It forces you to bite the bullet and really think about how systems must be able to give rise to intelligence, regardless of their physical makeup.
The wikipedia article that you linked has this quote:
"The sheer volume of the literature that has grown up around it inspired Pat Hayes to quip that the field of cognitive science ought to be redefined as 'the ongoing research program of showing Searle's Chinese Room Argument to be false.'"
Incorrect arguments are an important step in establishing correct ones, which is a central point of jsomer's argument.
It might be useless, but it's also not optimally useful. That is, I think, a large part of the problem PG points out in his essay.
So it inspired a huge waste of time. Doesn't really fit my definition of useful.
I guess the only way to "refute" it would be to create complete theory of human language and use it to prove that he isn't actually saying anything. But that doesn't seem very effective or promising as an undertaking to me.
Rephrased, maybe the problem with the chinese room is that it uses the fuzzy notion of consciousness, appealing to the vague emotions of it's audience rather than on logic. In so far as philosophy aims to clarify language, perhaps the chinese room could be useful as a bad example.
An example consequence of this interpretation: having 0.5 oz of pot is a minor crime. But if you mix it with 10 lb of lawn trimmings, you now have 10+ lbs of material with a detectable amount of a controlled substance, and you're theoretically guilty of a major crime. This is not a law written by science majors.
Giving credit to the legal system for sorting out such a broken law is like giving credit to Vista for having a stylishly designed BSOD.
You jump on the delicacy of the language and that's the point. jsomers doesn't argue _about_ this particular law, he was only giving an example on how pushing and pulling language can have direct pragmatic purposes and real political ramifications.
The point is that since law is mired in language, exploring language becomes an incredibly relevant task and pg's criticism seems to ignore this important function.
Later jsomers says philosophy was bad but has reformed.
So on the one hand he defends old philosophy. And on the other he claims philosophy was bad, but is OK now because it has reformed. These defenses are incompatible.
I don't know about that:
The world is everything that is the case. *
The world is the totality of facts, not of things.
The world is determined by the facts, and by these being all the facts.
For the totality of facts determines both what is the case, and also all that is not the case.
The facts in logical space are the world.
The world divides into facts.
Any one can either be the case or not be the case, and everything else remain the same.
I think that's kinda the whole point of the Tractatus: much of philosophy (metaphysics and ethics, particularly) has no sense. Strictly speaking, they mean nothing.
Wittgenstein's early work inspired the development of modern analytic philosophy both in its use of formal methods and its claim that much of what was then considered philosophy was meaningless. The decades immediately following Wittgenstein were concerned with linguistic analysis (what the authors of these papers take fault with), while more contemporary philosophy has conceded to a kind of naturalism, appealing to the sciences.
If you place any value on modern analytic philosopher (even as a Popperian), you have to at least give Wittgenstein some historical credit even if the philosophical travesties of the logical positivists can be attributed to misinterpretations of the Tractatus.
With regards to decent philosophers with direct influence from Wittgenstein, what's your take on Kripke and Anscombe?
Anscombe wiki has:
For years, I would spend time, in cafés, for example, staring at objects saying to myself: "I see a packet. But what do I really see? How can I say that I see here anything more than a yellow expanse?"
I think that stuff is a dead end. We should solve problems we have, not question all traditions simultaneously for no particular reason.
By the way, I do think there are good philosophers, who made useful progress, but they are largely neglected. e.g. xenophanes, godwin, burke, feynman. (neglected as philosophers)
In philosophy a method proposed by Descartes to find the foundations of knowledge was to doubt everything that possibly could be doubted which includes the external world. Wittgenstein in his Tractatus similarly starts from a blank slate and tries to define and describe the world without crossing his own boundaries and definitions of what can be considered sensible to say (and fails. To objectively describe the world is an attempt to step outside it and his bounds of sense).
I would also like to note that this early is work very different from his later work where he completely rejected the Tractatus, writing with a different style and focus. His later work (especially Philosophical Investigations) has some extremely interesting ideas regarding language, its use and development which I believe would interest those working in the areas of semantic web and NLP.
