Online research in philosophy

The creation-of-matter hypothesis of the Bondi-Gold-Hoyle steady-state cosmology requires that in an infinite time to which the first transfinite number may be assigned the number of atoms of matter produced would be equal to the cardinal number of the set of mathematical points in the continuum. The existence of a set of finite atoms with that cardinal number is physically unacceptable. The argument for the production of a non-denumerable set of atoms, in infinite time, is given in terms of a model which is shown to be isomorphic with the original Cantor "diagonal" proof for the existence of a non-denumerable infinity. An alternative model which meets the requirements of the steady-state theory is presented; in this model, the number of atoms is explicitly no greater than countably infinite, and remains countably infinite as long as the past time of the universe is restricted to the unlimited set of finite unit-time intervals. If the origin of the steady-state universe is taken as being within that infinite set, expressed by the negative natural numbers, the contradiction of an atom at every mathematical point does not arise. The contradiction does arise if the origin is not within the set of finite numbers, and accordingly there is a restriction as to which concept of infinite past may properly be maintained in the steady-state theory.

As every philosopher knows, “the design argument” concludes that God exists from premisses that cite the adaptive complexity of organisms or the lawfulness and orderliness of the whole universe. Since 1859, it has formed the intellectual heart of creationist opposition to the Darwinian hypothesis that organisms evolved their adaptive features by the mindless process of natural selection. Although the design argument developed as a defense of theism, the logic of the argument in fact encompasses a larger set of issues. William Paley saw clearly that we sometimes have an excellent reason to postulate the existence of an intelligent designer. If we find a watch on the heath, we reasonably infer that it was produced by an intelligent watchmaker. This design argument makes perfect sense. Why is it any different to claim that the eye was produced by an intelligent designer? Both critics and defenders of the design argument need to understand what the ground rules are for inferring that an intelligent designer is the unseen cause of an observed effect.

As every philosopher knows, “the design argument” concludes that God exists from premisses that cite the adaptive complexity of organisms or the lawfulness and orderliness of the whole universe. Since 1859, it has formed the intellectual heart of creationist opposition to the Darwinian hypothesis that organisms evolved their adaptive features by the mindless process of natural selection. Although the design argument developed as a defense of theism, the logic of the argument in fact encompasses a larger set of issues. William Paley saw clearly that we sometimes have an excellent reason to postulate the existence of an intelligent designer. If we find a watch on the heath, we reasonably infer that it was produced by an intelligent watchmaker. This design argument makes perfect sense. Why is it any different to claim that the eye was produced by an intelligent designer? Both critics and defenders of the design argument need to understand what the ground rules are for inferring that an intelligent designer is the unseen cause of an observed effect.

I was recently on an NPR program with skeptic Michael Shermer and paleontologist Donald Prothero to discuss intelligent design. As the discussion unfolded, it became clear that they were using the phrase "intelligent design" in a way quite different from how the emerging intelligent design community is using it.

The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can replace a universal proposition about any universe (finite or infinite, countable or uncountable) by a complex proposition (= sentence built up from atomic sentences and the connectives). But from the point of view of communication such a replacement is not possible if the universe is infinite.

The design argument for the existence of God is often criticized for resting on anthropocentrism. Some critics maintain that anthropocentrism explains the origin of the design argument. Such critics commit the genetic fallacy. Others say anthropocentrism explains the appeal of the belief that human beings are ends especially worthy of creation. They fail to appreciate that the design argument need not be framed in terms of the fitness of the universe for humanity. Lastly, some say the design argument requires a picture of value according to which it was true, prior to the coming-into-being of the universe, that our sort of universe is worthy of creation. Such a picture, they say, is mistaken, though our attraction to it can be explained in terms of anthropocentrism. This is a serious criticism. To respond to it, proponents of the design argument must either defend an objectivist conception of value or, if not, provide some independent reason for thinking an intelligent designer is likely to create our sort of universe.

Space is big. It is very, very big. On the currently most favored cosmological theories, we are living in an infinite world, a world that contains an infinite number of planets, stars, galaxies, and black holes. This is an implication of most “multiverse theoriesâ€, according to which our universe is just one in a vast ensemble of physically real universes. But it is also a consequence of the standard Big Bang cosmology, if combined with the assumption that our universe is open or flat, as recent evidence suggests it is. An open or flat universe – assuming the simplest topology[1] – is spatially infinite at any time and contains infinitely many planets etc.

It seems improbable that life would exist in a naturalistic universe. But if the universe were spatially infinite, then seemingly improbable events would be expected to happen; life would be expected to exist. It follows that the existence of life provides evidence that the universe is spatially infinite.

Did God create life? Or did life arise via naturalistic processes, along the lines of random mutation and natural selection as suggested by Darwin? Intelligent design proponents attempt to use William Dembski’s design inference to argue that the existence of intelligent life is due to design. I will argue that the design inference is flawed, because it does not take into account the fact that the universe is spatially infinite.

This paper addresses two main questions. How does one determine that something has the features it does as a result of design, as opposed to for example chance? How are inferences to design affected when one makes the (plausible) assumption that the universe is spatially infinite? I will show that arguments for the existence of God based on the improbable development of life don’t go through under the supposition that the universe is spatially infinite. I will also show that the model of design inferences promulgated by William Dembski is flawed, because it has the consequence that one can never infer design in a spatially infinite universe. My model for design inferences has the (desirable) consequence that there are circumstances where a seeming miracle can count as evidence for the existence of God, even if one would expect that type of event to naturalistically occur in a spatially infinite universe.