Formal Objectivism

[occam]

1. Have the axioms and arguments of Objectivism ever been presented in the formal language of symbolic logic?

a. If so, where can I find them?

b. If not, is there a reason why? (i.e. no benefit, pointless, etc.)

2. Does Objectivism use a preferred formal system of logic?

a. If so, are there any particular pedantic details of this system I should be aware of? (i.e. use of exitential import, etc.)

Answers, or directions to where I can find the answers, are greatly appreciated.

[DavidOdden]

No, they have not been. There is no descriptive calculus for semantics which allows a correct formalization of the statement "I choose to exist" inter alios, so such a formalization would be contrary to Objectivist epistemology. There are (probably) also more developments needed in quantifiers and sets (I'm vaguely referring to Generalized Quantifier Theory and domain restriction). At any rate, I'm reasonably certain that the intersection of required expertise in natural language semantics and knowledge of Objectivism is null.

As for "preferred" logic, it would be Aristotelean.

[occam]

To clarify, by "Aristotelean" do you mean the specific methods and principles explicitly put forth by Aristotle himself or just any system that does not deny any of his basic principles? In other words, are venn diagrams and truth tables non-Aristotelean? Or are you distinguishing it from non-classical systems that deny the law of excluded middle or some other fundamental principle? Thanks.

Edited September 21, 2006 by occam

[DavidOdden]

I mean, logic more as envisaged by Aristotle. H.B.W. Joseph's Introduction to Logic would be a good example.

[Free Capitalist]

Venn diagrams and truth tables are certainly not non-Aristotelian. If anything, they're exceptionally Aristotelian.

[occam]

David Odden,

I've been doing some thinking about what you said in your first reply. I am unable to understand why the statement "I choose to exist" could not be formalized in a fairly straight forward manner. Let us begin by identifying the speaker; the person who "I" refers to. In this instance let's suppose "I" refers to you, David Odden. Then we get:

*(Ex)(Dx & Cx)

Where-

D: _ is David Odden

C: _ chooses to exist

A direct translation would be: There exists at least one thing such that, that thing is David Odden and that thing chooses to exist.

A more natural way of saying this would be: There is at least one person named David Odden who chooses to exist.

Or simply: David Odden chooses to exist.

I would be interested in hearing what, if any, objections you have to this formalization.

*(Ex) is the existential quantifier ( I don't have a backwards "E" on my keyboard)

Free Capitalist,

That's good to hear. I would agree that venn diagrams and truth tables are in line with Aristotles original conception of logic. I was not sure though if by "Aristotlean" David Odden meant it in a historical or conceptual context. Historically speaking, they might be considered non-Aristotlean because they were explicitly developed long after Aristotle died. My concern was that he might be claiming that any developments in logic that came after Aristotle were somehow no good. Such an argument would almost certainly have to depend on an implicit call to tradition. That is probably not what he meant.

[DavidOdden]

I am unable to understand why the statement "I choose to exist" could not be formalized in a fairly straight forward manner.

You're using undefined terms (so you aren't giving me a well-formed formula). You're treating "choose to exist" as an atomic predicate, which it isn't; in addition, you haven't defined "choose". The representation of proper names is sticky, as is the representation of common nouns -- many modern theories take proper names to be beyond formalization, which isn't hopelessly wrong, but still it means that simple truths involving proper names can't be properly recognised as such. And lastly, you haven't formalized "exist" (and it ain't just an existential quantifier). Let me put it another way: let "P" equal "I chose to exist" -- then by saying "P", I have formalised the statement (or any other statement). Under standard understandings of what a formalization is, "P" isn't a formalization of anything.

Having said this, the first two axioms of Objectivism can be formally expressed as Ex and P(x). IMO, a better statement of the second is, using quantification over predicates, AxEP(P(x)). However, when you hit the third one, you will be squarely faced with the problem of formalizing the concept "consciousness".

[occam]

Looking at my paraphrase now, I suppose it is a bit convoluted. For some reason I felt it was necessary to insert a connective (i.e. &) as well as an existential quantifier (i.e. (Ex)) even though there are no explicit connectives or quantifiers in the original statement. A better, more direct paraphrase would be, simply:

Ci

Where “C” is the predicate “choose to exist” and “i” is the individual constant referred to as “I”. Though, my intuition is telling me, this is not quite what you had in mind.

