An [Ontological?] Argument for Free Will

Greetings,

I'm going to present to you an argument that human beings have free will. I have not seen this argument composed elsewhere, but if you uncover a similar argument from another source, I'd love to hear about it.

Here's how it will work. There are three "sets" of arguments. The first set has 5 premises, and should yield "C1"-- conclusion 1. The second set has 3 premises, and shoudl yielf "C2"-- conclusion 2. C1 and C2 should form an additional argument to yield C3. If you think my argument is wrong, it would be great for you to either attack one of the premises or argue that one of the conclusions do not follow from its respective premises. I'd love to hear your thoughts!

SET 1:
1. Either human beings can freely will or they cannot freely will.
2. If human beings cannot freely will, they either cannot will or they can will without freedom.
3. Human beings can will.
4. If a human being can freely will, we say that such a human being has "free will".
5. If a human being cannot will with freedom, we say that the human being is subject to "determinism".
C1: THUS, human beings either have free will or they are subject to determinism.

SET 2:
1. If human beings are subject to determinism, they perform the actions they perform but do not do so freely.
2. If one performs an action but does not do so freely, they do so because they were compelled.
3. If an entity is compelled to perform the action of evaluating an argument, they did so because they were compelled, regardless of beliefs about the validity of the argument.
C2: THUS, if an entity evaluates this argument to establish its validity, one was not compelled.

SET 3:
C1. Human beings either have free will or they are subject to determinism.
C2. If an entity evaluates this argument to establish its validity, one was not compelled.
C3: THUS, if an entity evaluates this argument to establish its validity, it did so with free will.

So, now we have C3: "If an entity evaluates this argument to establish its validity, it did so with free will". It's a conditional, and I'm fine with that. Let me ask you: did you evaluate my arguments to determine their validity? According to C3, if you cannot, you cannot reject arguments for free will. If you can, you have free will.

What are your thoughts? Is there a problem? Is it convincing, or do you find it lacking in some regard?

Graphic Novel Pseudo-Review: Logicomix

Logicomix: An Epic Search for Truth was written by Apostolos Doxiadis and Christos Papadimitriou. It tells about part of the life, ideas, and effects of Bertrand Russell and some of his writings, particularly Principia Mathematica. Common themes that are dealt with include the relation between logicians and madness (and whether there is a causal connection between the two), the arrogance of ignorance about mathematics, and the futility of systematic philosophy.


I call this a pseudo-review because it is not a legitimate review in any meaningful sense. I have only read one other graphic novel before (Bone, which, though it is phenomenal, is quite different in terms of content and intent from Logicomix), so don't know much about the medium. I haven't read a biography of Russell, either, so I can't confirm the historical accuracy of the work. Clearly, I am unqualified to write an actual review... so, what qualifies me to write a pseudo-review?

Well, I have some exposure to logic, meta-logic, and the Russell Paradox (and a few other issues the book raises). I have a strong interest in the topics, and a desire to learn more. I was sparked by the book to do some more research and learn a bit about his life and the lives of those around him. And, perhaps just as important, I appreciate good books.

This was a pretty good book. The reader is told, to some degree, why he or she should care about Russell's life, given a reasonable setting for his life story to be told, and treated to a clever mix of wit and wisdom. I'm led to believe that it is not entirely historically accurate, but then, it doesn't claim to be-- it's fairly explicit about its status as a storytelling device first and foremost. The narrative was fairly gripping and, although mostly predictable in content, was more or less unpredictable in execution. The reader knows at the outset that Russell shall find his way at the end of the book to a certain status, because he is introduced as bearing that status, but the path to get there is communicated vibrantly and through pretty great storytelling.

There are a few problems, however. In my opinion, this is not a work for readers unfamiliar with logic and/or modern analytic philosophy. If you did not have a background in logic or computer science, you would...

1. Be unable to identify figures, such as Wittgenstein and Frege, with respect to their actual significance; they would likely appear as mere caricatures.

