A Primer on Logic Part 3 (A New Scholardarity.com Article)

I've posted a new article, A Primer on Logic: Part 3, my new Scholardarity piece in which I give a brief introduction to Aristotelian logic. It's the latest entry in my introduction to formal logic.

Also, in case you missed Parts 1 and 2, which respectively cover logical preliminaries and propositional logic, you can check them out here:

Part 1


Part 2


If you have any comments / criticism, by all means share it!

A follow up on "An uncontroversial instance of moral knowledge?"

In this post I’m going to refine the position I advanced in my previous post, “An uncontroversial instance of moral knowledge?”. In that post I said,

No matter what else one may think about which actions—or types of action—are wrong, one must hold that if someone performs any action which they believe to be wrong they have acted wrongly. And if we know that anything is wrong, we know that doing something which one believes to be wrong is wrong.

This passage is ambiguous: It could be read as saying that if one believes some (particular) action A to be wrong but does A anyway, then A itself is a wrong action. But it could also be read as saying that if one believes some (particular) action A to be wrong but does A anyway then one has acted wrongly, even if A itself is not wrong. Since I wrote this passage a while ago I can’t be sure what exactly I had in mind, although I suspect I wasn’t thinking carefully enough to notice the difference. However, I now think that the second reading is more plausible, because of cases like the following.

Suppose Jones has been raised by parents who are ethical egoists, and has been taught that one should never act to help others unless it is one’s own interest to do so, except in a situation where helping someone else and not helping them would have precisely the same consequences for one’s own well being, in which case it is permissible to help that person and also permissible not to do so. Suppose that one day Jones spies a beggar on the street, and that Jones, moved by pity, gives the beggar some money that he would otherwise have used to buy his lunch. Nevertheless, in spite of his feelings, Jones still believed while he was acting that he shouldn’t help the beggar because in doing so he made himself (mildly) worse off by skipping lunch. 

In a case such as this, I find it intuitive to think that Jones’ action of helping the beggar was not wrong, but permissible or perhaps even obligatory. In spite of that, I think it is still at least plausible to hold that Jones did something wrong. For even if an action A is not wrong, it does not follow that in doing A one has not acted wrongly. For instance, by moving one’s finger in a certain way one may thereby also flip a switch and thereby turn the lights on. Similarly,  by doing A  one may also perform another action—call it ‘e’—namely violating one’s conscience, and it might be that e is wrong because it is always wrong to violate one’s conscience. However good it may have been for Jones to give his lunch money to the beggar, it would have been better still if Jones had thought that by giving away his money he was doing the right thing, or a least a permissible thing.

A Primer on Logic: Part 2 (A New Scholardarity.com Article)

Check out "A Primer on Logic: Part 2", my new Scholardarity.com article which is essentially a crash-course in propositional logic. It's the latest entry in my introduction to formal logic. (Also available as a PDF.)

Also, in case you missed Part 1, which covers logical preliminaries and vocabulary, you can check it out here. (Also as a PDF.)

If anyone has any comments / criticism, by all means share it!

Quote of the Day: Brand Blanshard on Linguistic Philosophy

Here is the philosopher Brand Blanshard on "Linguistic Philosophy". Keep in mind that Reason and Analysis, the book this quote was taken from, was first published in 1962.

The linguistic philosophers would rather philosophize in their own manner than talk about philosophy, and their programme cannot be fully appreciated without following them into their discussions of the language we use about time and induction and universals and fact and truth. It would be interesting to do this if there were space for it, which there is not. But I cannot think our main conclusions about this way of philosophizing would be greatly affected by such a review. We should find many fine hairs split into still finer hairs. We should find a virtuosity in ferreting out verbal distinctions, particularly in such masters of the craft as Austin, which would fill any unprejudiced reader with admiring astonishment. We should find many curious details in our use of such words as ‘if’ and ‘can’ and ‘seems’ and ‘ought’ lit up sharply by flashes of light. And yet at the end we should feel strangely unilluminated. Such a prodigal expenditure of power, acuteness and ink, adding up to—what? Disappointingly little in view of the powers that went into it

