The Analytic-Synthetic Dichotomy

[BaalChatzaf]

Yes: those statement do say something about the actual world (as well as every other possible world). In the case of the unicorn statement it says that nothing without a horn is a unicorn, and so if anyone attempting to prove the existence of unicorns brought in some hornless animal their claims should be rejected immediately. An analogous but more complicated statement could be made about the second, assuming that a sphere with more than 3 dimensions is even logically possible.

Also, note that ‘true in all possible world is definition’ (metaphorically) for ‘necessarily true’, not ‘analytically true’, and though I claim that all truths are analytic, I don’t claim that all truths are necessary.

Here is a true statement that is not analytic: I have three twenty dollar bills in my wallet. (I just checked). It is contingently true at this moment (08:20 EDT on the 14th of June, 2007). After I buy my breakfast at the local restaurant (sometime in the next hour) it will cease to be true.

It is a true statement that is not a necessary assertion about the interior of my wallet, which at other times have had as many as 23 twenty dollar bills inside. There are true statements that just happen to be true. For these statements it is possible for them to be false, hence they are not necessary.

As to a sphere of dimension greater than 3, let N be an integer > 3. Consider the Euclidean space R^N (the Cartesean product of R, N times along with the usual metric). Consider the set of points (x1 ... xN) in R^N such that x1^2 + ... +xN^2 = 1. This is the surface of a N-ball, hence an N sphere. It is not only logically possible, it is mathematically commonplace.

While we are at it, please note the adjectives -true-, -false- and -necessary- apply to propositions (or statements) not to facts. Facts are what is. A fact would be a fact even if there were no one about to assert it in any manner, form or language.

What is Out There is out there. What is In Here is in here. We must not confuse the two.

Ba'al Chatzaf

[tjohnson]

So why do we regard these distinct images as similar, as belonging to the same class?

You seem to be saying that it’s on the basis of perceived similarities. In effect, that is to say that we regard some objects as similar because we regard them as similar, which is to beg the question.

Brendan

We do this because it is advantageous for us to do so. This is the essence of abstraction, emphasizing similarities while ignoring differences. Abstraction occurs in lower level, non-verbal, perceptual processes AND on higher level, verbal cognitive processes. Our eyes are immersed in EM waves but we only sense a small range of frequencies and so we abstract (get some, but not all) of potential information from our environment. Language and scientific instruments, etc. can be considered an extension of the human nervous system that allows us to potentially increase our range of experience and so expose more detail of the underlying structure of our environment. But the structure is there, and if it did not manifest itself as similar repeatedly we would never be able to abstract it.

[tjohnson]

While we are at it, please note the adjectives -true-, -false- and -necessary- apply to propositions (or statements) not to facts. Facts are what is. A fact would be a fact even if there were no one about to assert it in any manner, form or language.

What is Out There is out there. What is In Here is in here. We must not confuse the two.

Ba'al Chatzaf

'Fact' is a word, period. The word 'fact' means different thing on different levels of abstraction. On verbal levels it means, roughly, 'a statement that most reasonable people would agree with' or something. But on objective, non-verbal levels, it refers to some occurence inside your nervous system, like some nervous activity resulting in a perceived noise. It can also mean an event outside our skin altogether.

Edited June 14, 2007 by general semanticist

[BaalChatzaf]

'Fact' is a word, period. The word 'fact' means different thing on different levels of abstraction. On verbal levels it means, roughly, 'a statement that most reasonable people would agree with' or something. But on objective, non-verbal levels, it refers to some occurence inside your nervous system, like some nervous activity resulting in a perceived noise. It can also mean an event outside our skin altogether.

Facts are What Is. Some declarative sentences assert facts but they are not facts other than being statements. The word is not the thing and the sentence is not what it asserts. FACTS = REALITY. True and False describe relations between assertions and Facts (Reality).

Ba'al Chatzaf

[Michael Stuart Kelly]

Tom (general semanticist),

In Objectivism, fact is a metaphysical existent that is independent of perception. It is an absolute and cannot be changed by any awareness of it.

Truth is the knowledge of a fact. If the mental units (knowledge) correspond to facts, they are true. If they do not, they are false.

