My most recent posts have been far too long by blogging standards, so I am determined here to be brief. Most philosophers (though not all, e.g., anyone who holds the Quine-Putnam indispensibility thesis) believe the following sentences are true:
(1) "'2+3=5' is true a priori"
(2) "'The earth is round' is true a posteriori"
The question is: are (1) and (2) true a priori or a posteriori? Put metaphorically, does experience teach us that logical theorems are known independently of experience? I am not sure there are any non-question-begging arguments to be given one way or the other; if there is one, I would love to hear it.
That's all I wanted to say. If you are curious about what motivated me to think about this question, keep reading. There are two motivating sources:
First, my dissertation, which deals with the academic year Carnap, Tarski, and Quine spent together at Harvard in 1940-41. In a private conversation Carnap had with Quine, one way they formulate the difference between themselves is as follows.
Carnap: 'p is analytic in language L' is itself an analytic statement.
Quine: 'p is analytic in L' is a synthetic statement, to be settled by a behavioristic investigation into the linguistic habits of L-speakers.
Granted, 'analytic' is not identical to 'a priori' -- but for Carnap, they were extensionally equivalent, and the question above is very close to this issue.
Second, for the last 10 years, van Fraassen has been suggesting that we think of empiricism not as a theory or assertion but as a stance. (See "Against Naturalized Epistemology" (1995) in On Quine and 2002's The Empirical Stance.) The primary argument he offers is that empiricism, if conceived as an assertion, is self-defeating: "All knowledge about the world is a posteriori" (or any other slogan intended to capture the empiricist's thesis) will be difficult to construe as having experience as its source. And, van Fraassen says, if the empiricist thesis cannot be justified on the basis of experience alone, then it fails to live up to its own standards, and is therefore self-defeating. But van Fraassen is assuming that "such-and-such is a posteriori" must itself be an a posteriori claim. And that is taking for granted an answer to my question above.
7/22/2005
On Rosenberg and Kaplan's "Physicalism and Antireductionism in Biology"
I've just finished reading Alex Rosenberg and D. M. Kaplan's "How to Reconcile Physicalism and Antireductionism about Biology" in the current issue of Philosophy of Science. The title describes its contents perfectly, and I can unequivocally recommend it to anyone interested in the topic (which is more than I can say for my foray into the subject). I'll quote the key part of the introduction:
Their basic rationale for calling the PNS a law of physical science -- in particular, of chemistry (59, 62) -- is this: if there is a kind of chemical molecule that (in some sense) replicates itself and has higher rates of 'survival' than other molecules in a given reaction (say, as a reaction moves towards equilibrium, this kind of molecule is favored), that molecule will be subject to the PNS. (It's not a law of physics simply because (sub)atomic particles cannot be construed as replicating.) Calling the PNS a law of chemistry instead of biology "is just a picturesque way of drawing attention to the fact that selection for effects only begins to operate at the level of chemical interactions... Similarly, we call the second law of thermodynamics a law of physics, even though it obtains for all systems -- physical, chemical, and biological -- since it is at the level of the physical that it begins to operate" (61). As an example of such chemical natural selection, they point to current models of origins of life research.
So far, so good. But I'm less comfortable with the other half of their claim in c. above, viz., that from the physico-chemical PNS a fully biological PNS can be derived. They rephrase this point later in the article:
So the question to Rosenberg and Kaplan is: does natural selection operate on the biological realm (whether it be genes, individuals, or even groups) because it operates on the chemical-molecular level? -- where that 'because' has the same force as the one in 'This mole of gas has a higher temperature than that one because this one's molecules have a higher mean kinetic energy.' Here's one way to press this worry. Look at their definition of the PNS quoted above, and convert it into 'the PNS for molecules':
For any molecule x and molecule y, if x is fitter than y, then...
Now they say that from this (and perhaps other PNSes), we should be able to derive higher level PNSes:
For any gene x and gene y, if x is fitter than y, then...
For any organism x and organism y, if... then...
But these higher-level PNSes don't appear to follow at all. Certainly, each follows from the general PNS quoted at the beginning; but from the fact that all chemical molecules behave a certain way, you cannot infer that organisms will behave a certain way -- unless organisms are chemical molecules. Rosenberg and Kaplan might say at this point: but all we are is an aggregate of chemical molecules: that is just the physicalist thesis which we profess in the title of our paper. But 'Aggregates of As are B' does not in general follow from 'As are Bs,' even for the most determined physicalist.
