New Blog

Hey guys. For those of you that either subscribe to my blog or visit here sometimes I know I haven't posted much lately. I'm moving my blog to and new host and changing it's name in hopes that that helps a bit. My new blog is http://analyticangles.wordpress.com


Proofs that P

Some "Proofs that p" that I find funny. I did not write these but I found them here and here


I can entertain an idea of the most perfect state of affairs inconsistent with not-p. If this state of affairs does not obtain then it is less than perfect, for an obtaining state of affairs is better than a non-obtaining one; so the state of affairs inconsistent with not-p obtains; therefore it is proved, etc.


The theory p, though "refuted" by the anomaly q and a thousand others, may nevertheless be adhered to by a scientist for any length of time; and "rationally" adhered to. For did not the most "absurd" of theories, heliocentrism, stage a come-back after two thousand years? And is not Voodoo now emerging from a long period of unmerited neglect?

Outline Of A Proof That P*:
Saul Kripke

Some philosophers have argued that not-p. But none of them seems to me to have made a convincing argument against the intuitive view that this is not the case. Therefore, p.

* - This outline was prepared hastily -- at the editor's insistence -- from a taped manuscript of a lecture. Since I was not even given the opportunity to revise the first draft before publication, I cannot be held responsible for any lacunae in the (published version of the) argument, or for any fallacious or garbled inferences resulting from faulty preparation of the typescript. Also, the argument now seems to me to have problems which I did not know when I wrote it, but which I can't discuss here, and which are completely unrelated to any criticisms that have appeared in the literature (or that I have seen in manuscript); all such criticisms misconstrue my argument. It will be noted that the present version of the argument seems to presuppose the (intuitionistically unacceptable) law of double negation. But the argument can easily be reformulated in a way that avoids employing such an inference rule. I hope to expand on these matters further in a separate monograph.

It is a model theorem that p -> p. Surely its possible that p must be true. Thus p. But it is a model theorem that p -> p. Therefore p.

SOCRATES: Is it not true that p?
GLAUCON: I agree.
CEPHALUS: It would seem so.
POLEMARCHUS: Necessarily.
THRASYMACHUS: Yes, Socrates.
ALCIBIADES: Certainly, Socrates.
PAUSANIAS: Quite so, if we are to be consistent.
ERYXIMACHUS: The argument certainly points that way.
PHAEDO: By all means.
PHAEDRUS: What you say is true, Socrates.


Sad But True

Q: How do you get a philosophy major off of your front porch?
A: You tip them for the pizza

I'm beginning to feel a bit apprehensive about my choice in a major. If this whole grad-school thing doesn't work out.......


Kant Attack Ad

Well I finally gave in. Here it is for both people who subscribe to my blog. It's been floating around the blog-o-sphere for quite some time. Enjoy....


Hempel's Account of Scientific Explanation

In his paper titled Explanation in Science Carl Hempel set out to give an account for the way in which facts relate to given general laws. In his explanation Hempel formulated what he called the deductive-nomological model. In this paper I will give a critical examination of Carl Hempel’s deductive-nomological model for scientific explanation which consists of his strictly universal form and the probabilistic-statistical form. I will begin by explaining Hempel’s position on both the strictly universal form and the probabilistic-statistical form and will follow each by looking at their strong points and will finish each section by examining the problems with each part of his deductive-nomological model.

The Deductive-Nomological Model

Carl Hempel’s account of the deductive-nomological explanation suggests a logical relationship between what he calls “particular facts” and “uniformities expressed by general laws”. In attempting to explain these Hempel gives us an account given by Dewey in his book How We Think about an observation that Dewey made while doing the dishes. As Dewey was washing the dishes he noticed that as he took some cups out of the hot-soapy water and turned them upside down on a plate and bubbles came out from underneath the cups rim, grew for a while, ceased and regressed back into the cup. Dewey’s explanation of this phenomenon went something like this: When the cup was placed on the plate cool air was caught inside, the inside the cup air was warmed by the cup, which caused an increase in air pressure inside the cup, which cause the bubble to grow and as the cup cooled the air pressure inside the cup returned to normal and the bubbles regressed into the cup.

Keeping this example in mind Hempel says that we can divide this explanatory account of the event (or what he calls the explanandum-event) into two groups: 1) particular facts; these would be facts like the immersion of the cups in hot-soapy water, the placing of the cup upside down in a puddle of hot-soapy water formed upon the top of a plate, etc. and 2) uniformity expressed by general laws; these would be implicit laws that are used when attempting to understand a given phenomenon (e.g. gas laws, laws about the behavior of soap bubbles, etc.). Hempel then goes on to demonstrate that the logical relationship between the two can be shown as such

C₁, C₂…, C₃
L₁, L₂…, L₃

Where C₁, C₂…, C₃ are statements describing particular facts and L₁, L₂…, L₃ are the general laws and that jointly these statements are connected to determine E, the statement describing the explanandum-event or just the explanandum. This entire formulation Hempel calls the deductive-nomological explanation (or later the strictly universal form).

Benefits of the Deductive-Nomological Model

Hempel’s account of scientific explanation has many benefits for the philosophy of science. It accounts for the relationship between the thing that is being explained and the laws that govern that thing. As Hempel says “…laws connect the explanandum event with the particular conditions cited in the explanans”3 because of this the explanans can be said to have explanatory power.
The deductive-nomological model can also be extrapolated and show the relationship between explanandum and explanans in other examples beyond Dewey’s washing of his dishes. An example of such might be the relationship between a bent spoon in water and laws of light refraction or the falling of a tree in the forest and the law of gravity. Thus Hemple’s Deductive-Nomological Model has explanatory power beyond his given example.

