Goodman, some properties (like being green) figure in good inductive reasoning, and other properties (like being grue) do not. In our terms: some properties are projectable and other properties are non-projectable. Explain precisely what he means by this (you will want to explain what he means by 'inductive reasoning', and give some examples of projectable and non-projectable properties.) In general, what makes some properties projectable and others not?
Philosophers have spent much time and energy debating back and forth ideas of induction and deduction. One of the most famous thinkers who have done so is Goodman who has drawn up his "new riddle of induction" that starts off by challenging Hume's proposition.
Hume set the following challenge to our cognition. We are apt to conclude that A follows B. And is deduced from B. As a matter of fact to the fact that we consistently see cause-and-effect happening on an unbroken and consistent pattern. For instance, we regularly conclude that fire emerges from match striking matchstick box because, time after time, without exception we have seen that result happening. The two, however, as Hume shows are distinct. Match strikes box is point A. Fire happening as result is point B. The fact that A (in this case) has always emerged from B (in this case) need not necessitate the fact that the same A will always consequent form the same B. In the future. Hume gives the instance of the sun rising form the East. The fact that the sun has always risen from the East need not necessitate that it will do so in the future.
Scientists have tried to deal with Hume's problem of deduction, and one of these was Hempel show showed that statements need not always absolutely follow; the best they can do is confirm, i.e. be proejctivebl oen from the other. For instance, we can project that because all Martians that we have seen are wise, therefore all Martians in existence are wise. Goodman, however, refutes this with his riddle and thinks that not only is no answer possible to Hume, but, more so, that no answer is necessary.
Differences between Induction and Deduction
The first thing that we need to do is question our definitions of deduction. Asks Goodman:
How do we justify a deduction? Plainly, by showing that it conforms to the general rules of deductive inference. . . . When a deductive argument has been shown to conform to the rules of logical inference, we usually consider it justified without going on to ask what justifies the rules. (63)
In other words, we accept deductive arguments due to the fact that they follow certain normative accepted rules. These rules, in turn, are also accepted and, so our existence of deductive arguments rests on a reiterative circle:
Principles of deductive inference are justified by their conformity with accepted deductive practice. . . . This looks flagrantly circular . . . But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. (64)
Induction carries the same theme:
All this applies equally well to induction. . . . Predictions are justified if they conform to valid canons of induction; and the canons are valid iff [i.e. If and only if] they accurately codify accepted inductive practice. A result of such analysis is that we can stop plaguing ourselves with certain spurious questions about induction." (64)
Hume was criticized for opening us up to skepticism (he is often called the Skeptic, and it was up to Kant to 'wake us up'). Goodman, however, destroys our confidence even more. If both deduction and induction are based on human rules and framework, the result is that our entire belief structure is based on humanly created, fallible rules consequenting in the conclusion that we may trust little or none of our statements. More so, the category of induction is even more vulnerable to skepticism and we see this by defining the difference between deduction and induction: Deductions are arguments that clearly follow one from the other, for instance "All German Shepherds are dogs. Spot is a German Shepherd; therefor Spot is a dog." Inductive arguments, on the other hand, are the reverse: they are specific premises that result in general conclusions. For instance: "all dogs that I have seen are German shepherds. Therefore, all dogs are German shepherds." These are instances of projectable and non- projectable situations. Deduction is more of a projectable instance where one instance can clearly be projected from the former; induction may be non-projectable. We cannot conclude with a certainty that one inference is projective from the other. The one may be true, but clearly does not always entail the other.
As Goodman notes:
As principles of deductive inference, we have the familiar and highly developed laws of logic; but there are available no such precisely stated and well-recognized principles of inductive inference. (65).
In other words, we can rely on logic to formulate and prove theorems of deduction. We can rely on no formal proofs, however, to demonstrate inductive statements.
In section three, Goodman plays around with various attempts to formulate canons for inductive arguments. His most famous attempt is the following (placed in logical form):
1. Emerald1 is green.
2. Emerald2 is green.
1000. Emerald1000 is green.
[therefore] C. All emeralds are green.
The modus ponens argument shows us that if a and b possess a certain attribute, then all following categories that possess this same attribute are x too. The argument makes sense to us for clearly one step does lead from the other resulting in a precise conclusion.
Goodman, however, causes us to question this by inventing a new term 'grue' (made up of 'green' and 'blue'), and then phrases the modus ponens argument in the following way:
An object is grue if and only if the object is either (1) green, and has been observed before now, or (2), blue, and has not been observed before now.
The argument (although stripped from modus ponens) makes sense since it provides us with clear conditions as to when we can define an item as 'grue'. On the other hand, it debilitates the inductive situation thusly:
1. Emerald1 is grue.
2. Emerald2 is grue.
1000. Emerald1000 is grue.
[therefore] C. All emeralds are grue.
Analyzing the above argument, the argument tells us that 1000 emeralds are grue which stands for blue and green and - placed in the format that it is placed -- the inductive argument seems to make sense. However, when we reduce the argument to its basics, it is rendered absurd for no way can an emerald be both 'green' and 'blue' (component of 'grue') simultaneously. It has to be either one or the other. And, therefore, the argument fails.
Accepting this, we have only two options:
1. To say that all inductive arguments of the same pattern are incorrect.
2. To attempt to make a distinction between the normative inductive argument and this one that follows the same pattern.
Let's try to poke holes in the term 'grue':
We can firstly say that 'grue' is illegitimate because it is confined to a certain time; i.e. that it refers to a color that has never been observed by us and therefore to one that is existent before the present moment. So we can therefore say that the inductive argument, in this instance, is illegitimate. In other words, we can argue that a syntactically universal hypothesis is lawlike if each of its predicates are qualitative and not positional. But the problems, says Goodman, is that we do not know whether a predicate is qualitative or positional. We cannot always tell the difference between the two.
The other thing that we can say is that 'grue' is a nonsensical term since it constitutes two colors existing simultaneously - something that can never be. But, as Goodman points out, things are not so simple:
An object is bleen if and only if the object is either (1) blue, and has been observed before now, or (2), green, and has not been observed before now.
This does seem like a perfectly comprehensible situation.
In short, the unusual situation that Goodman has invented (of an emerald being 'grue' i.e. both green and blue) may never occur. Nonetheless, the argument is solid and points to a problem in inductive reasoning. It is one that we have to answer to accept our habits of accepting non-projectable properties.
According to Goodman, the original problem with induction that philosophers tried to solve was that anything can follow anything else. People such as Hume, however, showed this to be impossible and so philosophers, such as Hempel, tried to loosen it to statements that could confirm another (i.e. project one from the other and be to some extent projectable).
Goodman showed, however, that inventing a word with an invented term such as 'grue' does not eliminate the former problem…