We are phasing this version of our SLU Philosophy Blog out, and have started a new version on the SLU Blogs platform. Our new blog can be found here: http://blogs.stlawu.edu/philosophy/
We will be gradually re-posting some of our old articles on the new site, and when that is complete, this blog will be taken down. So, please visit us at our new site now!
Thank you!
Friday, October 02, 2009
Saturday, May 09, 2009
Do We Have Free Will?
Some of my students and maybe even some of my colleagues seem convinced that psychology and/or neuroscience have convincingly proved that humans do not really have free will. Does anyone know what the argument is for this? I have not yet seen an argument that convinces me.
Friday, May 08, 2009
Metaphilosophy Essays
Our senior seminar students this year have written essays that they have posted on a Metaphilosophy Blog. Feel free to have a look!
Wednesday, April 22, 2009
Why is Logic So Hard?
I'm teaching Symbolic Logic this semester, and my students are doing very well. But when people hear that I'm teaching Logic, they often comment how hard they found the study of logic and reasoning. I have noted that too: that often students do find this very hard. Once you "get it," the principles are very clear. But why is it so hard to "get it"?
Recently someone I was talking with was wondering why logical errors of reasoning are so common. "You can spot errors of reasoning, and once you do, they are perfectly clear and obvious. So, why do people make errors of reasoning at all?"
I found myself answering: "It's because of the asymmetry of the conditional. That confuses people who haven't actually studied it and thought about it. Unless you really study it, it's not obvious that 'if A then B' does not always also mean 'if B then A.'"
Was I right? Is that the heart of the problem? Is this what makes logic so difficult, and errors of reasoning so common?
Recently someone I was talking with was wondering why logical errors of reasoning are so common. "You can spot errors of reasoning, and once you do, they are perfectly clear and obvious. So, why do people make errors of reasoning at all?"
I found myself answering: "It's because of the asymmetry of the conditional. That confuses people who haven't actually studied it and thought about it. Unless you really study it, it's not obvious that 'if A then B' does not always also mean 'if B then A.'"
Was I right? Is that the heart of the problem? Is this what makes logic so difficult, and errors of reasoning so common?
Tuesday, September 09, 2008
Is "Do We Have A Priori Knowledge?" an Empirical Question?
In his article "A Priori Knowledge" in the Oxford Handbook of Epistemology (2002), Albert Casullo canvases the array of accounts of a priori knowledge (what it means -- how we want the term to function).
One approach, which he calls non-epistemic, is to give a reductive analysis of a priori knowledge in terms of metaphysical notions (P is knowable a priori iff P is a necessary truth; P is knowable a priori iff P is an analytic truth). Such accounts, he argues, are predisposed to fail at answering the question "what about the knowledge is a priori?" And further, Kripkean examples seem to render any reduction to necessity a failure: it is knowable a priori that the meter bar (in Paris, London?), itself being what makes it true that certain lengths are 1 meter, is 1 meter long -- one would be making a mistake to measure it to be sure it was 1 meter long. But, it seems, the length of a meter could have been different, since it was just stipulated, and so `that stick there -- in Paris or where ever -- is 1 meter long' is true contingently). Also, "I exist" is not a necessary truth, since I might not have existed, yet this seems knowable via rational reflection.
Another approach, which Casullo attributes to BonJour, is this: "S is a priori justified in believing P iff S can intuitively "see" that S is a necessary truth." The same Kripkean worries apply to the last clause, but further, notice the regress: if 1+2=3 is knowable a priori, then one must be able to see the truth of "it's necessary that 1+2=3," and if one is to know the last modal proposition via reflection alone, then one must know that it is also necessary (it's necessary that it's necessary that 1+2=3), and off we go.
Another approach, which Casullo attributes to Chisholm, is an axiomatic understanding: S knows P a priori iff P is a consequence of facts that are axiomatic for S, where P is axiomatic for S iff P is true and S believes P and anyone who believes P is certain of it. Casullo objects to this approach on the grounds that is rules out it should be possible to have false a priori beliefs. For example, presumably we want to say that for thousands of years people believed a priori that one could not consistently deny the parallel postulate, but as it turns out, there are consistent non-Euclidean geometries. It seems right to say that we should understand a priori justification in a way that allows for varying degrees of confidence.