Heh. Something about this comment seemed very familiar to me, and after a while I figured out what it was: the distinctive sound of xlnt aka curi. Yay web history!
While I have an enduring if inexplicable affection for you, and get that you weren't being sarcastic, the last thing I want to do is have an argument about Wittgenstein together :)
Edit: Besides, there can't be that many people who go on about Godwin, Burke, and Feynman.
His work seems to follow logically from Wittgenstein's point that a lot of philosophy comes down to the precise meanings of words.
The Chomsky hierarchy -- a method of classifying formal grammars. Seems computer science-y enough that you'll consider it as something real. http://en.wikipedia.org/wiki/Chomsky_hierarchy
1) Graham found philosophy not useful and didn't understand it. This is basically a sample size of 1. Is this a meaningful sample or just a confirmation bias (or suppressed evidence)?
2) Graham believes the early philosophers were encouraged by the progress in maths. But was there really much progress before Euclid's Elements, written around 300 BC, one of the "the most successful and influential textbooks ever written"? Sokrates lived about 150 years earlier (c. 469 BC–399 BC), Plato 50 years earlier (428/427 BC–348/347BC) -- even Aristotle lived earlier (384BC–322BC). One might as well argue that the Greek tradition in philosophy encouraged Euclid to write his elements. The Elements might also have been inspired by Aristotle's logic. But that was obviously useless, according to Graham.
3) In hindsight, it's easy to say what's, for instance, the shortest way out of a labyrinth. But one needs to go many false routes to find out. Are these useless, then? Graham obviously thinks he could spot the shortest way out, by studying "useful" goals. But who really knows? It's easy to say: "I know what's the shortest way" but most people fail when put to a test. Even Wittgenstein was first "wrong" and wrote a rather abstract -- and Graham would probably say: useless -- treatment called "Tractatus Logico-Philosophicus" before he was able to articulate his critic of language. Sometimes you need a ladder before you can throw it away.
4) Graham also forgets that philosophic thinking inspired or formed many other schools of thought: for instance, the study of moral philosophy by Adam Smith marked the beginning of modern economics -- indeed, a useless art --, the study of natural philosophy and that of Malthus' work (an economist and demographer) lead to the discovery of "natural selection" by Darwin -- truly useless, I guess -- , the study of the philosophy of positivism by Comte started modern sociology -- yet another useless art --, theories guiding modern scientific thinking were formulated by philosophers (Popper, etc.) -- obviously useless, too --, even Russel and Whitehead's work was basically inspired by philosophy. And these are just the proverbial tip of the iceberg. Anybody who's a little bit careful can find these examples easily. Graham, however, failed. What does this tell us about his essay?
In summery, what he wants philosophy to do -- namely concentrating on useful stuff -- is already happening, for hundreds of years. It's called science.
2) I am having serious trouble figuring out how this dismisses PG's essay.
3) So this is the only item in your list that actually addresses Graham's central point at all. I'm not sure exactly what you're trying to say but I think you're circling around this idea: "Sure, pre-20th century philosophy got a lot wrong, but it was that wrongness that allowed certain modern philosophers to get stuff right. PG thinks he could've gotten through the wrongness quickly, but I think he's wrong about that."
Well, okay... but let me give some evidence against that: I independently came to the conclusion that most philosophy is bullshit before I encountered Paul Graham. I think I'm smart, but I'm also pretty sure that there have been a bunch of people in history who are just as smart as I am, and so I'm led to the conclusion that there have been people in history who realized that philosophy as it was being practiced was bullshit. Which implies that, yes, all those pre-modern philosophers were wasting their time, because we didn't need their "false starts" to get to the root of the wrongness with philosophy.
4) I admit that I don't know enough about the origins of various disciplines to talk about any of the things you brought up, but, to me, the fact that philosophy helped nurture "useful" disciplines and ideas doesn't automatically imply that philosophy itself is valid or useful. Every kind of thinking, even pretty dumb kinds, produces more thinking. And after more than two thousand years, it's statistically likely that some of a discipline's intellectual offspring will have merit, even if the discipline itself doesn't.