How the mind acquires knowledge of facts (identification of facts as percepts from sensory input, then integration of percepts into concepts, then identification of concepts including introspective awareness of consciousness processes, and integration of all this into broader concepts or more narrower concepts), i.e., truth, is the whole basis of Objectivist epistemology.

I don't know how these words work with GS, but that is their meaning in Objectivism.

Michael

[Wolf DeVoon]

integration of percepts into concepts, then non-contradictory identification of concepts

Little tiny amendment in bold above. You agree, Mike?

W.

[Michael Stuart Kelly]

Wolf,

Fully agreed. Thank you.

EDIT (Comment to Tom): Wolf's addition is a good example of how to think about this. "Non-contradiction" applies to truth, not to fact. Only knowledge can be contradicted. A fact merely is. It is true that we use the word "fact" to identify an existent, but that word denotes something that does not need a word or concept to exist. Also, "fact" in common usage is often a synonym for truth, like in court and in scientific experiments. In Objectivism, the meaning is narrower and more specific.

Michael

[BaalChatzaf]

In Objectivism, fact is a metaphysical existent that is independent of perception. It is an absolute and cannot be changed by any awareness of it.

Not if the existent is a subatomic particle. To locate a s.a.p. one must bounce photons off of it which buggers both its position and momentum.

If you want to know how hot your soup is you stick a thermometer into it. The thermometer cools the soup (just a wee bit) and the soup heats up the thermometer (a great deal). What you read is an equilibrium temperature which is achieved precisely because of the act of observation.

The Fact (which is the thing in itself) is not NOT known independent of observation and the act of observation alters the thing observed. To know and identify is to interact. To interact is to alter. That is the way the world works.

Your statement is indicative of the friction between Objectivism and quantum physics. They both can't be right.

Ba'al Chatzaf

[Michael Stuart Kelly]

The Fact (which is the thing in itself) is not NOT known independent of observation...

Bob,

Facts to not need to be known to be facts. That is the Objectivist meaning. You are not disproving anything here, merely ignoring this.

The QM observation thing is interesting and weird, but it does not invalidate the Objectivist meaning of fact. If the QM observation thing is true, which is still disputed (I mean the interpretation, not the experiment), it merely establishes a special category of facts that need an observer as an integral component of the existent. An observer also exists. Obviously, in the case of consciousness (i.e., the observer), awareness is part of the existent, so the existent's own awareness cannot be eliminated. But an observer exists regardless of who else observes him. In that sense, he is a fact.

Michael

[Gregory Browne]

Yes: those statement do say something about the actual world (as well as every other possible world). In the case of the unicorn statement it says that nothing without a horn is a unicorn, and so if anyone attempting to prove the existence of unicorns brought in some hornless animal their claims should be rejected immediately. An analogous but more complicated statement could be made about the second, assuming that a sphere with more than 3 dimensions is even logically possible.

Also, note that ‘true in all possible world is definition’ (metaphorically) for ‘necessarily true’, not ‘analytically true’, and though I claim that all truths are analytic, I don’t claim that all truths are necessary.

Here is a true statement that is not analytic: I have three twenty dollar bills in my wallet. (I just checked). It is contingently true at this moment (08:20 EDT on the 14th of June, 2007). After I buy my breakfast at the local restaurant (sometime in the next hour) it will cease to be true.

It is a true statement that is not a necessary assertion about the interior of my wallet, which at other times have had as many as 23 twenty dollar bills inside. There are true statements that just happen to be true. For these statements it is possible for them to be false, hence they are not necessary.

Yes, it, too, is analytic, even though it is probably contingent (since its truth depends in part on free will choices made by you and others). It is analytic because the predicate (having 20 bills in your wallet) is contained in the subject ('I', referring to Baal Chatzaf), because it the meaning of the predicate term is part of the meaning of the subject term (i.e., the referrent of the subject term--you), because it is the attribute of having 20 dollars in your wallet is an attribute that you did in fact possess, during the time that the sentence is you. Now you only contingently possessed the attribute, and so it was only contingently part of the subject term's meaning, and so the predicate was only contingently contained in the subject, but it the predicate nonetheless was conatained, and was part of the meaning, and was possessed by the subject (you).

