have existed at all.

Leaving now comparison with Bostock, let me add a bit more on Rand. In view of the implications I wrought from Rand’s further metaphysics and epistemology in my “Universals and Measurement” (JARS V5N2), we should readily notice also that although metaphysical possibilities are wider than physical possibilities, they are not wider than logical possibilities. For in Rand’s metaphysics, all concretes stand in some measurement relations to some other concretes in at least the ordinal-scale (or ordered-geometry) levels of measurement relations. And mathematical possibility will not extend further than logical possibility.

Stephen,

A very interesting post. I will have to request a back copy of JARS to read your article. (By the way, that is where my book is reviewed.).

Regarding the possible of nothing existing: assuming that 'nothing' means 'non-being, and being' and 'existence' are synonyms, then to say that is it is possible for nothing to exist is to say that it possible for non-being to be and that it is possible for non-existence to exist, both of which involve self-contradictions.

Now if 'nothing' means instead something else, such as void (vacuum), then I say that void can, and does, exist. Consequently, we can then ask why there is void in a certain place rather than something else, such as matter (body).

However, Peikoff would object to this. He says that while most philosophers believe, rightly, that it is absurd to ask there is something rather than nothing, they believe, wrongly, that it is not absurd to ask why something is the way it is rather than otherwise. So he seems to be objecting to the very concept of contingency. However, this would commit him to believing that all facts are necessary. Yet he admits that human free will choices are contingent facts (though he dislikes the terminology of 'necessary' and 'contingent'), and he admits that they could have been otherwise. He seems torn by his desire to ride of the dichotomies and his belief in this one dichotomy (which I agree is the only of them that is justified).

As to Bostock's reasoning: I don't see how the alleged possibility of nothing existing would motivate Bostock's two alternatives for logic.

Regarding the alleged differences between logical, metaphysical and physical possibility: I don't believe in them (though I would be interested in hearing how you define them, since different thinkers define them differently and most collapse them into two) nor do I believe in the alleged differences between the corresponding kinds of necessity. Rather, I believe in one kind of necessity (in the strict sense of the word), which we can also call absolute necessity, and various degrees of hypothetical necessity. The later goes at least as far back as Leibniz. As I define it, a statement h is hypothetically necessary if

(1) it is not absolutely necessary

(2) it follows from some (absolutely) contingent statement c (so that 'If c then h' is absolutely necessary), where c is not entailed by c

I think that truths logic, math, the social sciences, ethics, mechanics, chemistry, and biology, or most of them, are necessary, while those expressing free will choices (such as many truths of history) are contingent, and others expressing the consequences of free will choices (such as many other truths of history) are contingent. To use an example I gave in an earlier post, legislators presumably have a choice about whether to increase the minimum wage, and so whether they do or not is contingent, but they cannot avoid the laws of economics, such as those that say minimum wage increases tend to increase unemployment, and so if they enact the increase the resulting increase in unemployment was hypothetically necessary---it is not absolutely necessary, because it could have been avoided by not passing the increase in the minimum wage, but it is not absolutely contingent, because it followed inescapably from the increase in the minimum wage.

Edited by Greg Browne
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Greg,

I have discussed Leibniz’s distinction between hypothetical and absolute necessity in Section IV of my essay “Volitional Synapses.” That section begins on page 105 in V2N2 of Objectivity, which is available at Objectivity Archive. Here is a paragraph from page 109 of that section:

“For all of that, I think we can make some good sense of Leibniz’s distinction between absolute necessity and hypothetical necessity. He admits, at least by 1704, that eternal truths are fundamentally conditional. To say, for instance, that ‘any figure having three sides will have three angles’ is to say ‘if a figure is three-sided, then that figure will have three angles’ (NEU 447). I suggest we reconstrue Leibniz’s absolute necessity as existentially thinned hypothetical necessity, letting his hypothetical necessity be necessity about (as he would have it) concrete existents, as in ‘all quicksilver is evaporated by the action of fire’ (NEU 447). Concrete physical situations are thick with conditions; we thin out the conditions allowed to apply in our purely geometric scenarios.”