Also: "Anybody who's a little bit careful can find these examples easily. Graham, however, failed. What does this tell us about his essay?"
First: this is really incredibly obnoxious. Second: why do you think that attacking the construction or presentation of PG's argument is the same as dismissing the argument itself?
I'll try to answer some of your objections.
(1) You're right that "sample of 1" is an expression found in experimental science. But how do we know that a small sample is no sufficient reason to accept a hypothese if not by using logic?
Also: Read PG's essay once more and tell me: What reasons did he present to support his hypotheses, other than merely: "I didn't understand philosophy, therefore all current philosophy is useless"? He's basically making an appeal to authority, namely his own authority. Hardly a good reason.
2) PG asserts that early philosophy was inspired by maths. But was it, really? How does PG know? In fact, both fields probably inspired each other. This is one of the examples that makes some philosophy useful -- examples that PG simply ignored.
3) Just because you agree with PG (or had a similar experience) doesn't make any of you right. However, I agree that philosophy has had a quality problem every now and then. But that doesn't render all philosophy (or its method) useless.
Also: I'm wasn't trying to say: "I think he's wrong". I say: "Where are his arguments to believe his assertions that he can find a quick way?" Even the more practical sciences have had some really strange ideas when looking at them in hindsight. If usefulness is such a good guide, why did they run into these errors?
4) Indeed, all kind of thinking produces more thinking. Homo sapiens is about 40.000 years old. Then, what did they do the first 37.000 years if mere thinking is sufficient to find the meaningful and true statements?
Finally, attacking the presentation is often the same thing as dismissing the argument. For what are his arguments? PG can point to some bad philosophy, granted. Everybody can do this for all kind of fields. I can point at some really bad software. Is therefore all software engineering useless?
PG wants us to believe his assertions that the philosophical method is inherently flawed. But he presents no arguments other than his own experience, some selected examples and that's about it.
If you want to know what's useful about philosophy, look no further than Socrates: His way to ask people critical questions about the meaning of words, the reasons why they do have the believes they have, and his way to find the differences between good and bad reasons (namely by debate) still is what philosophy is all about. We need the bad thinking to find out why it's bad. Philosophy proceeds by discussing and recording these issues.
You might call it as well critical thinking.
Our small discussion here hopefully shows why this is useful. Trying to dismiss arguments makes you a better thinker.
Also, you may want to read PG's essay on essays (www.paulgraham.com/essay.html); his goal in writing an essay isn't to explicate every detail of a subject, it's to work through a subject to understand it--it is only tangentially that any other audience is involved. That I am convinced of the rough truth of his arguments is not solely based on what he has written, and he does not have to personally supply me with every bit of evidence to be right (although doing so would certainly make it easier for the reader).
2) I would not question the fact that Greek philosophers influenced the development of mathematics, and I expect PG would not do so, either (particularly since the Greek philosophers were typically also mathematicians, but even without that, it would seem an impossible claim to the contrary). A claim I have made, however, is that the things that the Greek philosophers wrote that could not now be seen as important in some other field currently extant, or in cognitive science--which ought to be thought of as its own field (although in many places it isn't yet)--were not themselves important to the development of mathematics or any other field. These aspects of their writing, when studied, critiqued, and emulated in modern times, are the only topic of concern to PG in his essay, or myself in this particular discussion.
3) This is a fundamental problem. Just because we disagree certainly does not make one of us right, and the only reason that at least one of us is guaranteed to be wrong about something here is because I just asserted that we disagree. An equally fundamental problem is your assumption that either PG or myself is talking about all of philosophy.
With regard to "strange" ideas, every field has had strange ideas when looking in hindsight. The fields for which those ideas are still in contention for validity are the ones with the greatest problem of lack of substance, in proportion with how many such ideas there are, and how "strange" they are (where by strange I do not mean counterintuitive, but rather running against other existing evidence).