As to a sphere of dimension greater than 3, let N be an integer > 3. Consider the Euclidean space R^N (the Cartesean product of R, N times along with the usual metric). Consider the set of points (x1 ... xN) in R^N such that x1^2 + ... +xN^2 = 1. This is the surface of a N-ball, hence an N sphere. It is not only logically possible, it is mathematically commonplace.

While we are at it, please note the adjectives -true-, -false- and -necessary- apply to propositions (or statements) not to facts. Facts are what is. A fact would be a fact even if there were no one about to assert it in any manner, form or language.

What is Out There is out there. What is In Here is in here. We must not confuse the two.

Ba'al Chatzaf

That's interesting: you apply 'necessary' to truths but not facts, while Peikoff applies them to facts but not truths.

I think that it can be applied to both, but I take Peikoff's point that the difference is not one of truth but rather of the fact the truth refers to. So I say that there are necessary truths and contingent truths, but they do not differ in their truth but in the facts they refer to: necessary truths are truths about necessary facts and contingent truths are truths about contingent facts.

In any case, facts can be necessary or contingent: if they cannot (and could never have been and can never be) otherwise then they are necessary, while if they can be (or could have been or could be) otherwise then they are contingent. This is why necessity and contingency are considered metaphysical properties, while analyticity and syntheticity are logical properties and aprioricity and aposterioricity are epistemological properties.

[Gregory Browne]

[He looks at three things and sees that there is something similar, that all of them have one part of their shape bigger than the other parts when going in a straight line.]

In her claim about the formation of the concept ‘length’, Rand makes a fundamental error which the above ‘explanation’ makes more glaringly obvious.

The error is to claim that ‘similarity’ can literally be observed, ie physically perceived. But ‘similarity’ is not a perceptual quality. Rather, we perceive specific objects, not ‘similarity’.

So when the child observes the three objects he cannot “see that there is something similar”. What he sees are three objects, not three objects plus “something similar”.

Brendan

It will clarify things in this debate to ask whether you are talking about overall similarities between things or similarities in a respect (i.e., in respect to a given attribute). The latter is what is mainly important, but modern philosophers tend to think only of the former.

[merjet]

It will clarify things in this debate to ask whether you are talking about overall similarities between things or similarities in a respect (i.e., in respect to a given attribute). The latter is what is mainly important, but modern philosophers tend to think only of the former.

I made the distinction in #315. The former seems especially important in the cognitive development of a child. Dimensionally specific similarity comes later. Your last sentence is pretty sweeping, but Rand's similarity examples in ITOE were the latter kind.

[BaalChatzaf]

The Fact (which is the thing in itself) is not NOT known independent of observation...

Bob,

Facts to not need to be known to be facts. That is the Objectivist meaning. You are not disproving anything here, merely ignoring this.

Some facts are determined by the very act of observation (i.e. interacting an observer process with an object). For example take spin. An electron's spin state is a linear super position of up/down right/left spin in/out spin states (aligned along orthogonal space axes). Put it through a Stern-Gerlach magnet oriented just so and its spin state is changed to either up/down or right/left depending on the orientation of the magnetic field. The very act of observation determines the fact (i.e. the spin). And we are not talking about some mystic relation between "minds" or "consciousness" and objects. We are talking about physical interactions. How you observe an object (i.e. interact an observer system with it) determines some of the the properties of the object. In general one can not observe an entity without altering unless it is in a pure state (no superposition). Then doing the same observation to it does not alter its state. So applying the Stern-Gerlach magnet that produced (say) up spin on an electron will maintain that spin again if applied to that electron quickly enough (before environmental factors buggers its quantum state).

The concept of a superposed state runs completely contrary to what you asserted. Quantum physics based on linear superposition (1) predicts accurately to 12 decimal places and (2) has never, ever been falsified by an experiment. That convinces me (anyway) that superposed states are as real as rain.

Ba'al Chatzaf

[Michael Stuart Kelly]

If the QM observation thing is true, which is still disputed (I mean the interpretation, not the experiment), it merely establishes a special category of facts that need an observer as an integral component of the existent.