Now the way in which we are thinning conditions as we move from physical situations to metaphysical perspectives is partly different from the way in which we are thinning conditions as we move from physical situations to purely geometric scenarios. Given that caveat, it has seemed to me not inconsistent to hold both to a distinction between hypothetical and absolute necessity, as above, and to distinctions between logical, mathematical, metaphysical, and physical necessities.

As example of a metaphysical necessity, I’m thinking of the proposition “It cannot be that various existents have never existed.” That would be affirmed I imagine by one holding “There are existents, not all the same.”

An example of a mathematical necessity would be as in the proposition “An angle cannot be trisected using only a straightedge and compass.”

An example of a physical necessity would be as in “It is impossible to construct a device that will extract only heat from its environment and produce mechanical work equal to the amount of heat extracted.”

The question of which modal logics are appropriate for those three kinds of necessity, as well as for logical necessity, is a part of contemporary philosophical investigation. I think this investigation may be able to deepen and precise our understanding of how logic figures differently in these different mutually supportive ways of comprehending existence.

I am unsure how far you and I are conceiving of the nature of necessity and contingency really differently. There does seem to be some difference that is not merely the difference in what we mean by the terms hypothetical and absolute necessity. I say that because I do not think of contingency as entering the world with free will. (I’m in league with Peirce on this, in opposition to you and Rand and Descartes.) Rather, physical contingency must already be in both the world and the living organism for free will to be possible. On this, you may want to check out my essay “Volitional Synapses” in Objectivity (V2N1, N2, N4) as well as the exchange between Rafael Eilon and me concerning it, under his Remark “In Defense of Full Physical Determinism” (V2N5).

Edited by Stephen Boydstun
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An example of a mathematical necessity would be as in the proposition “An angle cannot be trisected using only a straightedge and compass.”

An example of a physical necessity would be as in “It is impossible to construct a device that will extract only heat from its environment and produce mechanical work equal to the amount of heat extracted.”

No one has ever demonstrated that the Second Law of Thermodynamics is -logically necessary-. It has the same kind of provenance as do various symmetries in physical law. It turns out our understanding of the physical world requires such laws, but that is not proof of necessity. It is proof of our limitations of understanding.

On the other hand, trisection by straight edge and compass, as you point out, leads to a blatant mathematical (and therefor, logical) contradiction.

In my understanding, only mathematical or logical contradictions are absolutely impossible. All other contradictions rest on facts (properties) of the physical world (the world we actually live in) which happen to be the case. Put another way, the only a priori apodictic proposition I hold is the law of non-contradiction. If you want to prove something is radically false, show that it leads of a logical contradiction. If you want to prove something is contingently false, show that it contradicts a clear observation or a previously established fact.

Ba'al Chatzaf

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Stephen and Ba'al,

Greg,

I have discussed Leibniz’s distinction between hypothetical and absolute necessity in Section IV of my essay “Volitional Synapses.” That section begins on page 105 in V2N2 of Objectivity, which is available at Objectivity Archive. Here is a paragraph from page 109 of that section:

“For all of that, I think we can make some good sense of Leibniz’s distinction between absolute necessity and hypothetical necessity. He admits, at least by 1704, that eternal truths are fundamentally conditional. To say, for instance, that ‘any figure having three sides will have three angles’ is to say ‘if a figure is three-sided, then that figure will have three angles’ (NEU 447). I suggest we reconstrue Leibniz’s absolute necessity as existentially thinned hypothetical necessity,

I like your concept of something being existentially thinned, regarding both terms.