Problems with the Deductive-Nomological Model

The main problem with Hempel’s account of the deductive-nomological model is that it only accounts for a given phenomenon by using reference of general theoretical principals and does not account for explanations that are raised in a statistical way. An example of this might be that a certain individual has had a case of the flu and a given medicine is administered to her to help recover from the flu. The probability of her recovery after the administration of the given medicine is high. With that said the main problem with Hempel’s deductive-nomological model thus far is that these given explanans do not imply the explanandum. So to deal with this Hempel distinguishes between what he calls the strictly universal form, in which “all cases in which certain specified conditions are realized an occurrence of such and such will result” and the probabilistic-statistical form which asserts that “if certain specified conditions are realized, then an occurrence of such and such a kind will come about with such and such a statistical probability”.

Hempel’s Probabilistic-Statistical Form

Hempel’s Probabilistic-Statistical Form deals with general laws whose results can be implied from general laws or theoretical principals with a statistical probability. The example Hempel gives is of a man with hay fever. If a given man had a hay fever attack and he took 8 milligrams of chlor-trimeton then the probability for a recovery from hay fever upon the administering of the 8 milligrams of chlor-trimeton is high. He says however that this explanans does not “deductively” imply the explanandum as it is implied in the strictly universal form, but rather it is more or less likely to happen. He formulates it as...

p(O,F) is very high makes very likely

Where the “Oi” is the expression of the explanandum and it consists of a particular part that we consider (here i will be the subjects hay fever attack itself) and the outcome (O, which would be the cessation of the hay fever attack). This explanandum is explained by the two statements Fi and p(O,F), where the first part Fi corresponds with the first part of his strictly universal form (C₁, C₂…, C₃) and states that in all cases i the factors (F) were realized. The second part states that the probability for the outcome O to happen in all the cases where F is realized is high (close to 1). The double line separating the explanans from the explanandum indicates that the explanandum is not logically implied by the explanans but rather that the explanans only make the explanandum likely to happen.

Hempel also feels the need to differentiate between statistical probability and a concept of likelihood. He suggests that a statistical probability is a long run of how frequent a given event or occurrence (here, F) will be accompanied by a specific outcome of a specific kind (here, O). On the other hand he believes that likelihood is a relation that is not between the occurrences but between statements. A likelihood that is referred to can be shown to be the “strength of the inductive support” or the “degree of rational credibility, which the explanans confers upon the explanandum”.

Benefits of the Probabilistic-Statistical Form

The main benefits that we can see with the probabilistic-statistical form (PSF from now on) are that they are nomological in character, it fills in where the strictly universal form (SUF from now on) fails and they can be extrapolated out to be used in more that Hempel’s given example. The PSF is nomological in character because it, like the SUF bases itself on (or presupposes) general laws which, even though they are statistical (or inductive) rather than deductive in character. This inductive argument explains the phenomenon by demonstrating that (taking into account certain statistical laws) the occurrence of such and such an event was expected with a high logical probability.

In addition the PSF takes over where the SUF will not be able to account for the relationship between a given explanandum and explanans. The example of the woman with the flu given earlier may be the quintessential example of this. There is no strictly universal law that would account for her recovery since she was given a certain medicine that had a likelihood of curing her.

The last benefit of the PSF is that it has explanatory power outside of the Hempel’s given examples. One can take the example that I listed earlier (the woman with the flu) or we can take almost any statistical prediction and ally the explanans to the formula and arrive at an explanandum. Thus like the strictly universal form the probabilistic-statistical form has explanatory power beyond the given examples.

Problems with the Probabilistic-Statistical Form

Hempel himself notices that there is one problem with his given account of both the PSF and the SUF. The problem revolves the problem of induction for “the universal laws invoked in a deductive explanation can have been established only on the basis of a finite body of evidence”6. So we cannot verify for certain that any given law that is assumed (like a law of physics) will hold true in every future possible instance because we have only a “finite body of evidence”. Hempel assumes that this argument “confounds” a logical issue with an epistemological one. Going further Hempel says that it is true that...

Statements expressing laws of either kind can be only incompletely confirmed by any given finite set --however large-- of data about particular facts; but law-statements of the two different types make claims of different kinds which are reflected in their logical forms: roughly, a universal law-statement of the simplest kind asserts that all elements...have a certain characteristic...; while statistical law-statements assert that...a specified proportion of the members of the reference class have some specified property.

This however seems to ignore the entire objection by writing it off as an epistemological claim and reaffirming the already stated theory. If we are to accept his deductive-nomological model we need to have reassurance that at any given time or circumstance that the assumed laws will continue to hold true. If we cannot be reassured this then there is no reason to assume that a given explanans will accurately confer a given explanandum.

Besides not being able to account for the problem of induction the given models cannot be said to account for other attempts of scientific discovery apart from the so called hard sciences. In another scientific field like psychology statistical laws or natural laws will not be able to be applied to make explanandum predictions in the same way. One cannot take a statistical probability (like say the percentage of the population that suffers from a certain psychological disorder), apply it to a given patient and expect that somehow the statistical explanans inferred the explanandum.


Hempel’s account of scientific explanation is beneficial to help explain the relationship between the explanans and the explanandum. It has explanatory power outside of the secluded examples give by Hempel and it also accounts for nomological relationships between statistical and universal laws and given phenomenon. However there are still problems with either of his answer as to how scientific explanation works. The first shows itself in his theories inability to deal with the problem of induction. The second is the deductive-nomological model’s inability to be applied to all areas of scientific explanation.


Carl Hempel “Explanation in Science” in Scientific Knowledge, ed. Janet A. Kourany (Belmont, CA: Wadsworth Publishing, 1998)
Woodward , James Scientific Explanation Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/scientific-explanation/