You're treating "choose to exist" as an atomic predicate, which it isn't

You may be right. However, if “choose to exist” is not atomic, it is a compound. If it is a compound, it is either truth-functional or it is not truth-functional. If it is truth functional, one can paraphrase it using a truth-functional connective. If it is not truth-functional, there is no need and no means of making the compound explicit. If there is no need and no means of making a compound explicit, one may treat it as atomic. In either case, it is possible to paraphrase “choose to exist”.

The only exception to this that I know of might be causal relationships, which are not strictly truth-functional. However, these can still be adequately approximated with a truth-functional connective, namely, the conditional arrow. So, even though they are not truth-functional one should still make them explicit since there is a means of approximating them in a truth-functional way.

Possibly you are thinking that I am using the fallacy of arguing from ignorance. For example, it may seem I am saying that because we do not know that it isn’t atomic, it must be atomic. However, I am really saying that treating a predicate as atomic is the default way of treating it. Unless there is some compelling reason within the context that it is given, a predicate should not be treated as a compound. This is because atomic predicates are simpler than compound predicates. So, I am not using an argument from ignorance, but rather, Occam’s razor (No, not my razor, the other guy’s). My first paraphrase violated this and that is why I revised it.

You're using undefined terms

I assume you are not using any of these terms in an extremely quirky or unorthodox manner. For example, I assume your not using “choose” to mean ‘red’ or ‘dog’ instead of something like ‘select’. Furthermore, this statement was introduced by you. If anyone should be defining anything it is you. This is unnecessary though, since I only need to understand the meaning enough to identify the logical components in the statement and I do.

simple truths involving proper names can't be properly recognised as such.

This is true but that only matters if you are trying to communicate that simple truth. The purpose of paraphrasing is not so much to facilitate communication as it is to facilitate logical analysis. To communicate a simple truth it would be better to state it in a natural language such as English. For the purpose of analysis though, a formal language like symbolic logic is far superior. Its superiority comes from how it reduces the natural language it is based on into nothing but its logical components. By logical components I mean things like individuals, predicates, quantifiers, connectives, etc. This is why I asked my question in the first place. I would like to subject the arguments of Objectivism to a thorough analysis.

you haven't formalized "exist"

In symbolic logic, anything that is not a distinct logical component is included in the abbreviation of the logical component it is a part of. The word “exists” as well as “consciousness” by themselves are not logical components of anything and it would be inappropriate to abbreviate them as one. In the context of a simple predicate the convention would be to abbreviate them with an uppercase letter from the beginning of the alphabet. Beyond that I see no meaning to the statement “you haven’t formalized ‘exists’.” How would I formalize a single word?

then by saying "P", I have formalised the statement (or any other statement). Under standard understandings of what a formalization is, "P" isn't a formalization of anything.

Strictly speaking, ‘P’ alone does not constitute a direct paraphrase of any particular statement. Conventionally, ‘P’ is used as a variable for any atomic statement. So, you are correct, since “I choose to exist” is an atomic statement I could symbolize it as ‘P’. However, this would not be the direct paraphrase of the statement, which is ‘Ci’. Instead, “P” can be thought of as a paraphrase of a paraphrase. It directly paraphrases ‘Ci’ as well as any other paraphrase of an atomic statement. In the case of ‘Px’ the ‘P’ is used as a variable for any atomic predicate, instead of a complete statement(x is a variable for any individual.)

There is no […]correct formalization of the statement "I choose to exist" inter alios[…]

To clarify, what did you mean by “formalization”? I took it to mean, roughly, a direct paraphrase according to the current rules and conventions of modern symbolic logic. Secondly, what do you mean by “inter alios” in this context? I took it to mean there are other statements, similar to “I choose to exist”, that also have no correct formalization. So, I read your statement as meaning “…there is no correct way to paraphrase the statement “I choose to exist” using the current rules and conventions of modern symbolic logic. In addition there are other statements that also have no correct paraphrase.” Is this an incorrect reading of your statement? If so, please explain.

Edited October 5, 2006 by occam

[DavidOdden]

In either case, it is possible to paraphrase “choose to exist”.

This is a case where some applied Objectivism may help you to grasp epistemological details. My conclusion is that it is not possible to paraphrase “choose to exist” (as a compound function of defined predicates). The reason that it is not possible is the current lack of such predicates, i.e. nobody has explicitly reduced "choose" to the axiomatic. "Possible" is judged relative to something, for example your personal knowledge or the accumulated knowledge of mankind, or it might mean "is allowed by this theory". I do believe that it will become possible to perform such a reduction at some point in the future, but right now it is not possible. Often, when someone says "is possible" in a philosophical discussion, they mean "is imaginable, though we cannot point to evidence that it is true". Objectivism rejects that (mis)construction of "possible", and requires that the possible be concretely (perceptually) supported even if not proven. If a statement has no evidence in support or opposition, it would be arbitrary.