Regarding existentiality, I agree that necessary truths about kinds are non-existential and conditional. In the case of kinds, the conditionality of universal generalizations is something modern logic got right. We need to treat them this way because kinds are, as Rand put it, "open-ended" , and specifically, as I put it, "open-sided" or "wide" ("Wide Class" being my synonym for "kind"). For example, "All dogs are warm-blooded" means "If something is a dog then it is warm-blooded".

Regarding being thinned, that is the same as my concept of shallowness. Classes are shallower than individuals, Wide Classes (kinds) are shallower than Narrow Classes, and Shallow Kinds are shallower than Deep Kinds.

letting his hypothetical necessity be necessity about (as he would have it) concrete existents, as in ‘all quicksilver is evaporated by the action of fire’ (NEU 447). Concrete physical situations are thick with conditions; we thin out the conditions allowed to apply in our purely geometric scenarios.”

But ‘All quicksilver is evaporated by the action of fire’ is also a universal generalization about a kind, and so it translatable as a conditional and is non-existential, just at the first sentence is.

Yes, physical kinds are thicker (deeper) than geometric kinds, but chemical kinds are thicker than physical kinds, and biological kinds are thicker than chemical kinds, whereas arithmetic kinds are thinner than geometric kinds and logical kinds are thinner than geometric kinds; analogous remarks can be made about the concepts corresponding to each kind. So why select the difference between physical and geometric kinds as a more important than the others and as the basis for a dichotomy of truth?

Now the way in which we are thinning conditions as we move from physical situations to metaphysical perspectives is partly different from the way in which we are thinning conditions as we move from physical situations to purely geometric scenarios.

That part you did not quote. I look forward to reading your article, but can you tell us now the difference between the two ways of thinning conditions?

Given that caveat, it has seemed to me not inconsistent to hold both to a distinction between hypothetical and absolute necessity, as above, and to distinctions between logical, mathematical, metaphysical, and physical necessities.

'Logical necessity' (also called 'logical truth) can mean two different things: (1) the strongest kind of necessity--i.e., absolute necessity, whatever that is; and (2) necessity which we can ascertain by logic alone. 'All bachelors are unmarried' is logically necessary (logically true) in the first sense but not in the second: it requires a definition to translate 'All bachelors are bachelors', which is logically necessary in the second sense as well as the first, into 'All bachelors are unmarried', and this gets you into all of the problems of defining 'definition'. This was Quine's point. He said that logical truth in the second sense can be defined precisely, but it does not seem a very important distinction, whereas in the first sense he doubts that the distinction can be drawn.

So I say that truths of physics are not logically true or logically necessary in the second sense, but they, or some of them, are in the first sense--absolutely necessary, just as much and in the same way as 'All bachelors are unmarried' is absolutely necessary.

As example of a metaphysical necessity, I’m thinking of the proposition “It cannot be that various existents have never existed.” That would be affirmed I imagine by one holding “There are existents, not all the same.”

An example of a mathematical necessity would be as in the proposition “An angle cannot be trisected using only a straightedge and compass.”

An example of a physical necessity would be as in “It is impossible to construct a device that will extract only heat from its environment and produce mechanical work equal to the amount of heat extracted.”

The question of which modal logics are appropriate for those three kinds of necessity, as well as for logical necessity, is a part of contemporary philosophical investigation. I think this investigation may be able to deepen and precise our understanding of how logic figures differently in these different mutually supportive ways of comprehending existence.

As to the first, the claim that there must be existents seems to be same as denying 'It is possible for nothing to exist', and this latter is self-contradictory and absolutely impossible..

As to the second, see below.

I am unsure how far you and I are conceiving of the nature of necessity and contingency really differently. There does seem to be some difference that is not merely the difference in what we mean by the terms hypothetical and absolute necessity. I say that because I do not think of contingency as entering the world with free will. (I’m in league with Peirce on this, in opposition to you and Rand and Descartes.) Rather, physical contingency must already be in both the world and the living organism for free will to be possible. On this, you may want to check out my essay “Volitional Synapses” in Objectivity (V2N1, N2, N4) as well as the exchange between Rafael Eilon and me concerning it, under his Remark “In Defense of Full Physical Determinism” (V2N5).

