Something-from-Nothing Transformations
When we discussed Stephen Schiffer, we noted that he proposes what have come to be called pleonastic entities. Pleonastic entities fall under pleonastic concepts, which are characterized by being those used in something-from-nothing transformations. Examples of something-for-nothing transformations (which we will from here on out just call SfN transformations) would be things like:
Fido is a dog; therefore there is a proposition, ‘Fido is a dog’.
Fido is a dog; therefore Fido has the property of being a dog.
Fido is a dog; therefore Fido is a thing called a dog.
Fido is a dog; therefore there is a kind of thing that is a dog.
Fido is a dog; therefore there is a name, Fido, that can be applied to a dog.
Fido is a dog and Mimi is a dog; therefore Fido and Mimi are a pair of dogs.
In each case we have bolded the pleonastic concept. When we look at a large number of SfN transformations, we find that ‘something-from-nothing’ is a loose way of talking. What it indicates in context is that we have a legitimate argument (indeed, possibly a logically valid argument, which we will consider below) in which a concept is explicit in the conclusion that we don’t find in the premise(s). In reality this concept doesn’t come ‘from nothing’, nor is it really ‘for nothing’; it comes from the background that makes the original premises meaningful. There are many pleonastic concepts, identifiable by SfN transformations, that are in common use; Schiffer includes fictional character, of course, but other cases are measurement, concept, event, state, state of affairs, fact, term, and object. These are in common use, we said, but the number of possible pleonastic concepts, some of them quite weird, is immense, and we sometimes come up with them on the fly.
These are called ‘pleonastic’ because in SfN transformations we can recognize that the conclusion is a more conceptually expansive way of stating the premises. To be more exact, the conclusion is a more conceptually expansive way of stating the premises in light of the background to the premises. We should not, however, confuse this logical ‘pleonasm’ with rhetorical pleonasm; the conclusions are not merely more wordy, but highlight information used to understand the premises. This is key to why these are not illegitimate inferences. They are drawing out something that can already be there.
In particular, it seems that pleonastic concepts are an inevitable result of the fact that every proposition, including those used as premises, presupposes classifications. We can’t make sense of the terms of the propositions if we have no idea of the classification – or perhaps more often, of the family of classifications – in which they play a role. As we will see, not all pleonastic concepts are purely artifacts or byproducts of possible classifications, but in SfN transformations, at least, we are drawing on the fact that they play a role in classifications relevant to the premises. We see some confirmation of this in the fact that when we are trying to clarify things, or be more precise than usual, we ascend to pleonastic concepts in order to do so. Pleonastic concepts make it easier for us to compare different things, to state things precisely, and to clarify which of the different possible levels of reasoning we might be presupposing.
When we reason with classifications, we discover a kind of reasoning that is logically valid in a way that’s a bit different than we find in the kinds of logically valid arguments we usually study in logic classes. For instance, consider the following argument:
Fido is a dog; therefore Fido is a mammal.
If the premise is true, the conclusion has to be true; that’s a common way of thinking about logical validity, so this argument is logically valid. Why is it valid, though? It’s because the right kind of connection between premise and conclusion is guaranteed by the classification of the terms (in this case, dog being a species of the genus mammal). We can call this material validity or classificational validity. It seems clear that SfN transformations, when valid, are particular kinds of materially or classificationally valid inference. ‘That is Fido; therefore something has the name Fido; therefore something has a name’ is materially valid because ‘Fido’ is classifiable as a name.
If this were all there were to pleonastic concepts, they would be useful, if for no other reason than that it is sometimes convenient and even at times illuminating to say the same thing in different ways. But while pleonastic concepts are identified by their ability to show up in the conclusions of SfN transformations, they do not have the bare function of playing a role in SfN transformations. An obvious advantage of being able to move from ‘Fido is a dog’ to ‘There is a proposition, “Fido is a dog”’ is that it lets us compare ‘Fido is a dog’ specifically as a proposition to other pleonastic entities that are propositions. This ability plays an important role in applied logic, in which it is common to move from an argument to a logical discourse about the argument using pleonastic concepts like term, proposition, argument, premise, conclusion. In this logical discourse we can often more easily and directly assess specific features of the argument that are relevant to its structure and quality. Much of logic is thus founded on pleonastic concepts, and the same is true of mathematics. Pleonastic concepts, in fact, play a considerable role in any field that has a significant formal component.
It also becomes clear that while SfN transformations mark out pleonastic concepts, once we have the pleonastic concepts they can sometimes be reached in other ways. That is to say, they are not always purely part of our reasoning-apparatus. Schiffer identifies fictional characters as pleonastic entities, but fictional characters do not only show up in SfN transformations. In fact, most discourse about fictional characters has very little to do with SfN transformations, because our most common way of getting to fictional characters in in our discussions is not by SfN transformations but by testimony. We are told about them, or shown them, directly. Fictional characters are not bare pleonastic entities, nor are they bare artifacts of reasoning or the classifications we use in reasoning; once we recognize what fictional characters are, we can have direct evidence of them and about them.
Another good example of a pleonastic concept that does not reduce to SfN transformations is one mentioned above: measurement. Consider the following SfN transformation:
The stone is 5.2 kilograms; therefore the stone has a measurement of 5.2 kilograms.
This is a good SfN transformation. Therefore measurement is a pleonastic concept, and particular measurements like kilograms are pleonastic entities. But it is very obvious that measurements are not merely pleonastic entities, existing only as an artifact of classification or only as a formal reasoning device. There are entire methodologies of measurement, there are physical instruments used to measure, and measurements play important roles in practical things like building and chemistry as well as in theoretical explanations of the world. Once we have the concept of measurement, we don’t have to confine ourselves to SfN transformations (although they always remain viable). We can also just measure things, and in measuring things we have independent evidence that measurements exist.
Experiences and sensations would be another example. We have SfN transformations like, ‘I see red, therefore I have a sensation or an experience of seeing red’. But we don’t just find experiences in SfN transformations; we actually sense and experience things.
This all comes back to classification again. If our classifications were purely arbitrary we should never see this happen, but it is actually not all that uncommon. We can sometimes have independent direct evidence of pleonastic entities because our classifications are not always purely arbitrary. They do in fact latch onto the world. In fact, given the vast role pleonastic concepts and entities have in our view of the world (as seen, for instance, in their use in the arts, the formal sciences, and the physical sciences), it’s only because our classifications sometimes latch onto the world that we are able to reason very far about it. We understand the world in part by finding pleonastic entities in it.