The reason is not far to seek. Words give the philosopher no compass. The interest in usage is centrifugal and dispersive, and unless guided by something other than itself, dissipates among minutiae, some idle, some important; and mere usage cannot tell it which is which. When philosophers in the past asked themselves What is the nature of knowledge? instead of What are the uses of the verb ‘know’?, they usually did so with a conviction, having nothing to do with language, that some types of knowledge, or some claims to it, were of central importance—the insight of the mathematician, the scientific grasp of natural law, the claim of the mystic or the religious authoritarian. These types or claims were then fastened upon for special examination. The inquiries of the linguistic philosophers have, to be sure, thrown light on these claims. But if so, it is because a way of philosophizing different from their own, disruptive of their own, has not been wholly abandoned. A genuine philosopher can draw nourishment even from what W. E. Hocking has called ‘this new method of milking stones’. ‘If’, ‘can’, ‘know’, ‘true’, are after all key words, and one is bound to derive profit from their study. So our complaint is not that these studies are profitless, but that the profit is so meagre in proportion to the price. There are grains of wheat, many of them indeed, and of high quality, among the chaff. But why should one have to hunt for them in these bushels and bushels and bushels of words about words?

--Brand Blanshard, Reason and Analysis, pp. 380-81, Open Court, Paperback (second printing).

A Dilemma for Dialetheism

I've just published a revised version of my article "A Dilemma for Dialetheism" on Scholardarity.com, which was originally published in the Spring 2010 edition of the Stanford undergraduate philosophy journal The Dualist (vol. 15). In the article I argue that dialetheists, who believe that some sentences are both true and false, either cannot express the notion that some sentences are not both true and false, or else that their accounts suffer from "revenge" liar paradoxes that not even they can regard as being both true and false. If you like logic and paradoxes as much as I do, please check it out and let me know what you think.

My Review of "The God Delusion"

Check out my review of Richard Dawkins' The God Delusion  here on Scholardarity.com .

Launching a new website: Scholardarity.com

 

 

A friend and I are launching a new website Scholardarity.com to help out scholars in the humanities.

 

Our website is still a work in progress and subscriptions are still free. Readers will not need to subscribe. Our motto is “Free to read, but pay to publish!”

Scholardarity, in order to promote solidarity among scholars, is a new site for scholars in the humanities and all students interested in History, Philosophy, and Theology.

It is for all of us who have a degree that hasn’t opened any doors.  But all scholars, even with faculty positions are, of course, welcome. So many teachers, graduates, and academics are having trouble finding work or getting articles published. How could scholarly work bring an online income? We are working on that kind of support.

We want to give scholars access to the cutting edge of research in their fields via peer review and criticism. See our Conferences and Societies and consider presenting papers in your field. We want to find ways to help and support students interested in the humanities. Lately we hear that only science, math, and technology are in demand.

Our goal in Scholardarity is to create a community of scholars who help each other and push ahead the frontiers of knowledge for our readers.

Unlike many academic journals, both online and off, our articles will be available for all, free to read. Scholars will subscribe to have the benefits of having their profiles on the site, communicating on the message board, sharing their writing, e-publishing their manuscripts and books, and being able to advertise and sell their work through this site.

Subscribe to Scholardarity

Future Features:

• Find new faculty position openings
• Advertise your books and writings
• Sell your books online
• Make unpublished manuscripts available
• Receive peer critique and review
• Online introductory video lectures for students
• Online conferences
• Message boards to share ideas and coordinate research projects
• Downloadable podcasts and pdfs for e-readers
• Intra-site newsletter with editorials, book reviews, and interviews with scholars
• E-Publishing…and more!