The concept of a superposed state runs completely contrary to what you asserted.

Bob,

How?

Michael

[Gregory Browne]

You know, in physics we speak of 'electrons, bosons, quarks, neutrinos' and we will never see these. I'm surprised no one has mentioned this as an argument in favour of the existence of a 'mind'. If someone was to postulate the existence of a 'mind structure' at a subatomic level then of course it could never be shown. But subatomic particles leave evidence of themselves which CAN be seen and measured and can we say this about the 'mind'? If you postulate the existence of something absolutely NO physical evidence of it then you are being religious and I'm sure you don'y want objectivism to be thought of as a religion?

Yes, both subatomic particles (along with atoms) and the mind or mental states have been considered as theoretical entities, and in fact most current philosophies of mind treat them this way, in effect.

The problem of theoretical entities is tied in with the the dichotomies of the ASD, in the following way.

The principle advocates of the dichotomies Peikoff attacks in the ASD (and of lining them up) were the Logical Positivists. Now their forerunner, the postivist philosopher and scientist Ernst Mach (of Mach number fame), denied the existence of "theoretical entities", or at least unobservable ones, and so denied the existence of atoms. Well by the time Logical Positivism got going in the 1920s atomic theory was making great strides, and so denying the existence of atoms was not something that members of this school wanted to do. So at first they said that statements about theoretical entities could be translated into observational statements, and thereby legitimated. Atoms were theoretical entities, and they also treated mental states as theoretical entities. So they were led to develop Logical Behaviorism, the philosophy of mind which (in its early form) said that mental states were just behavior. So pain was wincing, groaning, weeping, saying "I am in pain", etc. Similarly, they might have defined thirst as 'drinking water'.

However, the Logical Positivists encountered difficulties justifying these claims. In the case of mental states, it was soon obvious that the same mental state is not always correlated with the same behavior. So, in 1937, the Logical Positivist Rudolf Carnap admitted dispositions (to have observable properties). These were expressed in the so-called "subjunctive" or "counterfactual" conditionals, which have the form "If p were true then q would be true". For example, fragility was considered a disposition, and defined thus:

'x is fragile' is true if and only 'If x is struck then x will break' is true. Now these are unlike the indicative conditionals, which have the form "If p is true then q is true', which Logical Positivists analyzed as the material conditional, with this truth table:

p q If p then q

T T T

T F F

F T T

F F T

But this seems unsuitable for scientific law, since the conditional is automatically true if the antecedent is false. For example, if I say "If I throw this piece of chalk in wastebasket then it will catch fire", and then destroy the piece of chalk, so that it is always false that I throw it in the wastebasket, the conditional is made true, which is absurd. So it seems we need a stronger conditional, with this truth table

p q If p then q

T T T or F

T F F

F T T or F

F F T or F

Whether the truth value of the conditional on the 1st, 3rd and 4th lines is T or F depends on whether there is the right kind of connection between p and q. And this is usually assumed to be a necessary or partially necessary connection. Since this would be a necessary connection between factual matters, Logical Positivists hated to admit this.

Nonetheless, counterfactual conditionals and dispositions started to be used in dealing with theoretical entities. In the specific area of philosophy of mind, the Logical Positivists modified their Logical Behaviorism, created a new, dispositional version of it, which said that mental states are dispositions to behavior. For example, 'Smith is thirsty' was defined as meaning 'If water were available then Smith would drink some'.

However, other problems were discovered. In the case of philosophy of mind, people kept find inadequacies with the definitions, which were made longer in order to cope with them: 'If water were available, and Smith did not believe it were contaminated or poisoned, and Smith were not fasting, and Smith were not conserving water, and Smith did not want it known that he was thirsty, etc., then Smith would drink some', and some of the conditions (such as the 2nd and 5th, and perhaps even the 3rd and 4th,) refer to or imply other mental states.

Eventually, in the late 1950s, most Logical Positivists gave up and admitted that there were unobervable theoretical entities whose theories contained statements that neither observational or dispositional to observations.