In considering the relation between the PNS [Principle of Natural Selection] and physical science, three alternatives suggest themselves:Before continuing, let me give their version of the PNS:
a. The PNS is an underived law about biological systems, and is emergent from purely physical processes. ...
b. The PNS is a derived law; it is derivable from some laws of physics and/or chemistry. ...
c. The PNS is an underived law about physical systems (including non-biological ones), and from it the evolution of biological systems can be derived... This is an alternative no one has canvassed, and one which we shall defend here.
For all x, y, and E: If x is fitter than y in environment E at generation n, then probably there is some future generation n', after which x has more descendants than y.Note that the domain of quantification has no restrictions.
Their basic rationale for calling the PNS a law of physical science -- in particular, of chemistry (59, 62) -- is this: if there is a kind of chemical molecule that (in some sense) replicates itself and has higher rates of 'survival' than other molecules in a given reaction (say, as a reaction moves towards equilibrium, this kind of molecule is favored), that molecule will be subject to the PNS. (It's not a law of physics simply because (sub)atomic particles cannot be construed as replicating.) Calling the PNS a law of chemistry instead of biology "is just a picturesque way of drawing attention to the fact that selection for effects only begins to operate at the level of chemical interactions... Similarly, we call the second law of thermodynamics a law of physics, even though it obtains for all systems -- physical, chemical, and biological -- since it is at the level of the physical that it begins to operate" (61). As an example of such chemical natural selection, they point to current models of origins of life research.
So far, so good. But I'm less comfortable with the other half of their claim in c. above, viz., that from the physico-chemical PNS a fully biological PNS can be derived. They rephrase this point later in the article:
According to this view, at each level of the organization of matter there turns out to be a PNS, and each one should be in principle derivable from the PNS for the immediately lower level or some other lower level(s), all the way back down to the PNS for molecules. (61)The problem is that they do not explain how this (in principle) derivation would proceed. They phrase the point slightly differently elsewhere (the PNS's "operation at higher levels of the aggregation of matter is a consequence of the operation of the underived PNS for molecules together with the rest of physical law" (62)), but they never actually spell out the derivation beyond this -- as far as I can tell. (In one place (top of p.62: "The rest is natural history"), they appear to hint that any higher-level PNS is a 'consequence' of chemical PNS in a historical sense: because the PNS acted on the primordial soup, today's organisms came into existence -- yet that is completely unlike any sort of reduction any philosopher of science that I know of has talked about. So I assume they can't mean that.)
So the question to Rosenberg and Kaplan is: does natural selection operate on the biological realm (whether it be genes, individuals, or even groups) because it operates on the chemical-molecular level? -- where that 'because' has the same force as the one in 'This mole of gas has a higher temperature than that one because this one's molecules have a higher mean kinetic energy.' Here's one way to press this worry. Look at their definition of the PNS quoted above, and convert it into 'the PNS for molecules':
For any molecule x and molecule y, if x is fitter than y, then...
Now they say that from this (and perhaps other PNSes), we should be able to derive higher level PNSes:
For any gene x and gene y, if x is fitter than y, then...
For any organism x and organism y, if... then...
But these higher-level PNSes don't appear to follow at all. Certainly, each follows from the general PNS quoted at the beginning; but from the fact that all chemical molecules behave a certain way, you cannot infer that organisms will behave a certain way -- unless organisms are chemical molecules. Rosenberg and Kaplan might say at this point: but all we are is an aggregate of chemical molecules: that is just the physicalist thesis which we profess in the title of our paper. But 'Aggregates of As are B' does not in general follow from 'As are Bs,' even for the most determined physicalist.
7/13/2005
This week's complaint about "Two Dogmas"
I am willing to admit that Quine's "Two Dogmas of Empiricism" has many virtues, and if I ever write anything one-tenth as intelligent or one-hundredth as widely read, I will count my philosophical career an unequivocal success. However, I find it a very frustrating piece when it is considered as a critique of Carnap's views on language circa 1950. A number of people who have considered "Two Dogmas" in this light have also felt that it does not directly rebut Carnap's views, but instead offers (to put it in Kuhnian terms) a different paradigm for understanding language (recently, see P. O'Grady's 1999 article in PPR). Interestingly, the first person to suggest this interpretation of "Two Dogmas" was apparently Carnap himself (see Howard Stein's "Was Carnap Entirely Wrong, After All?", Synthese 1992). This post is about my most recent round of frustrations in attempting to read "Two Dogmas" as a straightforward argument against Carnap.