Causation, God , and the Justification of Induction: Part 2

[Cross-posted at Reflections on Religion]

I think the argument of Part 1 is a good one, but it does not quite establish its conclusion: While it is highly likely, given IBE, that chance is not the true account of the regularity of the universe, metaphysically necessary causal connections are not the only alternative. Indeed, in some cases they are seemingly not even a possible alternative. For quantum mechanics tells us, on most of its interpretations, that many of the most basic regularities in nature are probabilistic. Unless we’re prepared to posit “probabilistic necessities”—i.e., that it could be necessary that something happens only in a certain percentage of cases—many of the regularities described by quantum mechanics cannot be necessary. So how could we explain them?

If we accept theism, there is a way. God, being all powerful, could surely act in such a manner that certain things happen only with a certain frequency, not all the time. But God, according to theists, is not merely some convenient metaphysical explanatory posit. He is a personal being. While perhaps not having a psychology like ours—God probably doesn’t think discursively, with one thought following after another—He is nevertheless an agent who acts for the sake of ends. Provided that those ends include creating a word that is regular—perhaps  because only such worlds are hospitable to life or sentience—it would be extremely probable, or even certain, that such a world would be actual.

Now, if we consider the matter in terms of “epistemic possibility”, there are many “possible Gods”, or “ways God could be”. A great deal of them would have no desire to create worlds that are regular. I don’t know of any good arguments to the effect that such “Gods” couldn’t have existed, so we can’t rule them out a priori. Instead, I think a theist should insist that given our actual evidence we aren’t justified in believing in them, because it is only if we posit a God who desires to create a world that exhibits regularities, albeit probabilistic ones, that we have reason to suspect such a world to be actual. If there is such a God we certainly have a better account than we would have if we thought such regularities were merely “an outrageous run of luck”. So the observed regularities in nature do cry out for explanation, but on this view their probabilistic nature favors a theistic account. Given the constancy of God’s nature and purposes, we are can confidently expect them to persist in the future. The above account, if true, would not constitute an airtight proof that the inductive schema of Part 1 is reliable, but I think it would give us a good (though defeasible) reason to accept it.

           

But all is not well. In Part 3 I’ll examine a couple objections to this account.

Causation, God , and the Justification of Induction: Part 1

[Cross-posted at Reflections on Religion]

Brand Blanshard (The Nature of Thought, vol. 2 , Ch. XXXII, “Concrete Necessity and Internal Relations”; Reason and Analysis, Ch. XI, “Necessity in Causation”) and A.C. Ewing (Non-Linguistic Philosophy: Ch. VI, “Causation and Induction”) gave similar arguments for the existence of “logical necessity” in causation. (Given that their views of logic are somewhat unorthodox by the standards of analytic philosophers, I think it would be more accurate and less confusing to talk of metaphysical necessity in causation, which I will do in what follows.) A “rational reconstruction” of their arguments goes something like this: If causal connections are not metaphysically necessary, the fact that similar effects follow upon similar causes, or that there are certain, seemingly exceptionless regularities in nature (which can be expressed in laws of nature) is quite remarkable. If “anything can cause anything”, as Humeans sometimes say, we have a tremendous coincidence, “an outrageous run of luck”, as Blanshard puts it (The Nature of Thought, vol. 2, Ch XXXII, “Concrete Necessity and Internal Relations”, p. 505 of the second edition), comparable to rolling a die and getting a 4 a trillion times in a row. But if causal connections are metaphysically necessary, we have a good explanation for the fact that similar effects follow upon similar causes, or that there are exceptionless regularities in nature: they obtain because they must. If events of type B necessarily follow upon events of type A, any token A event will be followed by a token B event. (Not, of course, that we can perceive this necessity: we could only perceive it if we had some kind of direct insight into the natures of type A events and type B events.) Granting that, it follows that we can justify instances of inductive inference that fit the following schema: Events of type A have always been followed by events of type B, hence, events of type A will always be followed by events of type B. 