The only exception to this that I know of might be causal relationships, which are not strictly truth-functional.

But they are truth-functional. However, that's a separate issue, and it's easy to get off track (which is good only when the track is a rut).

However, I am really saying that treating a predicate as atomic is the default way of treating it. Unless there is some compelling reason within the context that it is given, a predicate should not be treated as a compound.

It is true that this is the default treatment, and it is the wrong default (though, as I say, not a sinful default given that it actually is not possible at present to give a full formal description of some philosophical principle). Here is an example. The concept of "choice" depends on "volition" and "consciousness" (inter alios). This relationship is not something about Objectivism, it's about the concepts of "choice" and "consciousness", and other things. Objectivism does say that consciousness is an irreducible primary, and that living is man's fundamental choice. So in evaluating a principle of Objectivism, you need to distinguish between things that are statements of Objectivism, vs. those that are not. The definition of "choice" is ordinary and not specific to Objectivism. But an Objectivist principle about choice would entail something about consciousness. So you don't want to make the content of the concept choice totally inaccessible to philosophical inspection.

The fact is that most predicates really are compound, that is, higher order concepts built on low-level concepts, which are ultimately grounded in the sensorily axiomatic. A formalization of a statement about reality should reflect reality (see below): that is the purpose of a formalization.

I assume you are not using any of these terms in an extremely quirky or unorthodox manner. For example, I assume your not using “choose” to mean ‘red’ or ‘dog’ instead of something like ‘select’. Furthermore, this statement was introduced by you. If anyone should be defining anything it is you.

Well, I suppose it could be me for professional reasons, but let's leave that aside. You wanted to know about formal treatments of Objectivism, and I've explained that one of the prerequisites for such a treatment is that the principles of Objectivism be presented as well-formed formulas, meaning that they contain no undefined terms (undefined in a formal sense). When you appeal to "Yeah but everybody knows..." or "Nobody doubts what 'choose' means", then I would agree, but at the same time I argue that this is why formalization is unnecessary, and (for other reasons) it is downright harmful. I agree that one needs to understand the meaning enough to identify the logical components in a statement, and formalism is not necessary to do so.

For the purpose of analysis though, a formal language like symbolic logic is far superior. Its superiority comes from how it reduces the natural language it is based on into nothing but its logical components. By logical components I mean things like individuals, predicates, quantifiers, connectives, etc. This is why I asked my question in the first place. I would like to subject the arguments of Objectivism to a thorough analysis.

Alright, I have a challenge for you. Could you reduce the following to its logical components:

• "For the purpose of analysis though, a formal language like symbolic logic is far superior. Its superiority comes from how it reduces the natural language it is based on into nothing but its logical components. By logical components I mean things like individuals, predicates, quantifiers, connectives, etc."
  

The related question which I will put on the back burner is, what is the purpose of such a symbolic reduction? Perhaps the underlying issue is that we don't agree on the purpose of such translations.

To clarify, what did you mean by “formalization”? I took it to mean, roughly, a direct paraphrase according to the current rules and conventions of modern symbolic logic.

I do not agree that the concept of formalization depends on a social construct such as "the current rules and conventions of modern symbolic logic". Inductive generalization is not socially approved of in the modern symbolic covens, but induction is a valid mode of reasoning. Also, I don't know if "modern symbolic logic" is second-order logic or first-order logic. Do we include modal operators or not?

By formalization (of a statement), I mean the accurate (at the bare minimum, reference-preserving) rendering of a statement into an unambiguous and objectively stated/interpretable form. As you no doubt found in trying to render the above text in an objectively interpretable form, for many predicates it's difficult to render the meaning in an objective for so that we can see whether a particular conclusion does indeed follow from a premise, or is merely consistent with the premise (or even, actually contradicts the premise). The focus here is on objective specification.

In addition there are other statements that also have no correct paraphrase.” Is this an incorrect reading of your statement?

That's reasonably correct, with the understanding that I mean "objective, symbolic representation which preserves ...". This raises the question of what should be preserved, speaker's intent or literal semantics. We probably don't need to get into that problem now, but it's clear that you have to at least filter out sentences where there is a major disparity between literal reading and intention.