I will have to read your essays; they sound quite interesting.

For now I will say that perhaps other beings besides humans have free will.

....

An example of a physical necessity would be as in “It is impossible to construct a device that will extract only heat from its environment and produce mechanical work equal to the amount of heat extracted.”

No one has ever demonstrated that the Second Law of Thermodynamics is -logically necessary-. It has the same kind of provenance as do various symmetries in physical law. It turns out our understanding of the physical world requires such laws, but that is not proof of necessity. It is proof of our limitations of understanding.

I doubt that it is necessary, though it may necessarily follow from certain other facts about nature, and if thoase are not absolutely necessary, then the law is hypothetically necessary.

On the other hand, trisection by straight edge and compass, as you point out, leads to a blatant mathematical (and therefor, logical) contradiction.

In my understanding, only mathematical or logical contradictions are absolutely impossible. All other contradictions rest on facts (properties) of the physical world (the world we actually live in) which happen to be the case.

It is a commonly believed that only denials of truths of logic and math lead to contradictions that are absolutely impossible, because it is assumed that only these truths are (absolutely) necessary. However, Peikoff has already made a case against this, so now the burden of proof is on those who believe this to show that he is wrong. To assume this is to assume that only logic and mathematical attributes of things are necessary to them, while physical and other attributes are not. But why should we assume this?

Also, you are assuming that logical contradictions do not rest on facts, and that the facts about the actual world are never facts about all possible worlds (i.e., necessary facts), both of which need to be argued for.

Put another way, the only a priori apodictic proposition I hold is the law of non-contradiction.

You are assuming that the dichotomies are valid and all line up, so that necessary truths are all a priori, but this, too, needs to be argued for.

I say that even logic and math are knowable a posteriori (empiricall), because I believe that all concepts are empircal--that is, are (or can be) derived from experience--and I think that if a conceptual truth is derived from such a concept then it, too, is derived from experience and so empirical.

More importantly, you are assuming that contradicting the physical properties of something does not yield a logical contradiction. Peikoff useds the example of denying 'Cats give birth only to kittens' and supporting the denial by pointing out that we could conceive of tiny elephants emerging from a cat's womb. He and I would say that would contradiction the nature of a cat. It would contradict the necessary attributes of a cat, just as being 4-sided would contradict the nature of a triangle. The only difference is that cats are Deep Kinds and triangles are Shallow Kinds, which entails that it may require a lot of work to discover what a cat's body can and cannot produce, whereas the the number of sides of a triangle is something one learns as soon as learns the meaning of the term 'triangle'.

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Stephen and Ba'al,

So I say that truths of physics are not logically true or logically necessary in the second sense, but they, or some of them, are in the first sense--absolutely necessary, just as much and in the same way as 'All bachelors are unmarried' is absolutely necessary.

I doubt that it is necessary, though it may necessarily follow from certain other facts about nature, and if those are not absolutely necessary, then the law is hypothetically necessary.

Hypothetical necessity makes no sense. A proposition is either true on all possible worlds or it is not.

It is a commonly believed that only denials of truths of logic and math lead to contradictions that are absolutely impossible, because it is assumed that only these truths are (absolutely) necessary. However, Peikoff has already made a case against this, so now the burden of proof is on those who believe this to show that he is wrong. To assume this is to assume that only logic and mathematical attributes of things are necessary to them, while physical and other attributes are not. But why should we assume this?

Peikoff has made assertions. He has not made cases. That fact that his position can be coherently argued against shows that he has demonstrated nothing logically necessary.

Because we have not, nor can we, exhaust the physical cosmos to assert the contrary. All we can do is assume true what we have so-far observed. To assert, absolutely, the truth of some general statement that so far has been the case is to assert the impossibility of ever finding a counter example somewhere in the physical universe. Not only has this not been shown, it CAN'T be shown. We have not the time or energy to show it.