4) Relatively little thinking. We got a lot better at it when we didn't have to spend most of our time hunting and gathering. The course of human history has been the process of freeing up more time to spend thinking; at this point, we've freed up so much that we tend to use most of it in ways we typically later label as non-productive.
You say you can do this for all fields. Can you point to some bad math for me? That you would have much greater difficulty doing this than PG or I would have for finding bad philosophy is precisely PG's point.
Is there some other form of argument that could possibly exist to support his claim other than personal experience and selected examples? I'm not sure what kind of evidence you would like to see in PG's essay, but feel it lacks. The subject matter does not lend itself to effective experimental testing, and the claim is not mathematical in nature.
PG's, and my, problem, is that modern philosophers still rarely identify the fact that the bad thinking is bad. Understanding the utility of (and the utility of understanding) effective but civil critical debate remains unquestioned. The subject matter of these debates is what is under fire here, precisely because it is typically pervaded by faulty reasoning. Even if you want to use previous bad reasoning to learn why some reasoning is bad, this doesn't mean you need to continually create more examples of bad reasoning; surely those that already exist suffice.
But did he present any useless philosophy or just badly written philosophy? Or does it just appear to be useless because we don't immediately understand it?
The latter case basically boilds down to an argument from ignorance: "We don't understand some philosophers, therefore they must be useless (or bad or false)." Many people don't understand much of contemporary maths either, but that's hardly a good reason to call it useless (or bad or false). In contrast to maths, though, many people assume to be able to understand it.
The former case is also hardly a good reason to call something useless. Kant, for instance, is bloody complicated to read (at least, for me, and I'm German). However, his arguments still make sense -- one just needs to read the literature that explains Kant's ethics and meta-physics in a more accessible manner. They were also quite useful for other philosophers.
You say you can find bad philosophy more easily than I can find bad maths. Maybe, but since this is basically an empirical question, our small sample won't be sufficient to prove anything. On a side note: It's easy to find useless maths -- in the sense of published proofs that turned out to be wrong. Since they didn't prove anything, why have they been published, at all? For examples, look at the history to prove Fermat's Last Theorem. Quite a lot of them failed or were simply wrong. What a waste of time.
However, your test to find useless philosophy also suffers from the lack of a proper definition of "useless" and "useful". Just because you can't think of any use, doens't mean you're right -- this is just another argument from ignorance.
Let's consider ethics, for instance: It is basically useless concerning empiricial results. However, it's still useful in many contemporary discussions; for instance, animal's rights, abortion, women rights, death penalty, justice, atheism, and many other issues.
Concerning your question whether some other form of argument could possibly exist to support PG's claim? Sure, from an empirical point of view: A proper definition of "useless" and a proper random sample concerning philosophical works. This would at least support the conclusion that, say, 35% of philosophy turned out to be useless.
But PG made two additional arguments:
(1) Any resulting number of useless philosophy is due to the current philosophical method that is motivated by studying the most abstract problems.
(2) A different method that starts from studying practical problems and builds up to abstract problems will result in a smaller number of useless philosophy.
To support (2), an argument from analogy would help: Study a model of the proposed method (thankfully provided by science) and establish the empirical fact that is produced a smaller percentage of useless results.
Of course, this can easily be refuted by attacking the analogy. The methods of empricial science simply doesn't translate well to issues philosophers care about; such as ethics.
To support (1), one would need to start from the premise of the current method and deduce that it will lead to a certain number of useless philosophy and that there is no other possible explanantion. I doubt that it can be done, but I may be wrong.
Just to present a counter-example: to establish the habit of presenting arguments in a more formal way could help to distiguish good and bad philosophy much easier.
However, the point is that PG -- although his intention is apperently to "work through a subject to understand it" -- fails badly. He hardly worked though and he probably still doesn't understand it. Maybe, if he would have studied philosophy more carefully he could have made better arguments for his case.
Which shows how careful one should be about certain words: From a philosophical point of view, namely, PG's work was useless, indeed.
