I'm too tired (and too busy) for a proper review right now. All I'll say is that this is a great overview of some of the formal tools needed to undersI'm too tired (and too busy) for a proper review right now. All I'll say is that this is a great overview of some of the formal tools needed to understand philosophical issues: set theory, infinity, Turing machines and computability, formal semantics, probability theory. It's not a book on philosophical issues, it's a book on math and logic that is motivated by philosophical issues. The attempt is not to tackle these philosophical issues themselves, but rather to present the purely formal mathematical (not philosophical) tools needed to understand the debates going on regarding the philosophical issues. It's a sort of "mathematics for philosophers" book, and a very good one....more
I'm too tired to write anything substantial about this right now. It's a good (not great) book about the philosophy of science, at the introductory leI'm too tired to write anything substantial about this right now. It's a good (not great) book about the philosophy of science, at the introductory level but probably presupposing some familiarity with basic philosophical terminology and some understanding of related fields such as logic and epistemology. It is divided into two parts: the first one dealing with the scientific method (inductivism, falsificationism, theories and observations, the underdetermination problem) both also discussing the debate about scientific change, dealing with Kuhn and his "revolutions" and "paradigms" among other things; the second one dealing with scientific realism, its subtleties and variants and its critics. The second part also connects, naturally, to other issues not falling directly under the subject of scientific realism but being relevant in a discussion of it such as: underdetermination (again), theory change (which at least touches upon the issues raised in the earlier chapter on scientific change) and the role of explanation in scientific theories, all discussed in the context of how they are relevant in the debate regarding the viability of scientific realism.
Another thing I should mention is that something that makes it stand out at least a little bit is that each chapter is ended by showing a fragment of an ongoing discussion between two persons (apparently not highly knowledgeable in philosophy, sometimes espousing very naive views, seemingly an attempt to give the novice reader someone to identify with). It is a bit original, but I never felt that these very brief fragments contributed anything to the discussion or the understanding of it. It's a nice introduction to the subject, definitely a good book, but not excellent....more
I think my first real encounter of a clear abuse of Gödel's incompleteness theorem came when I was engaged (as I so often am) in the debate on religioI think my first real encounter of a clear abuse of Gödel's incompleteness theorem came when I was engaged (as I so often am) in the debate on religion, online as well as elsewhere. This was one of the former kind and in one of the lower subcategories of the bigger category of online venues for the exchange of ideas: YouTube... Some atheist or number of atheists had argued against religion, presumably (because the response regarded this aspect of the religious question, but it wouldn't surprise me much to learn that the atheist/atheists in question had in fact asked about the ethical standards of the Bible or something else completely unrelated, the intellectual integrity and rational capacity of the staunch Bible defenders most of the time leave something to be desired) specifically regarding the question of the rationality behind belief in god. The response went something along the lines of this: "Gödel proved that there are unknown/unprovable truths [he did nothing of the sort], and therefore... [something about how belief in phenomena without evidence isn't so crazy after all]". The whole thing was topped off with the brilliant argumentative tactic consisting in showing a photograph of Gödel standing next to Einstein and saying something like "Look what kind of friends he had! Kind of a smart guy that Einstein!" This feeble attempt got some responses of its own pointing out how this application of Gödel's theorem to a religious debate was... hrm, somewhat misguided (for an offense to reason of this magnitude, any adjective seems insufficient so why not use one that is so wildly insufficient as to call attention to the difficulty of finding the proper words to describe how bad it is?), though as I recall, the commenters, quite appropriately, used much harsher words. Regarding those who abused Gödel in such a horrible fashion in this particular instance, I hold little hope as to their ability to understand either the theorem itself or the actually fairly simple arguments needed to explain why it was not applicable to this situation, but in the hope that such attempts are not always entirely vain, here's a book clarifying the issues!