Another approach, which Casullo attributes to Putnam, is that S knows P a priori iff P could not be defeated by experience. Casullo rejects this as well, on the grounds that we should allow for testimony, an experiential source of justification, being able to revise our a priori formed beliefs. Consider a mathematician who is usually correct, but sometimes makes mistakes. She is doing a proof while her brain is hooked up to a computer which detects cognitive states which are associated with her making mistakes. She finishes a proof, thinks she's carried it out correctly, but the machine says an that an unreliable cognitive process came into play. Presumably we want to say that she should now be allowed to revise how certain she is with her result, or even choose to suspend believe in the theorem at hand.
Casullo ends the article with an absolutely striking suggestion. Perhaps we should settle the matter empirically: we should figure out what your mind would have to be doing to supply non-experiential justification to a belief, and then ask, does that ever happen to people? Talk about a plot twist! I curious as to what the readers of this blog have to say about this approach. I'm not sure what I want to say about it, other than that I think it's really interesting!
One approach, which he calls non-epistemic, is to give a reductive analysis of a priori knowledge in terms of metaphysical notions (P is knowable a priori iff P is a necessary truth; P is knowable a priori iff P is an analytic truth). Such accounts, he argues, are predisposed to fail at answering the question "what about the knowledge is a priori?" And further, Kripkean examples seem to render any reduction to necessity a failure: it is knowable a priori that the meter bar (in Paris, London?), itself being what makes it true that certain lengths are 1 meter, is 1 meter long -- one would be making a mistake to measure it to be sure it was 1 meter long. But, it seems, the length of a meter could have been different, since it was just stipulated, and so `that stick there -- in Paris or where ever -- is 1 meter long' is true contingently). Also, "I exist" is not a necessary truth, since I might not have existed, yet this seems knowable via rational reflection.
Another approach, which Casullo attributes to BonJour, is this: "S is a priori justified in believing P iff S can intuitively "see" that S is a necessary truth." The same Kripkean worries apply to the last clause, but further, notice the regress: if 1+2=3 is knowable a priori, then one must be able to see the truth of "it's necessary that 1+2=3," and if one is to know the last modal proposition via reflection alone, then one must know that it is also necessary (it's necessary that it's necessary that 1+2=3), and off we go.
Another approach, which Casullo attributes to Chisholm, is an axiomatic understanding: S knows P a priori iff P is a consequence of facts that are axiomatic for S, where P is axiomatic for S iff P is true and S believes P and anyone who believes P is certain of it. Casullo objects to this approach on the grounds that is rules out it should be possible to have false a priori beliefs. For example, presumably we want to say that for thousands of years people believed a priori that one could not consistently deny the parallel postulate, but as it turns out, there are consistent non-Euclidean geometries. It seems right to say that we should understand a priori justification in a way that allows for varying degrees of confidence.
Another approach, which Casullo attributes to Putnam, is that S knows P a priori iff P could not be defeated by experience. Casullo rejects this as well, on the grounds that we should allow for testimony, an experiential source of justification, being able to revise our a priori formed beliefs. Consider a mathematician who is usually correct, but sometimes makes mistakes. She is doing a proof while her brain is hooked up to a computer which detects cognitive states which are associated with her making mistakes. She finishes a proof, thinks she's carried it out correctly, but the machine says an that an unreliable cognitive process came into play. Presumably we want to say that she should now be allowed to revise how certain she is with her result, or even choose to suspend believe in the theorem at hand.
Casullo ends the article with an absolutely striking suggestion. Perhaps we should settle the matter empirically: we should figure out what your mind would have to be doing to supply non-experiential justification to a belief, and then ask, does that ever happen to people? Talk about a plot twist! I curious as to what the readers of this blog have to say about this approach. I'm not sure what I want to say about it, other than that I think it's really interesting!
Friday, June 06, 2008
Is Mathematical Knowledge Ethical Knowledge?
Why, in the planning of the philosopher-kings’ education in the Republic, would Plato reserve an entire decade for the study of mathematics, beginning with arithmetic and proceeding (respectively) to plane geometry, solid geometry, astronomy and harmonics? In his article “Plato on Why Mathematics is Good for the Soul,” M. F. Burnyeat addresses this question, and arrives at the striking conclusion that learning mathematics is not merely instrumental in coming to know the form of Justice, but that knowledge of mathematics is part of knowledge of Justice, or as he puts it, “the content of mathematics is a constitutive part of ethical understanding” (p. 6). While this suggestion would certainly explain why the study of mathematics holds such a prominent place in the education of the philosopher-kings, it is in no way clear how mathematical knowledge could possibly be ethical knowledge; how can learning about triangles or prime numbers be learning about Justice or the Good?