That empiricism doesn't apply well to ethics is part of PG's point; he does not believe that the philosophy of ethics is useful. From my definition, I would say that the philosophy of ethics can conceivably be useful, but rarely is in practice.
In vague support of argument one, you might try turning your other argument on its head. Philosophy and science (and, before science, engineering and early health care) developed in parallel over the course of human history; one of them primarily studied abstract problems and tried to make them more useful, one of them studied uses, and worked toward abstraction. Until the 19th century, it appears that abstract study was better for developing new fields, and concrete study was better for development of technology. After the mid-19th century, philosophy lost its firm grip on most forms of abstract study, and became (for the most part) the field that it is today; now other fields tend to be the starting point for the spawning of new fields, and tend to be better for the development of technology.
With regard to your counter-example, I will continue to present my counter-counter-example: mathematics.
Your final sentence is nicely ironic. If, as you've said earlier, you need bad philosophy in order to determine what the good philosophy is, yet PG's work is useless, then PG's work must not be bad philosophy.
Graham believes the early philosophers were encouraged by the progress in maths. But was there really much progress before Euclid's Elements...?
So how else can we know anything if we can’t use our senses? Well, like many others of his time, Socrates was a Pythagorean, a follower of the pre-Socratic philosopher Pythagoras. Now Pythagoras believed that the entire cosmos worked according to mathematical principles – in other words, that there was a plan, a great cosmic dance orchestrated by a divine intelligence.
So if that's true, then certainly Socrates’ worldview (as presented by Plato) was very Pythagorean, and the Pythagorean worldview was very much founded on the power of math. And you can find Socrates demonstrating math in some of the dialogues.
I think the problem of philosophy has not been following some false routes. That is necessary and good as you point out. The problem has been that a lot of talent has been wasted going around in loops.
In order to learn more about related phenomena, one needs multiple data points with varying initial conditions. In order to understand more details about a specific case, no further data points are needed or desirable. Graham's essay is about his interaction with, and opinions about philosophy; he doesn't need any other data points in order to tell you his opinion, nor do you need any other data points to talk about history.
2) Actually, one would nominally point to the start of both fields in Thales, who was seen by Aristotle to be the progenitor of Greek philosophy, and supposedly was the first person to note that the angle inscribed in a semicircle is always right. Note that, even before that, there definitely existed at least non-trivial arithmetical problems (such as finding the volumes of various solids), that were known literally a millennium prior (to learn more, consider the wiki pages for Thales, the history of mathematics, and Egyptian mathematics).
Of course, this is brushing under the carpet the fact that in Ancient Greece, the distinction between a "philosopher", a "mathematician", and a "scientist" did not yet exist (exception: physician was an independent job title); the Greeks could not have seen themselves as anything less than all three. Graham's claims have much more to do with the fact that philosophy, as an independent field, continued to exist long after this distinction became clear.
3) Your claim here is not entirely clear. Are you really trying to validate the failed methods of philosophy by saying that it's important that we try them now so that we don't make the mistake of trying them later?
4) Three of your examples date from 1750 to 1850, and are examples of how enlightenment thinking bridged the gap from philosophy into what could actually begin to be called science--these people were called philosophers because there was no other word yet extant to describe what they did, but we now recognize their results as belonging to other fields. The fact that they called themselves philosophers is irrelevant; their results did not in any way require the existence of the rest of the field of philosophy.
The important contributions of Russel and Whitehead to mathematics might have been inspired by their personal philosophies, but having such a philosophy does not require the existence, import, or study of the many misshapen works of the field.
Finally, Popper is an example of exactly what philosophy can do to actually be useful--answer a question about how to approach the gathering and use of knowledge.
In summary, what he wants philosophy to do is indeed science...so why are there still philosophers doing anything else?
But I agree with you in principle that this is a weak point. The essay's point was to respond to pg's attacks. jsomers never assumed that pg's single paper had somehow thrown philosophy into chaos and shambles.