Franzén has written an overview of the whys and hows of Gödel's theorem in a general, fairly non-technical way, so that one can see what exactly the theorem states, what it does not state (which we will focus on a little more soon), when and where it is applicable and what general conclusions can be drawn from it on purely mathematical grounds (which does include considerations in philosophy of mathematics as these are still bound by the technical details of the mathematics, but does not include metaphorical extensions of the theorem into other fields in ways that take no considerations of the mathematics needed to prove the theorem). The focus of the book is to guide the reader through the landscape of the theorem in order to show when it can be called upon and when it can not by exhibiting a number of bad arguments that try to lean on the theorem, but fail to produce convincing (or in many cases, even sensical) arguments for their conclusions due to failures to understand the theorem, misconceptions about its reaches and consequences, and showing how these arguments go wrong. The examples are gathered into different categories: there are those that, as in my anecdote above, relate to religious debates (but the examples found in the book tend to be more about atheists misapplying the theorem to try to show how the Bible is necessarily "incomplete" if "consistent", a grave error resulting from a misunderstanding of the theorem though the Bible is quite obviously "incomplete" in the sense of not being a complete guide to the universe as some Christians like to claim it is, but not an error showing a misunderstanding of the theorem anywhere near the level exhibited by the Christians on YouTube described above), to arguments against the possibility of a Theory of Everything in physics, bold proclamations of a "post-modern" era in mathematics following Gödel's theorem (!), and various arguments about the implications of the theorem both for the supposed limits of the human mind to grasp all truths and for the limits of computers as contrasted against human minds concerning their ability of proving theorems.
None of these attempts at deriving interesting conclusions in other fields from the proof of Gödel's theorem follow at all in fact. The main points Franzén use to show this is that there is a requirement upon any system exhibiting incompleteness first that it is a formal system (in a technical sense meaning that it is a set of basic axioms with a set of rules for deriving new theorems), second that it is possible to do a certain minimal set of basic arithmetic in the system (a requirement that needs no further elaboration here other than noting that this requirement is specified exactly), and third that even when a system does exhibit these characteristics, the incompleteness is still only a property of the arithmetical component of the system, the theorem says nothing about the completeness or incompleteness of the system with regards to the other, non-arithmetical, statements included in it. Taking this as a starting point for evaluating claims of incompleteness found in other areas, or supposed philosophical implications of the theorem (of which there are many that are legitimate), Franzén goes on to show what kind of misunderstandings that seem to lie behind the abuses of this famous theorem.
We need not let the details of Franzén's investigation prolong this text needlessly, but some deliberation on the kind of things people have been found to claim in regards to the theorem deserve mention. Many seem to think that Gödel showed that the peculiar sentence "This statement is not provable in the theory PA" while shown to be indeed, not provable in PA, has somehow still been shown to be true and that it has been shown to be true in some fashion that goes beyond formalization. The view seems to be based on the observation that this formal theory has been shown to not be able to prove the statement whereas this fact is just what the statement says so we can see that it is true after all. So far so good (unless I'm misrepresenting things a bit here myself, I have to be careful not to do what the people exhibited in the book are called out for doing): Gödel did show the statement to be unprovable and if it is indeed unprovable, it is true since this is what it says. The problem with overinterpreting this is that if we do see that it is true, we do so by some further deliberation, probably by evaluating the claim and seeing that the statement's unprovability in PA is just what makes it true. This further deliberation is necessary to see this though, and Gödel's theorem by itself by no means shows that the statement is unprovable but true (the only way it could be shown to be true by a proof carried out in the system PA is if it could be proven in PA, which is exactly what can not be accomplished). So no conclusions regarding "true but unprovable statements" follow: the statement is unprovable in PA, not in any absolute sense (there is no absolute sense of being provable). Another source of confusion is that people generally fail to understand that Gödel proved only that if the theory in question is consistent, then it is incomplete, not that it is incomplete. So the question of the incompleteness of the theory depends on whether it is consistent or not, but this is something which, according to the second incompleteness theorem, the theory itself cannot prove if it is consistent. In other words, with additional reasons to suppose the theory to be consistent, we can draw the conclusion that it is indeed incomplete, but we can not prove it to be so unless we can also prove the theory's consistency, which needs another theory which will itself be incomplete if consistent and unable to prove its own consistency if consistent and so on. This all complicates matters to a degree rarely taken into account in the many attempted uses (turned abuses) of the theorem.