2. Be unclear about some of the actual arguments-- for example, while the authors admirably attempt to explain the effects of set theory on infinite sets with the classic hotel-room example, I myself was confused-- and I knew how it worked! If a reader without prior exposure to infinite sets, much less set theory, read the explanation, I'm fairly confident that they would likely be more perplexed by the end than they were at the beginning. I may be incorrect, though.

3. Be uncertain why Russell matters. [SLIGHT SPOILERS AHEAD! TREAD LIGHTLY!] The authors seem fairly dismissive about Russell to me, and reduce him in the end to being a Subjective-Responsibility-Drone. While he's presented as having done a great job of tearing down mathematics, we're lead to believe that he was unable to add anything new to the conversation (Principia Mathematica was moot when it was published, as the story goes), and we're not lead to believe, at least as far as I gathered from my initial reading, that he had any longlasting positive contribution to philosophy.

Additionally, the madness/logic debate is tossed around a bit, but not very convincingly argued-- there's some promising moments throughout the work, but don't expect any masterful resolution or innovative views on the issue.

However, don't let me discourage you; despite its problems, Logicomix is a great work, and I really did enjoy it! I read the entire thing during a single, several-hour sitting at a fast food restaurant, and really enjoyed it. If nothing else, it taught me a little about Russell's life and sparked my interest to do more research outside of the book.

Plus, it was an enjoyable book. And that's saying something, too.

Logic and the Rules of the Internet

Greetings,

While there not, of course, official rules of the internet, there exists a set of unofficial rules; not all of them originated on the internet, but many are constantly referenced. I'm not going to post the full list here-- not all of them are likely to be appropriate for a blog post-- but some of them are at least mildly philosophically interesting.

The first rule we'll look at is the Danth's Law. This law states, "if you have to insist that you've won an internet argument, you've probably lost badly.” In other words, if it is not obvious and noncontroversial that you have proven your point, and yet you state that you have proven your point, the odds are good that you have already shown the weakness of your argument, and are past the point of no return. If the validity of your argument is not obvious from the argument itself, it is invalid; if your argument's form and content is insufficient to have achieved validity, asserting that it is valid will make it necessarily invalid.

Certain rules are numbered, due to their longstanding solidarity with message-board subculture, such as "Rule 14": "Do not argue with trolls-- it means they win". A "troll" is one who posts intentionally inflammatory material and/or responses, often ignoring basic logical principles such as validity, coherency, and relevancy. No logical argument, no matter how carefully constructed, can be valid if one denies the basic axioms of the logical system one works in. Trolls, who often make fallacious arguments such as Reductio ad Hitlerum (described below), do not hold the philosophical motivations of the pursuit of truth or even coherency; rather, they seek either to win or to create a reaction. Thus, do not engage in a philosophical debate with one who does not act in good faith; you won't be productive, and will probably just end up frustrated.

Another rule is Godwin's Law, originally stated by Mike Godwin in 1990, which claims that, "as a Usenet discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches 1." The reason? Across the internet, people are less personally accountable for their statements, and thus are less likely to concede to their opponents' arguments. Thus, a universal absolute is difficult to find. While individuals certainly exist who, online, would deny that the Nazis were in fact "evil", it is one of the few relatively non-controversial premises in an online argument. Therefore, it is likely to be used when there is no common ground.

A closely related rule was actually stated by Leo Strauss in the 1950's, which is Reductio ad Hitlerum, which argues that, "If Hitler liked P, then P is bad, because the Nazi's were bad", or, "If Nazis liked P, then P is bad, because the Nazis were bad." This actually seems to be a problem with the "is" function-- the "is of identity" versus the "is of predication. "Bachelors are unmarried men" is an example of the "is of identity"-- A is the same as B. "Nazi's are bad", however, is the "is of predication"-- B is merely a property of A. The Reductio ad Hitlerum argument states, [Nazis=Bad], [Nazis=(One who likes P)], therefore [(One who likes P)=Bad]. The arguer is mistaking the "is of predication" to be the "is of predication" (and vice versa). Some philosophical training on the differences between the two should be sufficient to show why such arguments are fallacious.