In philosophy of mind, that meant that Logical Behaviorism faded out and gave way to theories that admitted that mental states were some kind of inner state that caused behavior, but were not identical to behavior nor identical to dispositions to behavior: Mind-Brain Identity Theory Materialism, Functionalism, various forms of Dualism, etc.

Now exactly what theoretical entities, theoretical statements and theoretical kinds were was disputed.

Well it seems to me that the problems with theoretical entities arose from a failure to recognize Deep Kinds, as the earlier problems with conditionals arose from a failure to recognize necessary factual truths at all (including necessary conditionals and necessary causal connections). We need to recognize that things and some kinds of things (i.e., Deep Kinds) have a much greater depth to them than the surface that we are familiar with and capture in simple definitions and concepts. With Deep Kinds, as with individuals, we can say "I know that there is more to this than I (or anyone) knows (at least right now)"; we can refer to things that extend beyond our knowledge.

(It is ironic that Logical Behaviorism, an extremely materialist or physicalist philosophy of mind, rested on a philosophic foundations of modified idealism: they believed, or acted as if they believed, that if we can't measure it then it doesn't exist.)

[Gregory Browne]

My question was provocative. Perceiving greenness or smoothness, like similarity, does require selective focus.

One does not perceive -greenness-. One perceives and green this or a green that. Greenness is an abstraction manufactured by the brain as a result of perceiving a lot of green thises and thats.

Ba'al Chatzaf

Perhaps you are making the common assumption that all attributes are universals. But I think that there are individual attributes, also called "tropes" and various names. For example, consider a brown table with two copies of a brown book in front of it. In this case there is the brownness of the table, the brownness of one book and the brownness of the other book. The browness of the table may not even be exactly like the brownnesses of the two books. And even the brownnesses of the two books, which are presumably exactly alike, since they copies of the "same" book, are still two brownnesses, not one.

If we suppose tropes, then we don't need to suppose universal attributes at all. If attributes were universal, then the table and two books (and everything else brown) would share the attribute of brownness--or at least the two books would share that exact shade of browness--and that shade would be literally be "shared" and literally be "in common", like some body parts of Siamese twins: the whole of the attribute would be present in each book at the same time. Or else the attributes would not be physical at all, but exist in some other world, as Platonic ideas are supposed to.

Without universal attributes, "sharing" attributes and having them "in common" are just metaphors: what is really going on is resemblances (similarities, likenesses) among attributes---in the case of the two books, exact resemblances.

By the way, 'abstraction' refers to a process by which we selectively focus on an attribute or attributes of a concrete thing, and in this way create an abstract idea (abstract concept, abstract thought). The attribute itself is not an abstraction: greenness is not an abstraction but rather an attribute of green things (or, to be more precise, green things have greenness tropes that resemble each other by being greenness tropes); it is the idea (concept, thought) of greenness is an abstraction. To think otherwise can lead one to deny the existence of attributes outside the mind, or to postulate abstract entities existing apart from concretes and/or shared among them, or both. You need not do either if you understand abstraction correctly.

[Gregory Browne]

Michael,

Regarding your post of 'Jun 10 2007, 05:05 PM', I have several comments.

1. It does appear that Branden is a Property Dualist, and that, if he is right, so is Rand.

2. His view does not seem so much like Locke's view (if that really is Locke's view: there is some dispute; anyway, it is the view of Gustav Bergmann: the view of substances as "Bare Particulars").

3. I found you laying out of the view of causes as being entities (things, substances, ousias) rather than events or attributes very helpful. It clarifies the position of Rand and Aristotle very much, and you make it sound very plausible.

I still have troubles saying that an entity causes its actions, rather than that it simply performs them, and incline to the view that attributes or facts are causes (of other attributes or facts).

4. You say that it has been inductively shown that all entities are physical. But what do you mean by 'physical'?

5. Your further quotations from Rand seem to show that he, and Rand, if he is right, are specifically Elemental Property Dualists rather than Emergent Property Dualists (and Peikoff, in OPAR, seems to leave the door open such a view). The later seems to be your view. And it does seem, as you seem to say, that "Dual Aspect Theory", is better applied to Elemental Property Dualism, since both labels are put on Spinoza's philosophy.