It comes down to the old chestnut the induction is not a necessarily valid mode of inference. It is just a good guess and the kind of guess we have no choice but to make because there is no practical alternative.

Also, you are assuming that logical contradictions do not rest on facts, and that the facts about the actual world are never facts about all possible worlds (i.e., necessary facts), both of which need to be argued for.

Argument: Write a truth table. QED. Given the semantics of logical connective and negations, anti-tautologies are in ALL CASES, false. A logical contradiction is not a particular statement of fact or otherwise. It is an instantiation of a general form p AND not-p. Always and forever false, given the meaning of AND and NOT.

Factually true particular (non-universally quantified) statements about the physical world may be true, if if true they so happen to be true. We know of no universally quantified statement about the physical world that is true so a particular cannot be asserted by universal instantiation. We will never know if all crows are black because we cannot exhaustively check the set of crows in space and time. We can only assert universal statements about the world hypothetically based on incomplete evidence.

Bottom line: Logical tautologies tell us nothing particular about the world. Their main use is that if any assertion contradicts a tautology or implies a contradiction to a tautology we know it is false, right then and there. Tautologies are very handy for elimination, but little else.

Ba'al Chatzaf

Edited by BaalChatzaf
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I will respond to some parts of ##491-93 in a day or two. Meanwhile, here are the entries for possibility, contingency, and necessity in the Subject Index for Objectivity. Some readers may find this resource useful, and anyway these entries indicate some of the relationships and subdivisions of these concepts.

Possibility

and Actuality V1N2 34, 55, V1N3 34, 45, V1N4 14, 47, V2N2 9–10, 64, 106, V2N4 228, V2N5 98;

and Alternatives V1N2 47–49, 54–55, V1N4 26, V1N5 37, V2N5 150;

and Art V1N2 69–71, 90, V1N3 65–66, V1N6 156–57, V2N3 43, V2N5 47–49;

and Conceptual Consciousness V1N1 29, 35, 37, V1N2 48, 56–61, V2N1 132, V2N2 70–71;

and Conceivability V1N3 3, 17, 21–23, 26–27, 37–38;

and Imagination V1N3 58, 67–69, 82–90, V1N5 35, V2N1 132, V2N2 69–71, 79;

Logical V1N2 8–9, V1N3 33–34, V1N4 26, 56, V2N1 1–2, 15–16, 28, V2N2 66–67;

Mathematical V1N2 6–7, 8–9, V1N3 17, 46, 49–51, V2N1 1–11, 13–14, 25;

Physical V1N3 9, 22–23, 25–27, 30, 33–40, V1N4 26–27, V2N1 1–3, 12–13, 20–28, V2N2 68–71, V2N4 99;

and Potentiality V1N3 35–38, 40–43, 45, V2N4 186–87, 191;

Supernatural V1N3 2–3, V1N4 39, V2N2 65–66, 105–6.

See also Necessity.

Contingency V2N4 184–87

and Contradiction V1N2 8, V1N3 3, 5, 33, 40–41, V2N2 105, 110, V2N4 184–85;

and Contrary Conceivability V1N3 16–17, V1N4 8, V1N5 113;

and Choice V1N2 54–56, V1N3 2–3, V1N5 37–38, V2N2 82, 106–7, V2N4 187–88;

of Existence V1N2 34–35, V1N3 2, 4, 5, 16, V1N5 113, V2N2 106, V2N5 152;

and Free Will V1N2 54–56, V1N3 2–3, V1N5 74, V2N2 110–16, V2N4 23–24, 187–88, 190–93, V2N5 162;

of Future Events V1N3 35, 37–39, 86–87, V1N4 26–28, V1N5 74–75, V2N2 82, 114–16, V2N4 23–24, 186–87, V2N5 155–56;

and Life V1N4 84–86, V1N5 4–7, 10–12, 36–42, V2N3 7, 11, 17–18, V2N4 188–91, 197–202, V2N5 162;

of Natural Laws V1N3 2–4, 35, 40, V2N2 107;

and Prediction V1N3 37–41, 86–87, V1N4 27, V2N4 183–87, V2N5 152–53, 159–62;

and Reasons V1N2 9, 54–55, V1N3 17, 21–23, 27–30, 35–41, 86–87, V1N4 15, V2N1 132, V2N2 106–7, 115.