My gripe here concerns section 4 of the paper, "Semantical Rules." Quine writes (page numbers from From a Logical Point of View):
It seems to me that the next question we should ask is: how does Carnap characterize these semantic rules? Is it as unclear as Quine alleges? To answer that, we have to look at an extremely underread book: Carnap's Introduction to Semantics (1942). There Carnap says:
-'Chicago' designates Chicago etc.
-The truth-tables for the usual propositional connectives
Now I want to know what Quine finds unacceptable (unclear, unexplained, 'unintelligible' he says elsewhere in "Two Dogmas") about Carnap's characterization of semantic rules. This isn't just a matter of my pounding or kicking the table and saying 'I really do understand them' -- rather, it seems to me that if Quine is right that these things are unclear, then logic (at least logic that is not purely syntactic/ proof-theoretic) is unclear. In order to specify an artificial language in model-theoretic terms at all, we need to be able to say things like "Modus Ponens is an inference rule in such-and-such language" -- and if that is not clear, then logicans working in model theory are stumbling around in an unintelligible haze. If we cannot (intelligibly) lay down/ identify semantical rules such as this one and the others Carnap mentions, then the logician cannot (intelligibly) specify interpreted languages to study.
Thus concludes my main rant. A couple further things should be said before signing off, though. First: Quine, in "Notes on the Theory of Reference" and elsewhere, says that "'Chicago' designates Chicago," "'Snow is white' is true iff snow is white" and the like are basically comprehensible (p.138 in From a Logical PoV). That this is in tension with Quine's criticism in "Two Dogmas" has been pointed out (in different terms) already, by Marian David in Nous 1996. Second, there is one real difference between the semantic rules Carnap uses and the ones Quine favors and we usually use today, pertaining to hte interpretation of predicates and relation letters. Carnap sets up the following as a semantic rule: 'Blue' designates the property of being blue.
And here Quine would have a (more) direct disagreement with Carnap: Quine rejects intensional languages in general, and properties (for Carnap) are to be understood intensionally. So to generate a clean Quinean argument against semantic rules from the above quotation, we can fall back on Quine's rejection of non-extensional discourse as unclear and unintelligible. But this view of Quine's has won far fewer supporters than his rejection of the analytic-synthetic distinction.
My gripe here concerns section 4 of the paper, "Semantical Rules." Quine writes (page numbers from From a Logical Point of View):
Once we seek to explain 'S-is-analytic-for-L' for variable 'L'..., the explanation 'true according to the semantical rules for L' is unavailing; for the relative term 'semantical rule of' is as much in need of clarification, at least, as 'analytic for.' (34)So Quine is telling us that there is no decent explanation or clarification of the term 'semantical rule of,' if we generalize away from particular languages.
It seems to me that the next question we should ask is: how does Carnap characterize these semantic rules? Is it as unclear as Quine alleges? To answer that, we have to look at an extremely underread book: Carnap's Introduction to Semantics (1942). There Carnap says:
a semantical system [is] ... a system of rules, formulated in a metalanguage and referring to an object language, of such a kind that the rules determine a truth-condition for every sentence of the object language, i.e., a sufficient and necessary condition for its truth. In this way the sentences [of the object language -GFA] are interpreted, i.e., made understandable. (22)What are some of Carnap's examples of semantic rules? (Where English is both the object and metalanguage):
-'Chicago' designates Chicago etc.
-The truth-tables for the usual propositional connectives
Now I want to know what Quine finds unacceptable (unclear, unexplained, 'unintelligible' he says elsewhere in "Two Dogmas") about Carnap's characterization of semantic rules. This isn't just a matter of my pounding or kicking the table and saying 'I really do understand them' -- rather, it seems to me that if Quine is right that these things are unclear, then logic (at least logic that is not purely syntactic/ proof-theoretic) is unclear. In order to specify an artificial language in model-theoretic terms at all, we need to be able to say things like "Modus Ponens is an inference rule in such-and-such language" -- and if that is not clear, then logicans working in model theory are stumbling around in an unintelligible haze. If we cannot (intelligibly) lay down/ identify semantical rules such as this one and the others Carnap mentions, then the logician cannot (intelligibly) specify interpreted languages to study.