A problem with Emergent Property Dualism is that it says that mental properties are always accompanied by certain physical properties, on which they depend, but the nature of this dependence is unclear. Apparently, it is supposed to be causal, but the causality appears to be Humean, for it can hardly be necessary, for then Emergent Property Dualism would collapse into a reductive kind of Materialism (and the example given by Emergent Property Dualists such as Polanyi of an emergent property in the physical world---that of the liquidity of water, which emerges when atoms of hydrogen and oxygen, which are both gases, are put together--is that , as Jaegwon Kim pointed out, the properties of water in fact can be reduced to the properties of oxygen and hydrogen). So Elemental Property Dualism seems to be me to be more plausible.

However, unless we want to endorse the implausible view of Spinoza that everything (at least as a part of the whole of reality) has mental properties, we have to admit that some things (substances) have elemental mental properties and some do not, and that is Substance Dualism!

Moreover, Branden attributes to Rand the view that the mind is a separate entity--which is her word for substance (ousia). That would make her a Substance Dualist!

However, Substance Dualists do not have to adhere to the Cartesian version, which says that minds are unextended. They can instead adhere to what Paul Churchland called "Popular Dualism", which says that minds are extended. Indeed, it is logically compatible with Popular Dualism to say that minds have impenetrability, inertial force and indeed every other attributes of matter, except the attribute of not being conscious.

6. You say "And as various people including you and Rand have pointed out, what a thing is (its actuality/form) determines what it can do (its potential/matter)." But, according to Aristotle, a thing is a union of both matter and form, and so what it is formed matter, and that determines what it can do. Yes, matter is a potential to take on various forms, and forms narrow yet further the range of possibilities---narrow it all the way, except in humans, if the Peikoff view on necessity is correct, and if Peikoff and Rand were to fully accept Aristotle's form/matter doctrine.

Edited June 15, 2007 by Greg Browne

[Michael Stuart Kelly]

Greg,

To be fair, I think you are referring to my post here. If that is the case, most of the discussion is by Roger Bissell from a post I quoted, especially the part about Rand's and Branden's views. However, where you did quote my words (in your Item 6), this was from another post.

I have to do some heavy digesting on your comments because I am not familiar with the works of many of the writers you mentioned. I will get back later on this after getting a notion. Time to do some Googleing...

Michael

[Brendan Hutching]

GS: “We do this because it is advantageous for us to do so.”

If you’re saying that we pick out some features of the environment and ignore others, and that this process has survival value, I agree. But that’s not the issue at point, which is the status of a term such as ‘similarity’.

“But the structure is there, and if it did not manifest itself as similar repeatedly we would never be able to abstract it.”

If you mean that some things look alike, or that the same thing looks alike at different times, again I agree. But that’s not the same as saying that things manifest ‘similarity’.

Brendan

[tjohnson]

GS: “We do this because it is advantageous for us to do so.”

If you’re saying that we pick out some features of the environment and ignore others, and that this process has survival value, I agree. But that’s not the issue at point, which is the status of a term such as ‘similarity’.

“But the structure is there, and if it did not manifest itself as similar repeatedly we would never be able to abstract it.”

If you mean that some things look alike, or that the same thing looks alike at different times, again I agree. But that’s not the same as saying that things manifest ‘similarity’.

Brendan

Actually, I'm saying there must be some structure to events around us, for example, we see the sun 'rise' everyday' (if it's not overcast) . This is a similar event that occurs repeatedly and that similarity exists independent of any observer. This is an assumption of course since to prove it we have to observe it. 'Knowledge' represents 'similarity of structure', in other words when our language is similar in structure to the events. This means that the language is such that it 'explains' the event and can predict events reasonably well. If the knowledge ('theory', etc.) no longer can explain events then it is altered periodically, like when special relativity was introduced to account for the fact that the speed of light always measures the same no matter what the relative speed of the observer.

All of this would be impossible if there was no similarity of events around us as there would be no structure to them then.

[BaalChatzaf]

All of this would be impossible if there was no similarity of events around us as there would be no structure to them then.

It is like the color of light. Half of it is In Here and half of it is Out There.

Ba'al Chatzaf

[Gregory Browne]

Greg, this is a follow-up on #168.