See also Necessity.

Necessity V2N4 184–87

Absolute v. Hypothetical V1N2 4–5, V2N2 105–6, 109–10, 112–16, V2N4 185, V2N5 100–102;

Biological V1N2 38, 51, V1N3 99, V1N5 36–39, V2N2 77, 93–95, V2N4 190–93, 198–201, V2N5 100–104;

Causal V1N3 2, 4, 10–12, 17, 21–27, 30, 32–33, 35–36, V1N4 10, V1N5 112, V2N1 133–35, V2N4 191, V2N5 23, 99–102, 149;

Logical V1N2 5, 8, 33–37, V1N3 5, 10–11, 15–16, 21–24, 27–28, 33–35, 40–41, 50, V1N4 8, 13, 15–17, 26, 43–52, 55–56, V1N5 112–13, V2N2 106, V2N5 184–85;

Mathematical V1N2 2–6, 8–13, 37, 41–42, V1N3 17, 34–35, 46–47, 50–51, V1N6 56, V2N2 106–9, V2N4 96, 101–7;

Metaphysical V1N2 33–35, V1N3 3, 5, 12, 15, 16–17, 21–27, 30–31, 40–43, V1N4 8, 16–17, 19, 26, 45, 49–52, 56–57, V1N5 112–13, V2N4 184–85, V2N5 98–100, 152, 155–56, 160–61;

Moral V2N5 97–104;

of Past V1N3 33, 47–48, V2N5 152–53, 159;

Physical V1N2 35, V1N3 9–12, 21–40, V1N4 10–11, 15, 27, V1N5 72–73, V2N1 134, V2N2 107–9, V2N4 184–85, 190, V2N5 151–53, 159–61;

Practical V2N5 97–99;

Psychological V1N2 35, 38, 55–56, 67–74, 77–80, 83–91, V1N3 2, 7, 20, 27, V1N4 10–11, V2N2 99, V2N4 103, 108.

See also Contingency; Possibility.

Edited by Stephen Boydstun
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We know of no universally quantified statement about the physical world that is true

This asserts that no one knows anything, including yourself, which is self-impeaching. It resembles the Liar's Paradox, an abuse of language. 'Physical world' is redundant; there is no other world except physical. It is always wrong to denigrate the skills and abilities of others. Hence the most that one can legitimately claim and profess is your own ignorance.

Existence exists and has identity - a universal statement about the world.

W.

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We know of no universally quantified statement about the physical world that is true

This asserts that no one knows anything, including yourself, which is self-impeaching. It resembles the Liar's Paradox, an abuse of language. 'Physical world' is redundant; there is no other world except physical. It is always wrong to denigrate the skills and abilities of others. Hence the most that one can legitimately claim and profess is your own ignorance.

Existence exists and has identity - a universal statement about the world.

W.

Absolutely untrue! We know millions of particular statements pertaining to the world that are true. I was referring to -universally quantified- statements over indefinite or infinite domains. The only way to check such a statement empirically is to check all of its instances empirically. But if there are an indefinite set of instances in space and time that cannot be done. We -assume- universally quantified statements for which there is evidence and no falsifying instances are true. For example Newton's Law of gravity which is universally quantified over all pairs of masses and all non zero distances at all locations for all times. There is no way to check such a law empirically to assure its truth. It turns out to be false as it does not predict the motion of Mercury (for example) correctly.