Socrates tells us at 525c that the study of mathematics will be useful only if “it leads the soul forcibly upward and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies.” A fundamental reason, then, that the study of mathematics is critical in the development of philosopher-kings, is that it is instrumental in learning to looking beyond the realm of sensible particulars and toward the world of the forms. Also, studying mathematics is especially useful for rulers, for example in planning a battle (522d), or in understanding the shifting seasons (527d). But Plato is clear on this: Socrates explains again and again (at Glaucon’s expense, for example at 525c, 527d-e and 528e-529) that such practical ends are not why the future philosophers ought to study mathematics.
What Socrates has to say about astronomy and harmonics helps us see how mathematical knowledge might be constitutive of ethical knowledge. Socrates holds that, as currently practiced, astronomy will be of no use in the education of the philosopher-kings. Instead, the future philosophers will study a new science of astronomy, which will concentrate on the nature of motion and movement of solid bodies in general, and thus Socrates suggests: “let’s study astronomy be means of problems, as we do geometry, and leave the things in the sky alone.”
Similarly, of mathematical harmonics, Socrates says that since the current practitioners are “measuring audible consonances and sounds against one another, they labor in vain, just like present-day astronomers” (531a). The philosophers-to-be shall abandon the empirical methodology of “[seeking] out the numbers that are to be found in these audible consonances,” and instead, once again, “make the ascent to the problems,” and investigate “which numbers are consonant and which aren’t or what the explanation is of each” (531c).
The future philosophers will study the harmony of the mathematical ratios (which are used in Greek music theory to represent harmonic relationships), rather than studying the harmonics of the audible sounds themselves. Why study the mathematics of concord and consonance in themselves, independent of sound?
Anyone who has read the Republic will have noticed that the idea of concord plays a large roll throughout the arguments. There are multiple passages where this of concord plays a crucial function. Drawing from both (410a-412b) and (441e-442a), Burnyeat maintains that purpose of their musical and gymnastic training is that it “will harmonise the two elements in their soul, the spirited and the philosophical (as if they were strings on a lyre), relaxing and tightening them as necessary to ‘tune’ the soul to be both brave and temperate” (p. 53-4). More crucially, Burnyeat points out (p. 54) that in Book IV, temperance gets defined as “a kind of harmony” (431e), and that justice gets defined as a well-ordered attunement of the soul (443c-e):
“[Justice] isn’t concerned with someone’s doing his own externally, but with what is inside him, with what is truly himself and his own... He puts himself in order, is his own friend, and harmonizes the three parts of himself like three limiting notes in a musical scale — high, low, and middle. He binds together those parts...and from having been many things he becomes entirely one, moderate and harmonious. Only then does he act. And when he is doing
anything... the action is just and fine that preserves this inner harmony...”
Passages like these explain why, when Socrates discusses the study of harmonics, he denies that harmony must be a relation between sounds. Harmony should be given a systematic, general mathematical treatment because, as Burnyeat argues (p. 56), “the important task of ruling is not day-to-day decision-making, but establishing and maintaining good structures, both institutional and psychological.” If the philosophers are to create and maintain harmonious and concordant institutional structures, they will require a thorough understanding of what harmony is, not as it is sometimes instantiated in audible sound, but its general mathematical nature.
And yet, Burnyeat’s suggestion here is not so different in kind than Glaucon’s many praises of mathematics for its usefulness to the rulers. I think the more important point is the following epistemological one. If the philosophers are to know what Justice is, then they must be able to give a full account of it, for being able to give an account is a necessary condition for knowledge for Plato (as in the dialectic). But, according to the treatment of Justice in the Republic, given in terms of harmony and attunement, one would need a thorough understanding of these notions central to the very nature of Justice, viz., harmony and attunement. Thus, to be able to give a full account of moral forms such as Justice, the philosophers-in-training must learn quite a bit about the main components of the idea of Justice. This explains the intensity of the philosopher-king’s mathematical regimine, as prescribed by Socrates, because it explains why the content of mathematics is relevant, and not merely that it requires abstracting away from sensible objects, or that it will be indispensable to the practical tasks of ruling.