For the major varieties of structuralism in contemporary philosophy of mathematics, see:

Hellman, Geoffrey 1989. Mathematics without Numbers. Oxford.

Shapiro, Stewart 1997. Philosophy of Mathematics: Structure and Ontology. Oxford.

Resnik, Michael 1997. Mathematics as a Science of Patterns. Oxford.

Chihara, Charles 2004. A Structural Account of Mathematics. Oxford.

Some of these structuralists are more realist, some more nominalist. So I expect they have a range of ways in which they would distinguish mathematical truth from physical truth. The more nominalistic structuralists seem to be the closest to formalism, but even the nominalist Chihara rejects the fictionalist spin that used to be placed on formalism and nominalism.

Stephen,

Of the 4 works on structuralism which one do you recommend that a beginner start with?

Greg

Edited June 15, 2007 by Greg Browne

[Dragonfly]

You still haven't proved that non-definitional truths are synthetic, because you need to prove that it is only definitional truths whose denial yields a contradiction.

A proposition that is not analytic cannot yield a contradiction upon denial, as it cannot be 100% certain, in contrast to an analytical proposition.

More importantly, that sentence was only an illustration. His general claims are:

(1) If a statement is true, then it is analytically true

A statement can be true while we don't know that it is true. In that case we can't logically derive the truth of that statement, and therefore it is not an analytic statement.

Yes, you do have to argue for what you claim, unless it is self-evident or your opponent concedes it, because you are claiming the existence of these dichotomies: it is not up to your opponents to prove that the dichotomies do not exist

It's just the other way around. Peikoff argues that the dichotomy doesn't exist; I've shown the flaws in his argument, that's all, I don't have to prove anything.

It can be self-contradictory even if you cannot be sure of its truth.

But in that case you don't know that it is self-contradictory, so you can't say that the statement is self-contradictory, in contrast to self-contradictory analytical statements, where you can categorically say that they are self-contradictory, they don't need any empirical evidence for that. That is the essential difference that Peikoff and you can't argue away.

I don’t deny that there is a difference: I just deny that it is the difference you think it is.

The difference is between truths about Shallow Kinds, on the one hand, and truths about Deep Kinds, Narrow Classes and individuals, on the other. Regarding the former, you will have certainty if you analyze the concepts right to come up with your basic truths, and then make deductions without making any mistakes. For example, we can analyze the concept of triangles to come up with the basic truths of trigonometry, we can analyze the concept of bachelors to come up with statements such as ‘All bachelors are unmarried’, and we can analyze the concept of ice to come up with statements such as ‘All ice is solid’. Regarding the latter, you may not have certainty, or any degree of knowledge, because you have to discover the basic truths: you have discover that water is H20, and that gold has atomic number 7, and you’d have to discover that all ice floats on water—if it did, which in fact it does not, which also had to be discovered.

A statement can be logically true, while it doesn't refer to a fact in reality. If I define "oil" as the solid form of water, the statement "oil is a solid" is an analytical truth. Of course this doesn't at all correspond with what we know of what we commonly call "oil" and "water", therefore such a definition would be useless as it contradicts common usage. It is much more efficient to use definitions of physical things that reflect our empirical knowledge about those things, we prefer that the analytical truth doesn't contradict our empirical knowledge. But that doesn't alter the fact that such a statement is true independently of our empirical knowledge. If we acquire new knowledge that no longer corresponds to that analytical statement, we'll have to adapt our definition(s), which has happened often enough in science.

However the above facts do not require us to conclude that truths about Shallow Kinds are not known by empirical means: we can still say that all concepts, including those of triangles, bachelors and ice, are empirical, and if that is true we can say that truths discovered by analysis of those concepts, such as the truths of trigonometry discovered by analysis of the concept of triangles, are known empirically.

Certainly not. Those truths follow logically from the axioms and definitions in mathematics, they cannot be falsified by empirical evidence.

But this matters little to me, because, as I have said, scientists are not authorities in this field. It is you who have been invoking their authority. Let's use our own arguments for our claims.