Do you know the difference between a particular statement and a universally quantified statement? Apparently not.

And while we are at it how does one show that -all- crows are black? One would have to examine every crow that ever was, that currently exists and that will exist in the future. How is that possible? It isn't. It also turns out not to be true. There exist non-black crows. They are rather rare, but they exist. You can falsify a universally quantified statement with certainty by producing a single counter example. You cannot show the true of a universally quantified statement empirically, unless its domain of application is sufficiently limited to be checked out in all instances.

Ba'al Chatzaf

Edited by BaalChatzaf
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Bob,

I hate to sound like a Randroid, but going from your premise, what makes you think empirical checking exists and is valid, or will tell you anything true?

Another question is: What does true mean to you, since you use it as a standard?

A third question: "Absolutely untrue!" Those are your words. Absolutely? You mean like in "true"?

And if something can be "absolutely untrue," why cannot something else be "absolutely true"? Do we live only in a universe of negatives? Or negative knowledge? Is that "absolutely true"?

Or are you comfortable with the fudge, i.e., saying that 100% positive knowledge is "absolutely untrue", and conform yourself to the contradiction?

Anyway, how do you know that negatives are the only absolutes? By what standard?

Michael

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Bob,

I hate to sound like a Randroid, but going from your premise, what makes you think empirical checking exists and is valid, or will tell you anything true?

The way you tell that a particular (non universally quantified statement) is true is to check the world. For example the statement "there is a five dollar bill in my wallet". You go and look.

Another question is: What does true mean to you, since you use it as a standard?

A third question: "Absolutely untrue!" Those are your words. Absolutely? You mean like in "true"?

And if something can be "absolutely untrue," why cannot something else be "absolutely true"? Do we live only in a universe of negatives? Or negative knowledge? Is that "absolutely true"?

Or are you comfortable with the fudge, i.e., saying that 100% positive knowledge is "absolutely untrue", and conform yourself to the contradiction?

Anyway, how do you know that negatives are the only absolutes? By what standard?

Michael

True means either logically consequential to a true statement or empirically established, as in correspondence with the world. For example: If the statement X is German beer is true then it follows that X is a beer. How do you know X is a German beer? You check the label on the bottle you poured it from. It will say where its content is manufactured or brewed.

My statement about absolutes pertains to universally quantified statements (do you know what that means)? You cannot establish the truth of such statements absolutely if the domain of the quantified variable runs over an infinite or indefinite set of individuals. In short, there are too many cases to check out. But a single counterexample absolutely falsifies and universally quantified statement.

You can absolutely verify an existentially quantified statement by producing an example. Falsifying an existentially quantified statement absolutely is generally not possible unless the domain of application is finite and can be exhausted.

For example how does one prove a green crow does not exist? One way is by looking at every crow that ever was, is or will be. If you don't find a green crow than you have falsified the existentially quantified statement there exists a green crow. But the domain applicability of the predicate green conjunction crow is indefinite so it cannot be done empirically. On the other hand you can absolutely prove a green crow exists by producing one. Look! Over there! A green crow!

This is logic 101. Consult any logic text which deal with first order logic.

This should also give you a clue why enumerative induction is not a logically valid mode of inference. Induction is the basis of a good guess or a hypothesis, but it lacks the validity of deductive inference. If it is true that a implies b and it is also true that a, then it is surely true that b. (This is good old modus ponens).

On the other hand suppose you have a container with a million marbles which are either black or white. Suppose you pick out a half million marbles from the container and they are all white. Can you infer ALL one million are white? No you can't. A draw that does not exhaust the container does not eliminate the possibility of a black marble. Induction is necessary in order to learn (one forms hypotheses based on a limited number of instances). But it is no guarantee of truth.

Ba'al Chatzaf

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Ba'al:

>Do you know the difference between a particular statement and a universally quantified statement? Apparently not.

Not untypical either.

Untypical of what or who?

Ba'al Chatzaf

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