Thus concludes my main rant. A couple further things should be said before signing off, though. First: Quine, in "Notes on the Theory of Reference" and elsewhere, says that "'Chicago' designates Chicago," "'Snow is white' is true iff snow is white" and the like are basically comprehensible (p.138 in From a Logical PoV). That this is in tension with Quine's criticism in "Two Dogmas" has been pointed out (in different terms) already, by Marian David in Nous 1996. Second, there is one real difference between the semantic rules Carnap uses and the ones Quine favors and we usually use today, pertaining to hte interpretation of predicates and relation letters. Carnap sets up the following as a semantic rule: 'Blue' designates the property of being blue.
And here Quine would have a (more) direct disagreement with Carnap: Quine rejects intensional languages in general, and properties (for Carnap) are to be understood intensionally. So to generate a clean Quinean argument against semantic rules from the above quotation, we can fall back on Quine's rejection of non-extensional discourse as unclear and unintelligible. But this view of Quine's has won far fewer supporters than his rejection of the analytic-synthetic distinction.
7/10/2005
Self-preservation
Two days ago, the Pennsylvania House of Representatives, using the ideas and resources of David Horowitz's group Students for Academic Freedom successfully moved to create a committee to investigate the alleged liberal bias in Pennsylvania state schools -- and that includes the University of Pittsburgh. (The text of the motion can be found on their website.) One of the House members who opposed the formation of the committee has made a fairly detailed request for assistance from teachers at these schools. For those around here who would like to help the Representative (and yourself), his contact information is at the end of the linked request.
7/08/2005
Naturalism and the alleged continuity between philosophy and science
There are probably as many varieties of naturalism as there are naturalists. Either despite or because of this variety, many philosophers today are naturalists (though noteworthy dissent also exists). Philosophers of science, in particular, seem to be uncompromising naturalists. Here is one slogan that I think does a decent job of expressing the basic naturalistic position in a minimal enough form that most naturalists would accept it:
For any question, approach and answer that question the way a scientist would approach and answer that question (leaving the particulars open at this level of abstraction).
In other words, philosophers should defer to scientists on both questions of both method and factual content.
Another tenet of many modern naturalisms is "science is continuous with philosophy," a phrase which traces back to Quine. There is certainly something right about this notion, for we can point to current thinkers whose work does not fall neatly into science or philosophy: the late, great Rob Clifton is a paradigmatic example, as well as many other technical philosophers of physics working today. There are similar cases in other sciences too: should Sober and Wilson's Unto Others be classed as biology or philosophy?
However, it seems to me that "Science is continuous with philosophy" is also in some tension with the original naturalist slogan. If you asked an interdisciplinary team of scientists to answer the questions:
"Am I a brain in a vat (or being deceived by an evil demon, etc.)?"
"Is knowledge justified true belief?"
"Is the meaning of a sentence identical with its truth-condition?"
"Is the fundamental aim of science truth or empirical adequacy?"
they would (I think) say that such questions are not scientifically tractable -- in such cases, the 'scientific approach' (whatever exactly that might be) cannot answer that question. I think this would be the scientists' answer on the grounds that none of these questions -- or the vast majority of the others that appear in The Journal of Philosophy, Nous, The Philosophical Review, etc. -- are ever addressed in Science, Nature or other leading scientific journals.
In short: scientists do not view science and philosophy as continuous (even though there are borderline cases in technical philosophy of the special sciences), so a philosopher who views them as continuous is not fulfilling the naturalist's commitment to defer to the sciences. (Though the first stirrings of this discontinuity were felt earlier in the 17th C., I would guess that it becomes explicit with Newton and his rules of philosophizing.) So what is a philosopher (who is not Rob Clifton) to do? I think part of the appeal of naturalism is that science is seen as epistemically privileged, and if we can lump philosophy in with science, then that epistemic privilege and prestige will rub off on philosophy. I think the moral to be drawn from the discontinuity is just that philosophy lacks science's epistemological privilege -- and that is a conclusion a naturalistically-inclined philosopher might happily accept anyway.
For any question, approach and answer that question the way a scientist would approach and answer that question (leaving the particulars open at this level of abstraction).
In other words, philosophers should defer to scientists on both questions of both method and factual content.