Of course scientists are authorities in this field, perhaps not in all the linguistic niceties, but certainly in the foundations of physics and mathematics, of which most philosophers don't know anything (Rand and Peikoff included). Only philosophers with a solid scientific background like for example Bernard d'Espagnat can be taken seriously in this regard.

You are making an Argument from Authority: you are saying that we ought to believe in these dichotomies because all or most scientists believe in them, and they are authorities in the matters, and so we should take their word for it.

No, you are making an Argument from Authority, by saying that scientists are not authorities in the field, implying that philosophers are, so the opinion of scientists is in your view of little importance. I merely deny that.

However, an appeal to the authority which asks us to believe what most scientists believe about general, basic scientific principles, including principles of general scientific methodology, and to believe it merely on the ground that most or all scientists believe it, is invalid. The basic principles of science, including those of scientific methodology, are principles that any intelligent person with a modicum of education should be able to grasp and analyze intelligently.

And that is a big error. I'm not saying that every scientist is an authority on scientific methodology, but I do say that a philosopher without a solid background in science is definitely not an authority, and certainly not Peikoff, in view of all the nonsense he has said about science (which I've documented elsewhere on this forum).

Again, 'does not depend on reality' is a little vague, but I will assume it means 'true in all possible worlds, i.e., necessary'. This then is the classic argument of some Logical Positivists such as Wittgenstein, who said that necessary truths are not factual (i.e., not about the world) because they are true no matter how the world is. However, being true no matter how the world is, i.e., being true in all possible worlds, does not mean that it does not say anything about the actual world---on the contrary, it means that it says something about each and every possible world, including the actual world.

No. Its referents may refer to things in the actual world, but not necessarily. With the usual definition of unicorn the statement "a unicorn has a horn on its head" is an analytical statement, or in your words, it's true in each and every possible world. But does it say anything about the actual world? We can calculate the volume of a 254306-dimensional sphere embedded in 254307-dimensional Euclidean space, which also forms an analytic statement. Does it refer to anything in the actual world?

Yes: those statement do say something about the actual world (as well as every other possible world). In the case of the unicorn statement it says that nothing without a horn is a unicorn, and so if anyone attempting to prove the existence of unicorns brought in some hornless animal their claims should be rejected immediately.

No, the statement doesn't say anything about the actual world, even if it uses a referent (the horn) from that actual world, as the unicorn doesn't exist in the actual world.

An analogous but more complicated statement could be made about the second, assuming that a sphere with more than 3 dimensions is even logically possible.

It is certainly logically possible. And I wonder how you could make an analogous statement, as in this case the proposition doesn't contain any referent from the real world.

I wasn’t talking about applicability in so many words, but if you want me to address it, I will: how could a theory be applicable to the world if it is not “factual” (i.e., “about the world”)?

Because there is an important distinction between the mathematical theory and the physical theory. The physical theory is about the world, it describes phenomena we observe and it can make correct predictions. It makes extensively use of mathematics in its models, but that doesn't make the mathematical theories dependent on reality. The physical theory can be falsified, the mathematical theory not. As I mentioned earlier, Rand decided that the concept "imaginary number" was a valid concept, while it could be applied to physical models. But the possibility of applying a mathematical concept to practical purposes has nothing to do with its validity - applicability is not the same as validity.

[Michael Stuart Kelly]

Dragonfly,

Don't we have to learn how to count before we learn higher math? And don't we start by counting things we observe, like fingers and toes?

That's one connection to reality at the start.

Michael

[Dragonfly]

Don't we have to learn how to count before we learn higher math? And don't we start by counting things we observe, like fingers and toes?

We may learn to count fingers first, as our intellectual machinery is not immediately sufficiently developed to tackle the abstract formalism. But when we improve our abilities, the fingers and toes can be thrown away. In calculating the volume of a 1234-dimensional sphere the only use for our fingers is to handle a pen or type on a keyboard. Astronomy grew out of astrology, chemistry out of alchemy - that doesn't imply that astronomy is the same as astrology or that chemistry is the same as alchemy, even if some of the activities look similar. Neither is mathematics the same as counting fingers and toes, even if it originally may have grown out of such activities. The essential step in that development was in fact throwing away those fingers and toes, the switch from the empirical to the abstract.