In sum, Plato’s reserving of an entire decade for the study of mathematics is explained by knowledge of mathematics being constitutive of knowledge of the moral forms. Since the moral forms are defined by properties like harmony, one must understand harmony in order to give a full account (a necessary condition for knowledge) of Justice. This explains why the future philosopher-kings end their study of mathematics with harmonics, the general mathematical study of concord. Burnyeat point is very interesting because we no longer have to look at the Republic's definition of Justice at the soul as mere metaphor where there should be argument: the talk about harmonics here can be taken literally.
Socrates tells us at 525c that the study of mathematics will be useful only if “it leads the soul forcibly upward and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies.” A fundamental reason, then, that the study of mathematics is critical in the development of philosopher-kings, is that it is instrumental in learning to looking beyond the realm of sensible particulars and toward the world of the forms. Also, studying mathematics is especially useful for rulers, for example in planning a battle (522d), or in understanding the shifting seasons (527d). But Plato is clear on this: Socrates explains again and again (at Glaucon’s expense, for example at 525c, 527d-e and 528e-529) that such practical ends are not why the future philosophers ought to study mathematics.
What Socrates has to say about astronomy and harmonics helps us see how mathematical knowledge might be constitutive of ethical knowledge. Socrates holds that, as currently practiced, astronomy will be of no use in the education of the philosopher-kings. Instead, the future philosophers will study a new science of astronomy, which will concentrate on the nature of motion and movement of solid bodies in general, and thus Socrates suggests: “let’s study astronomy be means of problems, as we do geometry, and leave the things in the sky alone.”
Similarly, of mathematical harmonics, Socrates says that since the current practitioners are “measuring audible consonances and sounds against one another, they labor in vain, just like present-day astronomers” (531a). The philosophers-to-be shall abandon the empirical methodology of “[seeking] out the numbers that are to be found in these audible consonances,” and instead, once again, “make the ascent to the problems,” and investigate “which numbers are consonant and which aren’t or what the explanation is of each” (531c).
The future philosophers will study the harmony of the mathematical ratios (which are used in Greek music theory to represent harmonic relationships), rather than studying the harmonics of the audible sounds themselves. Why study the mathematics of concord and consonance in themselves, independent of sound?
Anyone who has read the Republic will have noticed that the idea of concord plays a large roll throughout the arguments. There are multiple passages where this of concord plays a crucial function. Drawing from both (410a-412b) and (441e-442a), Burnyeat maintains that purpose of their musical and gymnastic training is that it “will harmonise the two elements in their soul, the spirited and the philosophical (as if they were strings on a lyre), relaxing and tightening them as necessary to ‘tune’ the soul to be both brave and temperate” (p. 53-4). More crucially, Burnyeat points out (p. 54) that in Book IV, temperance gets defined as “a kind of harmony” (431e), and that justice gets defined as a well-ordered attunement of the soul (443c-e):
“[Justice] isn’t concerned with someone’s doing his own externally, but with what is inside him, with what is truly himself and his own... He puts himself in order, is his own friend, and harmonizes the three parts of himself like three limiting notes in a musical scale — high, low, and middle. He binds together those parts...and from having been many things he becomes entirely one, moderate and harmonious. Only then does he act. And when he is doing
anything... the action is just and fine that preserves this inner harmony...”
Passages like these explain why, when Socrates discusses the study of harmonics, he denies that harmony must be a relation between sounds. Harmony should be given a systematic, general mathematical treatment because, as Burnyeat argues (p. 56), “the important task of ruling is not day-to-day decision-making, but establishing and maintaining good structures, both institutional and psychological.” If the philosophers are to create and maintain harmonious and concordant institutional structures, they will require a thorough understanding of what harmony is, not as it is sometimes instantiated in audible sound, but its general mathematical nature.