I want to credit an excellent article by the Telegraph for compiling many of these "laws", as well as several others I did not talk about. If you're interested, definitely worth a read. As well, a simple search for "rules of the internet" will yield a fairly solid list, with some minor variations depending on whose list it is.

The Paradox of the Unexpected Hanging, Part II

Zach and Anonymous commented on my last post on the paradox of the unexpected hanging. While their thinking is interesting, I doubt that they are on the right track toward a solution. Let me present an alternative version of the paradox (also drawn from Martin Gardner's article) and challenge them to see if their attempt at a solution applies to this form.

So a man is presented with ten boxes, each one numbered and all empty except for one, which contains an egg. He is told to open each box in sequence. He is also told that he will not know before opening the box that contains the egg that it contains the egg. So once again, the same reasoning applies. The egg cannot be in box 10 because if the man opens box 9 without having discovered the egg, he will know that it is in box 10. Elimination of the other boxes proceeds as before.

Maybe this less sinister and more basic formulation of the paradox will help in their search for a solution.

The Paradox of the Unexpected Hanging

You have been sentenced to death by hanging. The judge who condemns you to this fate informs you that your execution will satisfy two conditions. First it will take place some time in the early morning on one of the days of the following work week. Second you will not know which day you will die until the executioner appears in your jail cell to lead you to the gallows. You will be surprised. There does not appear to be any reason to think that your hanging cannot take place just as the judge has ordered. But a seemingly plausible argument leads to the conclusion that the judge's conditions are unrealizable.

In my last post I celebrated the birthday of Martin Gardner. Continuing in this theme, I now recount a paradox discussed by Gardner in one of his columns (and reprinted in his book The Unexpected Hanging).

Your execution must take place no later than Friday. Suppose you make it to Thursday afternoon. You now know that you will be executed on Friday, violating the second of the judge's pronouncements. So you cannot be executed on Friday. Now suppose you make it to Wednesday afternoon. Since Friday has been eliminated, you know on Wednesday that you will be executed on Thursday, again violating the surprise condition. So Thursday is out. The same reasoning will rule out Wednesday as well. Continue this line of reasoning until you have eliminated Monday. Therefore on no day of the week can you be surprised by the hangman.

As with all logical paradoxes, seemingly impeccable reasoning leads to a conclusion that is clearly at odds with reality. For having been convinced by your reasoning that you will not be executed, you are understandably surprised when the hangman arrives on Wednesday morning to carry out the orders of the judge.

So I leave it to you to resolve this paradox with the words of Bertrand Russell, who urged those who think about logic "to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science."

Zach's Ontology of Truth

Greetings once again, everyone,

Last night's meeting on the philosophical implications of the governmental censorship of obscenity was evocative, edgy, and yet hopefully still both fun and educational.

After the meeting, a few of us hung out and discussed something I had been pondering for some time, but had not actually written out until earlier that day: my proposed ontology of truth. For those who don't know, "ontology" refers to the science or study of the nature of existence. This is not an ontological argument for truth; rather, it is an attempt at classifying what I believe are actual kinds of truths.




Let the predicate "P" refer to "...Coheres with...", so that "Pxy" refers to "x coheres with y".
Let the predicate "S" refer to "...Is a statement", so that "Sx" refers to "x is a statement".
For "Objective Truths", let "T" refer to the one-place predicate, "...Is true", so that "Tx" refers to "x is true".
For "Subjective Truths", let "T" refer to the two-place predicate, "...Is true for...", so that "Txy" refers to "x is true for y".
In these propositions, "x" refers to statements that individuals make, and this test seeks to show whether a statement "x" is.
In these propositions, "y" can be interpreted different ways, depending on your approach to various epistemological issues. I personally find it easiest to think of "y" as a paradigm, as Kuhn considered it. If you have issues with Kuhn's summation of paradigms, think of "y" as a worldview or a summation of perceptions of sorts.
In these propositions, "z" refers to a a subject. "Txz" would thus mean that "x is true for z".