Franzén does an excellent job exhibiting some common (and perhaps some not so common but nevertheless sever and therefore, attention worthy) abuses and explaining carefully why they are abuses. In doing so, he also covers the landscape of related results, additional ways to prove incompleteness that do not rely upon Gödel's strange self-referential formula showing, importantly, that the theorem is not just something having to do with self-referential (always a suspect in intellectual discourse) exotic sentences never encountered outside the proof of the theorem. Though doing so is necessary to understand the theorem thoroughly enough to appreciate who and why uses of it go wrong, but Franzén tends to take these mathematical side stepping too far, going into the many (interesting but nonetheless inessential to the question of the abuses of the theorem) details of the theorem and its implications (even when it is done in a mostly informal fashion) does little to inform the reader of why many popular attempts to draw conclusions from the theorem go wrong, and the facts that this does little to inform the reader in this is evident in how Franzén uses these issues in exhibiting the failures in the abuses: not much at all. Again and again, when he demolishes yet another piece of bad writing referring to Gödel, he comes back to the main points mentioned above: the theorem only applies to formal systems powerful enough to support a certain amount of arithmetic and even so, only to the arithmetical component. The additional details of different axioms for mathematics, variants of arithmetic and so on are of course very important for understanding the implications as well as the applications of the theorem, but are only relevant to a exposition of the abuses of the theorem when such details can be used to show the errors in the abuses, otherwise they belong instead in a much more encompassing work on the reaches and limits of Gödel's theorem, a work that would not be focused on explaining how and why so many of the attempts at using Gödel's theorem outside its field fail. Such a book would be extremely interesting, but it would need to be much, much, long than the current text which does seem to want to be about the abuses. It is also clear from the text that the abuses are in focus since the rest is just there to "set the stage" and asides into the land of mathematics not directly related to any abuses of Gödel's theorem only arrive when the discussion slides into them. In these cases, Franzén should have backed off a bit more readily and kept his focus on exhibiting abuses which would, on some occasions, have been more interesting and enlightening had there been a few more pages devoted to them.
Another problem with Franzén's willingness to take up so many related issues regarding the theorem is that the reader can easily be overwhelmed by all the terminology in a book that is, after all, written for non-experts. It's even claimed to be accessible to people with no previous background in logic, a claim I'm by no so tired of commenting upon that I mostly force myself to do so due to some sense of obligation: it's technically (though not in the mathematical sense of course) true that no previous knowledge in logic is required since every bit of terminology needed to understand the argumentation is defined in the book, but considering the number of such definitions, any reader not already at least familiar with logic and Gödel's theorem is bound to be confused fairly quickly. Franzén does do a good job of commenting upon when a certain technicality is essential for understanding the rest and when it is not, but this is hardly sufficient since any reader not already familiar with the terminology will probably fairly quickly lose track of which of these terms he or she needs to remember and which only appears parenthetically. These kind of claims of the lack of a requirement of previous knowledge are so common in logic texts (and I suppose in other areas as well though I suspect it's somewhat peculiar to formal science where such claims seem necessary as to not scare away potential readers) that I've gotten used to it, but I still feel the aforementioned duty to report on them.
It is in any case a very good book and, as far as I understand, a very original one. It does an excellent job of showing how Gödel's theorem can be abused and how to respond to such abuses, but it is not the best choice for an introduction to the theorem or it's implications. It is not primarily a guide (or at least not among the best of those) to what the theorem does mean but what it does not mean....more
After finishing Consciousness Explained recently and liking it very much, feeling convinced Dennett tackles the issues in the appropriate way, I feltAfter finishing Consciousness Explained recently and liking it very much, feeling convinced Dennett tackles the issues in the appropriate way, I felt a need to read this one next. Here, Dennett elaborates on his ideas that in order to understand consciousness, we need to take empirical findings seriously and if we do, we realize that there is no room for any center of consciousness in the brain. Rather, we find that activities are spread out over different areas having different functional roles, somehow adding up to conscious experiences. He sketches a theory of how and why certain activities result in conscious awareness, reshaping his earlier attempts through the multiple drafts model and fame models of consciousness, into the fantasy echo theory, according to which our consciousness is explained in terms of our ability to recall experiences which results in episodic memories being possible. As I understand Dennett here, he calls attention to an important difference between lower forms of attention, such as that exhibited by lower forms of life who we agree do not enjoy consciousness, at least not of our kind, and higher forms of attention that requires the ability to form experiences of episodes. It is just this ability to experience not just simple inclinations towards reacting in certain ways in response to perceptions, but complete episodes that can be memorized and recalled that explains our conscious experiences. An important aspect of the theory is that any conscious experience consists simply in a multitude of lower, unconscious states in the mind which come together to form the experience and that there is no one moment in which something enters into consciousness but that there is competition at any moment between different sets of lower brain states to rise in activity.