2.I agree with you here that there is little distinction between these fields in Greece. But that's an interesting fact isn't it--it's essentially conceding that at least initially philosophy played an important role in the development of math and science (one certainly can't assume that the development of philosophy and math were going in two different tracts in the same man's head).
3.He's not saying that philosophy failed. He's arguing that pg is finding fault ex post facto. It's easy to fault Kant after you've read a response but perhaps without Kant the response (and the progress that supposedly came with it) never would have occurred.
For an analogous situation--Galois developed his theory which allowed for a proof that no polynomial of order 5 or greater was guaranteed a solution by radicals. Does this mean that Ruffini was a putz because he could only do most of the proof for order 5 polynomials? After all--he was clearly taking the wrong approach.
Or, do we think Pascal is an idiot because Newton developed the calculus that solved the problems he could not? No.
The point is that everything builds on everything. I think somers' Kant tree is a great example of this.
4. This is backwards. The point is that philosophical reasoning often led to the creation of entirely new fields of thought. Economics, politics, law and linguistics are great examples of this.
Would we have modern legal thought without the works of philosophers like Locke, Berkeley, Hume and Hobbes?
Would we have modern economics without the work of Smith, Pareto and Mill?
Would we have modern sociology without Marx and Gramsci?
That they called themselves "philosophers" is not irrelevant whatsoever. It demonstrates that philosophy often lays the groundwork for entirely new fields.
It's strange you say that their results did not require the existence of the rest of the field of philosophy. I suspect they would disagree as they seemed to rely on other philosophers in their own work.
5. What is your metric for "useful"?
We might not have had modern political science without Locke, Berkeley, Hume, and Hobbes. But we would have had Hobbes even if he had not been classified as a philosopher, and thus we would have had the rest of them.
We might not have had modern economics without Smith, Pareto, and Mill. But we would have had Smith even if he had not been classified as a philosopher, and thus we would have had the rest.
We might not have had modern sociology without Marx and Gramsci. But we would have had Comte even if he hadn't been classified as a philosopher, and thus we would have had the rest.
I mention these three individuals' work because they (1) fundamentally began what came to eventually be their fields, and (2) did not really build these fields incrementally out of the rest of the philosophical body of knowledge at the time. This demonstrates that it isn't some kind of unifying thread within the study of philosophy that causes these fields to spin off from them; philosophy was just what you called it when you were studying problems that weren't in their own field yet. This no longer occurs in modern times, so we don't see philosophy spinning off new fields in the way that it used to; computer science (as a whole) sees its roots in modern mathematics, not philosophy. Psychoanalysis, as a modern field (unlike psychology as a whole, which also often refers to much older studies), clearly descends from biology. Electrical engineering. Nuclear physics even has it in the title.
The study of the works of "philosophers" can still be relevant within other fields, but to study philosophy is to spend one's time looking at what's left. It is this study, in modern times, that pg and I are attacking as vague, useless, and prone to wars of semantics.
One of the most interesting things I find about pg's essays is that they always take such an interesting position on a problem or issue. I've always thought that there is at least one interesting counter position for all of his essays. We need to see more of these; I think it would lead to many fruitful discussions.
"The simplest flaw in PG’s account is its scope: it implicates most philosophers up to the present"
That's what he's trying to argue with, and that is PG's claim (not that all philosophy is worthless). But then he simply concedes at the end, like he forgot his own thesis.
My "most," in other words, includes less than his.
Also, while I'm sympathetic to the intent of this essay -- easy criticism of the humanities goes back to Aristophanes -- it falls flat because it reads like a philosophy paper. A philosophy paper written in defense of academic philosophy is going to lose in the gut regardless of how correct it is to the reasoning mind (this is also why we still love Aristophanes).
The biggest disagreement I see between the author and pg is the current state and value of philosophy. This is why I view the authors concession that most current philosophy might be garbage as largely irrelevant.
He mentions that one particular philosopher of the mind generated some testable hypotheses about how the mind works. Why not, then, test them? Why don't we see many philosophers flitting back and forth between thought and action? In other words, where are the Hofstadters?