And yet, Burnyeat’s suggestion here is not so different in kind than Glaucon’s many praises of mathematics for its usefulness to the rulers. I think the more important point is the following epistemological one. If the philosophers are to know what Justice is, then they must be able to give a full account of it, for being able to give an account is a necessary condition for knowledge for Plato (as in the dialectic). But, according to the treatment of Justice in the Republic, given in terms of harmony and attunement, one would need a thorough understanding of these notions central to the very nature of Justice, viz., harmony and attunement. Thus, to be able to give a full account of moral forms such as Justice, the philosophers-in-training must learn quite a bit about the main components of the idea of Justice. This explains the intensity of the philosopher-king’s mathematical regimine, as prescribed by Socrates, because it explains why the content of mathematics is relevant, and not merely that it requires abstracting away from sensible objects, or that it will be indispensable to the practical tasks of ruling.
In sum, Plato’s reserving of an entire decade for the study of mathematics is explained by knowledge of mathematics being constitutive of knowledge of the moral forms. Since the moral forms are defined by properties like harmony, one must understand harmony in order to give a full account (a necessary condition for knowledge) of Justice. This explains why the future philosopher-kings end their study of mathematics with harmonics, the general mathematical study of concord. Burnyeat point is very interesting because we no longer have to look at the Republic's definition of Justice at the soul as mere metaphor where there should be argument: the talk about harmonics here can be taken literally.
Thursday, November 15, 2007
Moral Explanation?
Is it true that killing is bad? Or is there a fact of the matter? Many of us like to think so, yet we can't really describe what this fact consists in. Somehow, a state of affairs, a collection of stuff, is normative. A main motivation being a moral realism is the accompanying power of explanation. Why do I think Hitler is bad? Because he really was a horrible person.
I recently came across a fascinating article by Gilbert Harmen, who points out an asymmetry between scientific and moral explanation. Harmen asks us to consider a scientists who is conducting an experiment. She is working with a theory that predicts that she will see some phenomenon X in her cloud chamber. Now, if she looks in her cloud chamber and does see what the theory predicted, then her theory being true would explain why she saw what she saw.
Harmen then asks us to consider seeing a group of boys doing a horrible thing: burning a cat for fun. He says that most people would have something like a `moral observation' where we just see this as bad. Now, let's say we have a theory, a moral theory, under which it is a fact that burning cats is bad. But it being true that burning cats is bad doesn't really seem to explain why we would have the `moral observation' we have. The reason why we think this is bad, the explanation of why we think cat burning is bad, has to do with the way we were raised, facts about our psychology and how we were brought up. So, Harmen alleges, even if there were moral facts, it is not clear that they would take part in explanation, they way we think scientific facts do.
I don't know what to think of this. My first reaction is that it can't be that big a blow against realism. One possible way around is the Platonist route. There can be moral facts, but they are not knowable empirically but rather through some kind of rational moral intuition (like a Kantian picture with reflection on maxims or something). Or moral truths are self-evident. The other way to go is to simply deny Harmen's claim that moral truths can't explain why we have certain moral observations. Why can't they? Harmen seems to just help himself to the fact that the explanation of why we feel the ways we do must come only from psychology. But why can't moral facts supervene on physical states in a way our psychology is sensitive to?
I recently came across a fascinating article by Gilbert Harmen, who points out an asymmetry between scientific and moral explanation. Harmen asks us to consider a scientists who is conducting an experiment. She is working with a theory that predicts that she will see some phenomenon X in her cloud chamber. Now, if she looks in her cloud chamber and does see what the theory predicted, then her theory being true would explain why she saw what she saw.
Harmen then asks us to consider seeing a group of boys doing a horrible thing: burning a cat for fun. He says that most people would have something like a `moral observation' where we just see this as bad. Now, let's say we have a theory, a moral theory, under which it is a fact that burning cats is bad. But it being true that burning cats is bad doesn't really seem to explain why we would have the `moral observation' we have. The reason why we think this is bad, the explanation of why we think cat burning is bad, has to do with the way we were raised, facts about our psychology and how we were brought up. So, Harmen alleges, even if there were moral facts, it is not clear that they would take part in explanation, they way we think scientific facts do.
I don't know what to think of this. My first reaction is that it can't be that big a blow against realism. One possible way around is the Platonist route. There can be moral facts, but they are not knowable empirically but rather through some kind of rational moral intuition (like a Kantian picture with reflection on maxims or something). Or moral truths are self-evident. The other way to go is to simply deny Harmen's claim that moral truths can't explain why we have certain moral observations. Why can't they? Harmen seems to just help himself to the fact that the explanation of why we feel the ways we do must come only from psychology. But why can't moral facts supervene on physical states in a way our psychology is sensitive to?
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