The different models come together more or less, and can be seen as elaborations on each other. In the multiple drafts model, Dennett made the analogy to academic articles. There are often no one canonical version of the article, it can be in circulation as one or several different drafts, be published in a conference proceedings and then in a slightly different version in a journal and so on. There simply is no answer to the question of when the article is officially published and Dennett suggested, by his multiple drafts model, that there similarly is no answer to the question of when a something first enters into consciousness. It is a gradual process of many lower brain states being activated together yielding conscious experiences that arise as "drafts" that get revised multiple times. The fame model describes the situation in other terms: different conscious experiences have a potential at any moment to arise from the activity of the brain, with these potential experiences competing for the "fame" of attention. In the fantasy echo model, Dennett seems to focus on another aspect of this. With the previous models, he attempted to explain how there is no one moment when something reaches a point of awareness, that there's an ongoing process by which conscious experiences shifts and changes gradually. Now, he lays down a theory of how conscious experiences are explained by focusing on our ability to recall events, to shape memories and experiences into episodes, which supposedly is meant to explain how we get rich experiences and not merely the primitive responses of unconscious life forms (let's take bacteria, for an uncontroversial example of a responsive yet unconscious life form).
The other side of this view of conscious experiences is that they are analyzable, at least potentially, in terms of lower, unconscious brain states and this is where Dennett spends a lot of time, I think rightly, to attack the idea of qualia and to show what goes wrong if some intuitions are left unexamined when considering some classic thought experiments meant to prove the existence of qualia. Philosophical zombies and Mary the color scientist are treated at length and the analysis seems to hold, but I'm not going to try to summarize them here now.
In conclusion, Dennett is to the point, unimpressed by intuitions, and carefully considerate of scientific results. His models are attempts to account for something beyond that which science can currently investigate fully, but he provides suggestions informed by scientific results for where to look for a theory of consciousness rather than, as Chalmers and others seem to be doing, suggest that consciousness is some sort of fundamental building block in our ontology such that no scientific, third-person, investigation can ever explain it. It's a lovely book further explaining Dennett's views of consciousness, perfect reading for anyone who has already read Consciousness Explained. The only reason I'm giving it only four stars (and I would have given it four and a half if that had been possible) is that there are times when Dennett writes tiny dialogues in which he pits his views against those of his opponents. Such passages can be enlightening and interesting (as we know from Plato...) but Dennett does not do a very good job with them. Even though I agree with most of his conclusions and think he does a good job of defending himself against his opponents, I think he does so best when he quotes them and picks apart their arguments one by one. In the dialogues though, he mostly succeeds in creating straw men that are way too easily defeated. I think the qualia people are misguided and confused but, as is shown when Dennett does quote them, their arguments take some time to pick apart and he does not do any of his opponents justice by making them go down so quickly as he does in the dialogues. Thankfully, these passages are few and short so they do not harm the reading experience too much, but it's enough that the rating needs to fall short of the full five stars. Another, tiny, flaw is that there are several passages that are repeated twice (and some, if I remember correctly, thrice). Dennett comments on this in one chapter, attributing it to the text of that chapter being a revised version of a lecture he gave which included material from the papers being the bases of the other chapters. This is understandable, but I'm pretty sure there was another repetition or two in the latter chapters. Perhaps this comment by Dennett was meant to apply to several of the last chapters. In any case, it doesn't matter much but the repetition was a minor annoyance which, in combination with my comment above on the badly written dialogues, necessitated the four out of five stars. I do, nevertheless, consider it a must read for anyone interested in theories of consciousness....more