Our argument for this schema is neither deductive nor inductive: We have not deduced, and neither have we seen through “rational insight”, that it is necessary that type A events will always be followed by type B events based on knowledge of their natures, nor have we concluded that type A events will always be followed by type B events just because they have always been so followed in the past. Our argument is rather this: In certain cases we take ourselves to have established that every observed event of type A has been followed by an observed event of type B. We also note that, since type A events are observed very frequently, it is extremely unlikely (though possible) that their association with type B events is a matter of chance. So there are two alternatives: Either the association is an astronomically improbable coincidence, or there is a necessary connection between them, albeit one that we are not able to discern.  Next we consider the principle of Inference to the Best Explanation (IBE): This principle says, very roughly, that if we have multiple hypotheses vying to account for some phenomenon, it is most reasonable to accept the hypothesis which best explains it as being true. And if we think that having any explanation is rationally preferable to having none—assuming we have no evidence which rules out all of the candidate explanations, or which renders them extremely improbable—then IBE tells us that it is always more reasonable to accept an explanatory hypothesis over a non-explanatory one. Since coincidence is no explanation, in the present case IBE counsels us to accept the hypothesis that there is a metaphysically necessary connection between type A events and type B events. Because of this necessary connection, we can conclude that in the future type A events will always be followed by type B events, just as they always have been. So we have justified our inductive schema neither deductively nor inductively, but by IBE.

Note that in the above we have not invoked the principle of sufficient reason or the idea that every event must have a cause; we are only saying that it is more reasonable to believe in a necessary connection than an astronomical coincidence. Thus the objections that can be raised against them cannot be raised against the present argument.

At this point you might be wondering about IBE. What justifies us in accepting it? Why should we believe that the hypothesis which best explains a phenomenon is the most rationally acceptable one? I think it can be justified, although it can neither be justified deductively, nor inductively, nor by IBE. It cannot be justified deductively because IBE is clearly not a truth of logic or mathematics. It also cannot be justified inductively, at least not by the kind of inductive inference being considered on the present account, because we are trying to use IBE to justify those inductive inferences, and to use them to justify IBE would be circular. Finally, to use IBE to justify itself would also be circular. Instead, I think IBE can be justified “transcendentally”. It is essentially a case of “this or nothing”. If we did not regard better explanations as more rationally acceptable, it would be extremely difficult, if not impossible, to justify anything that goes beyond our beliefs about elementary logic and our immediate perceptual experiences. (For one instance of this problem, see my post on Bertrand Russell's Five Minute hypothesis, God, and abduction. ) This does not refute skepticism, but it does show that anyone who rejects skepticism is entitled to use IBE; or, at the very least, that they cannot consistently criticize those who do use it.

“But how does God figure into all this?”, you might ask. If you want to know, stay tuned for Part 2!

Testing the limits of your imagination...

…literally.

In his Meditations on First Philosophy, Descartes distinguished between imagination and conception, or between mental images and concepts. Thus he supposed that one can conceive of a chiliagon, a polygon of a thousand sides, although one cannot form a mental image that represents it—none, at any rate, that wouldn’t represent a circle equally well. This shows that imagination has its limits, and that one can conceive of things that one cannot (adequately) imagine.

In order to discern what these limits are, I invite my readers to test the limits of their own imaginations in an experiment based on Descartes’ example. Since it concerns only what you can imagine, you don’t have to resort to a lab—in this case a “thought experiment” and a real experiment coincide!

Now, I’m sure you can imagine a polygon with the least possible number of sides—a triangle. I’d wager that you can also imagine a square, a pentagon, a hexagon… but not a chiliagon. It would thus seem that there is some number n such that you can imagine an n-sided polygon but not an n+1-sided polygon. (Note: For the purposes of this experiment you only count as imagining a polygon if you can imagine the whole thing at once.) Let’s call this n-sided polygon your limit polygon. I have two questions: First, what is the number of sides of your limit polygon? Second, do you notice anything about the phenomenology of your limit polygon? If so, what?