There's a significant community of modern philosophers/logicians actively contributing to developments in CS. Also, check out the Philosophy department at CMU: they've got someone employed full-time to work on implementations of philosophically-inspired causal inference systems.
Calling mathematics "incontrovertibly true" and stating that abstractions used in mathematics can be explained concretely in simpler terms are philosophical positions and the justifications for and against these positions are debated outside mathematics in philosophy. You praise the rigor of mathematics while ignoring the rigor in which philosophy searches for the justifications of assumptions for all fields of human knowledge including mathematics and science.
That any philosopher might continue to debate this issue is, while sadly true, irrelevant. A logical system without modus ponens can either define modus ponens, or is clearly not extensible enough to define anything. A logical system with modus ponens is either inconsistent, or at most as general as mathematics. Thus, there can be no extensible system of truth in which mathematics is false, validating my claim that it is incontrovertible.
As to whether or not mathematics can be explained in simple terms, I will suggest that this appears to be the case empirically, since some people become mathematicians, and they all seem to use the same terminology, more or less. To prove that every mathematical result in existence can be explained simply would require that I actually explain every mathematical result simply, and that is beyond the scope of an HN comment.
Finally, philosophers do not "search for the justifications of assumptions for all fields of human knowledge including mathematics and science" with the level of rigor I specified in my comment; indeed, the entire point of this discussion is that they tend not to use any level of rigor at all. Insofar as philosophy actually does anything to "justify the assumptions" for any field, it occasionally achieves useful results; however, much of philosophy is focused solely on a continuing failure to agree on semantics.
That mathematics corresponds so well to the world we perceive is amazing. Why should this be the case? How can we be sure that mathematics and science holds for all cases which we do not observe or that they will continue to do so? Can rigorous justifications be given for these questions that do not rely on circular arguments and blind faith?
There are no solid, incontrovertible definitions. Only solid incontrovertible proofs (even there, we don't generally actually know whether or not a proof is incontrovertible, because proofs are rarely verified on that level...but, within mathematics, it is at least POSSIBLE to either verify a proof on that level, or provide a verifiable flaw). Definitions are a matter of convenience.
That the semantics of mathematics sometimes change does not imply that any of its terminology are ever inherently complex in the sense that those who don't understand it, "Don't get it." Indeed, since semantics in mathematics are only ever a shorthand, every mathematical construct could conceivably be expanded into the language of logic, and every mathematician (modulo human error) would agree that the expansion was valid. This underlying agreement on meaning is precisely what is missing from fields like much of literary criticism and philosophy.
Before studying philosophy I was a green idealist, but after studying philosophy I centered on a pragmatic philosophy.
Also it enhanced my ability to argue immensely. If I have an argument with someone I can easily detect logical flaws and shady arguments in general.
Also I like to think my study of multi-modal logic systems has enhanced my ability to suggest alternatives and question assumptions (where reasonable).
In short, a philosophy degree might not be all that useful full time, but to compliment something more practical, like CS, I've found it to be valuable.
Advanced calculus and "pure math" courses had precious few uses in the day to day grind of many jobs. Pure math might teach logic in some way, but philosophy tends to focus on argument itself, which lends itself to more obvious practical uses.
What about linear algebra? Do you really think that understanding its applications in computer graphics doesn't/wouldn't improve your employability?
Certainly, if you're a janitor, having studied philosophy vs. mathematics does not significantly affect how you do your job (though it probably does affect how easy it is for you to get a different job). But mathematics--even advanced mathematics--has more and more obvious applications than philosophy.
That sounds as if studying philosophy convinced you that philosophy is useless ;-) But I admit that I don't have any idea what "pragmatic philosophy" is.
It's very frustrating to be told to write in a concise style and then asked to read some really obfuscated nonsense.
Plus ten style points for irony. Minus a thousand for writing that sentence at all.
Meanwhile, fails to distance himself from Wittgenstein, and responds to pg's claim that philosophers argue semantics by defending it! (BTW Popper is one of the philosopher who does not argue semantics.)