Another tenet of many modern naturalisms is "science is continuous with philosophy," a phrase which traces back to Quine. There is certainly something right about this notion, for we can point to current thinkers whose work does not fall neatly into science or philosophy: the late, great Rob Clifton is a paradigmatic example, as well as many other technical philosophers of physics working today. There are similar cases in other sciences too: should Sober and Wilson's Unto Others be classed as biology or philosophy?
However, it seems to me that "Science is continuous with philosophy" is also in some tension with the original naturalist slogan. If you asked an interdisciplinary team of scientists to answer the questions:
"Am I a brain in a vat (or being deceived by an evil demon, etc.)?"
"Is knowledge justified true belief?"
"Is the meaning of a sentence identical with its truth-condition?"
"Is the fundamental aim of science truth or empirical adequacy?"
they would (I think) say that such questions are not scientifically tractable -- in such cases, the 'scientific approach' (whatever exactly that might be) cannot answer that question. I think this would be the scientists' answer on the grounds that none of these questions -- or the vast majority of the others that appear in The Journal of Philosophy, Nous, The Philosophical Review, etc. -- are ever addressed in Science, Nature or other leading scientific journals.
In short: scientists do not view science and philosophy as continuous (even though there are borderline cases in technical philosophy of the special sciences), so a philosopher who views them as continuous is not fulfilling the naturalist's commitment to defer to the sciences. (Though the first stirrings of this discontinuity were felt earlier in the 17th C., I would guess that it becomes explicit with Newton and his rules of philosophizing.) So what is a philosopher (who is not Rob Clifton) to do? I think part of the appeal of naturalism is that science is seen as epistemically privileged, and if we can lump philosophy in with science, then that epistemic privilege and prestige will rub off on philosophy. I think the moral to be drawn from the discontinuity is just that philosophy lacks science's epistemological privilege -- and that is a conclusion a naturalistically-inclined philosopher might happily accept anyway.
7/04/2005
First real post: abduction from limited evidence
I am currently teaching a summer session class called "How Science Works." The aim of the class (according to the course description) is to "introduce science and scientific ways of thinking to students who have not had much contact with science." One of the big-picture themes I am trying to develop in the course is that, in many cases, scientific reasoning is just extra-careful common-sense reasoning made precise. Thus, for some of their homework assignments, I ask students for an example from their lives where they (or someone they know) have used whatever scientific strategy we are studying that day.
On their last homework assignment, I asked them to give an everyday example of an abductive inference that is supported by independent sources of evidence, a very common kind of inference in good scientific practice. There were some very clever answers; the most common one was the cheating significant other: I never see the significant other with someone else, but I do observe her staying out late, hanging up the phone immediately when I stop by unexpectedly, and various other secretive behaviors.
But, unsurprisingly, some students did not quite understand the requirement for evidence from multiple independent sources, and gave an example of an abduction from just one. (These examples often involved some sort of roommate malfeasance: "My favorite CD is no longer in its case, so my roommate must have taken it without asking.")
But this mistake raised one version of a question I've been wondering about off and on for a while now. This version of the question is:
My gut-feeling answer is that such inferences are regarded as 'merely hypothetical' or otherwise second-class citizens -- like atomic theory in the 19th C, for example (for an account of this historical episode very congenial to my point, see Penelope Maddy's "A Problem in the Foundations of Set Theory, Journal of Philosophy Nov. 1990, pp. 623-625). Often such abductions from limited evidence are pronounced ad hoc. And, in biology, this also seems to be the reason many people call certain adaptionist accounts of certain biological traits "just-so-stories": if the only evidence we have for that adaptationist account is the way the animal looks or acts now, then we just don't have strong reason to accept that account. If we found enough sources of independent evidence for our conjecture, even the strong anti-adaptationists might come around.
I think this question (of the status of abductive inferences based on only one evidential source) is an interesting one in its own right. But it seems it also has implications for philosophy proper: many philosophical positions purport to explain only one thing, and lack the kind of consilience that good abductive inferences in the sciences enjoy. To take just one example, scientific realism aims to explain the success of science -- and as far as I can tell, that's it. (At least some other realisms will definitely fall in the same boat.) Certain critics of scientific realism (van Fraassen, for one) criticize all instances of "inference to the best explanation" (IBE), and use that criticism as an argument against scientific realism (which is supposedly the result of an instance of IBE). However, we may not need to throw out all instances of IBE in order to have a good argument against the realist -- we need only act like the scientists (as I portrayed them in the previous paragraph): accept only those instances of IBE for which we have more than one independent source of evidence.