That should hopefully do it. If anyone has a hard time reading the image or interpreting the notation, let me know, and I'm happy to help.

At any rate, here's the gist. Note that the examples I provide are not meant to be insightful and provocative insomuch as they are meant to be noncontroversial. The difficult questions can come later.
For x to be an Objectively Absolute truth, it must correspond to all y paradigms that correspond with reality. If there exists a y paradigm that corresponds with reality, but x does not correspond with this y paradigm, x is not an Objectively Absolute truth. Most (if not all) mathematical axioms, such as that the successor of zero does not equal zero, would fall under this category.

For x to be an Objectively Relative truth, it must correspond to at least one y paradigm that corresponds with reality. If there exists a y paradigm that corresponds with reality, but x does not correspond with this y paradigm, this is not a problem, because this truth is relative. There are possible worlds, perhaps, where paradigm y does not correspond with reality; nevertheless, y corresponds to some reality, so x is true, at least in an Objectively Relative sense. As an example of an Objectively Relative truth, consider the statement, "the universe is constantly expanding".

For x to be a Subjectively Absolute truth, it must correspond to all y paradigms that correspond to reality, and there must exist a subject such that x is true for that subject. These truths require a subject in order for them to be true. For example, consider, "I ought not do that which is wrong". Such a statement requires the existence of a subject, an "I", in order for it to be possibly true. If there does not exist a z such that, for z, this x statement is true for z, x is not true at all.

For x to be a Subjectively Relative truth, it must correspond to at least one y paradigm that corresponds with reality and there must exist a subject such that x is true for that subject. As an example of a Subjectively Relative truth, consider, "Ice cream is my favorite cold desert". This statement corresponds with a y paradigm-- my current one-- that also corresponds with reality. However, at a future point, that y might no longer correspond with reality; I might pick a different cold desert as my favorite. Thus, truths under this category are Subjectively Relative, as opposed to Subjectively Absolute.

Thoughts/comments/suggestions? Criticisms? Applause? Disgust? Hunger for ice cream? Thanks for your comments!

The Dreams of Madmen

It is unusual for me to have time to read just for fun this late in the semester. But I was happy to have a couple of free hours this afternoon to read a short, beautifully written novel, A Madman Dreams of Turing Machines, by the physicist Janna Levin.

Being a student of logic and analytic philosophy, I was of course very eager to read this book as it moves back and forth between the lives of the great logician Kurt Godel and the mathematician and computer pioneer Alan Turing, mixing fact and fiction, though Levin's account remains very faithful to the lives of these two tormented and tortured men. Along the way we read about encounters with other notable figures of 20th century thought, among them Moritz Schlick, the dominant figure of the Vienna Circle or logical positivists, who was murdered by a deranged student with Nazi sympathies, Oskar Morgenstern, one of the founders of game theory, and, of course, Ludwig Wittgenstein, perhaps the greatest philosopher of the last century. The discussion between Wittgenstein and Turing during a Cambridge seminar is both fascinating and frustrating, as is the overall contrast between the deterministic Turing and the mystically-minded Godel, who sees his Incompleteness Proof as a decisive refutation of many of the trends in 20th century philosophy. The final chapters on the  decline and death of the two are harrowing, especially the vivid portrayal of what amounts to torture of Turing by the British authorities seeking to chemically suppress his homosexuality. It was Turing's work that led to the breaking of the German Enigma code during the Second World War, an important contributing cause to the defeat of the Nazis. It is nothing less than a tragedy that Turing was treated after the war not as a hero but a criminal. 

In sum, I recommend Levin's book to anyone even remotely interested in 20th century philosophy.