On their last homework assignment, I asked them to give an everyday example of an abductive inference that is supported by independent sources of evidence, a very common kind of inference in good scientific practice. There were some very clever answers; the most common one was the cheating significant other: I never see the significant other with someone else, but I do observe her staying out late, hanging up the phone immediately when I stop by unexpectedly, and various other secretive behaviors.
But, unsurprisingly, some students did not quite understand the requirement for evidence from multiple independent sources, and gave an example of an abduction from just one. (These examples often involved some sort of roommate malfeasance: "My favorite CD is no longer in its case, so my roommate must have taken it without asking.")
But this mistake raised one version of a question I've been wondering about off and on for a while now. This version of the question is:
What is the epistemological status of abductive inferences (also known as 'inferences to the best explanation') that have only one (independent) source of evidence?To make this a slightly more well-posed question (or at least a question more amenable to philosophers of science), we can pose the question more naturalistically: how does science regard and treat such inferences?
My gut-feeling answer is that such inferences are regarded as 'merely hypothetical' or otherwise second-class citizens -- like atomic theory in the 19th C, for example (for an account of this historical episode very congenial to my point, see Penelope Maddy's "A Problem in the Foundations of Set Theory, Journal of Philosophy Nov. 1990, pp. 623-625). Often such abductions from limited evidence are pronounced ad hoc. And, in biology, this also seems to be the reason many people call certain adaptionist accounts of certain biological traits "just-so-stories": if the only evidence we have for that adaptationist account is the way the animal looks or acts now, then we just don't have strong reason to accept that account. If we found enough sources of independent evidence for our conjecture, even the strong anti-adaptationists might come around.
I think this question (of the status of abductive inferences based on only one evidential source) is an interesting one in its own right. But it seems it also has implications for philosophy proper: many philosophical positions purport to explain only one thing, and lack the kind of consilience that good abductive inferences in the sciences enjoy. To take just one example, scientific realism aims to explain the success of science -- and as far as I can tell, that's it. (At least some other realisms will definitely fall in the same boat.) Certain critics of scientific realism (van Fraassen, for one) criticize all instances of "inference to the best explanation" (IBE), and use that criticism as an argument against scientific realism (which is supposedly the result of an instance of IBE). However, we may not need to throw out all instances of IBE in order to have a good argument against the realist -- we need only act like the scientists (as I portrayed them in the previous paragraph): accept only those instances of IBE for which we have more than one independent source of evidence.
7/02/2005
Justifying my existence
Who am I and why am I here?
I am an academic philosopher whose primary interests are in science and logic. Often, after I've read a provocative article or book, or had an interesting conversation with someone in or around my department, my mind is swarming with obscure and confused ideas. These ideas bounce around in my head for a short while, and I sometimes scratch an especially persistent one on the back of an envelope -- but usually they just lose their mental inertia and evaporate, crowded out by thoughts of dinner, my cats, or whatever.
I decided to create this blog in order to give those ideas something (very slightly) higher to aspire to than the back of the envelopes Capitol One keeps sending me. Hopefully, posting them here will force me to make them a bit more clear and distinct. And if anyone ever reads this blog, they could help me cut down on the obscurity and confusion as well.
Why the title?
For those who are not historians of philosophy: Descartes, Leibniz, Spinoza and certain other 17th C. philosophers thought large chunks of our supposed knowledge are based on "obscure and confused ideas." I don't know whether this view is true in general, but it certainly holds in my particular case.
I am an academic philosopher whose primary interests are in science and logic. Often, after I've read a provocative article or book, or had an interesting conversation with someone in or around my department, my mind is swarming with obscure and confused ideas. These ideas bounce around in my head for a short while, and I sometimes scratch an especially persistent one on the back of an envelope -- but usually they just lose their mental inertia and evaporate, crowded out by thoughts of dinner, my cats, or whatever.
I decided to create this blog in order to give those ideas something (very slightly) higher to aspire to than the back of the envelopes Capitol One keeps sending me. Hopefully, posting them here will force me to make them a bit more clear and distinct. And if anyone ever reads this blog, they could help me cut down on the obscurity and confusion as well.
Why the title?
For those who are not historians of philosophy: Descartes, Leibniz, Spinoza and certain other 17th C. philosophers thought large chunks of our supposed knowledge are based on "obscure and confused ideas." I don't know whether this view is true in general, but it certainly holds in my particular case.
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