By Ng Ling Xuan
Logical empiricists worked towards a “formal theory of confirmation”. This “formal theory” is an extension and application of deductive logic. In this essay, I will first explicate the workings and merits of deductive logic. Secondly, I will describe science’s close ties to inductive logic. Next, I will explain the motivation for the “formal theory of confirmation”. Subsequently, I will describe Goodman’s “Grue Problem” and explain how it potentially threatens “formal theory of confirmation”. I will lastly lay out an argument in favour of the formal theory.
In deductive logic, an argument is deductively valid if the premises of the argument are true, then the conclusion must guarantee to be true as well. One example of deductive logic would be:
1. All men are mortal.
2. Donald Trump is a man.
3. Therefore, Donald Trump is a mortal.
The argument form:
1. All A’s are B.
2. x is an A.
3. Therefore, x is B.
The virtues of deductive logic are that the truth of the conclusion is guaranteed regardless of predicates or content used in its premises, and it provides a clear and unambiguous standard in distinguishing between good and bad arguments. As long as an argument takes a deductively valid form, and the premises are true, then the conclusion is guaranteed to be true. The form of a deductively valid argument, like the above example, is the basis of a good argument. Meanwhile, for inductive logic, there can never be a complete transmission of truth in an argument, there will only be degrees of truth. Inductive logic also aims to establish generalizations from a large quantity of particular observations. (Godfrey-Smith 2003)
We generally assume science to fall under the scope of inductive logic. The scientific model is about testing, comparisons and ‘confirmation’ between hypotheses, predictions and observations. (Godfrey-Smith 2003) In virtue of gathering empirical data in observations, science is largely an empirical affair. Hence, science is likened to an inductive and empirical activity.
Impressed by the clear and unambiguous guarantee of truth in deductive logic, the logical empiricists wanted science to operate in the same manner as deductive logic. Hence, the logical empiricists wanted to bridge the gap between scientific method and deductive logic. In attempting to bridge deductive logic to scientific method, the logical empiricists wanted to formalise the process of induction. (Godfrey-Smith 2003) Hence, this is termed as “the formal theory of ‘confirmation’”. The logical empiricists thought this is a worthwhile pursuit due to their wish for science to be as clear and unambiguous as deductive logic, thus raising the credibility and rigour of science.
In their attempt for a “formal theory of confirmation”, Goodman’s “New Riddle of Induction” or “Grue Problem” arose. The merger of deductive logic and scientific model is not a straightforward affair. In Goodman’s “Grue Problem”, the example of emerald colour investigation is used. In the initial stage, the investigation yielded this inductive argument form:
1. All the many emeralds observed in different conditions before 2016 have been green.
2. Therefore, all emeralds are probably green.
This is a fairly simple inductive argument form. With the introduction of a new terminology – “grue”, the new modified argument would now look like this:
1. All the many emeralds observed in different conditions before 2016 have been grue.
2. Therefore, all emeralds are probably grue.
The definition of “grue” is as follows: ‘An object is “grue” if and only if it was first observed before 2016 and is green, or if it was not first observed before 2016 and is blue.’ The initial and modified “grue” arguments can be condensed into its bare form as shown below:
1. All the many E’s observed in different conditions before 2016 have been G.
2. Therefore, all E’s are probably G.
From this definition of “grue”, the grass at the local park right now is grue and the clear skies in 2030 would also be grue. There is a timeframe reference in this modified argument where one is inclined to believe that emeralds observed in the future, after 2016, will be blue instead, in virtue of the definition of “grue”. (Godfrey-Smith 2003) To infer that emeralds could simply turn blue after a certain time goes against the inductive truth that emeralds are generally green.
The observational differences between the initial argument and modified “grue” argument show the beginnings of the problem in the “formal theory of confirmation”. This problem is especially acute because the initial and modified inductive arguments both adopted the same argument form. Inspired by deductive logic, it was thought that to retain a good argument form is a positive trait. A good deductive argument form is logically immune to changes to its predicates or contents used in its premises, hence the motivation for the replacement of “green” to “grue”. However, as observed here, while retaining the identical argument form, one argument can be good and other bad. (Godfrey-Smith 2003) This is disastrous for the logical empiricists who trusted the clear and unambiguous standard of deductive logic. It is now left wholly uncertain if the logical empiricists are able to formalise induction and whether it is indeed plausible to adopt good argument forms to the inductive arena of science at all.
With the integrity of the argument form preserved in both cases shown earlier, it seems like it is the introduction of the new terminology “grue” that brought the problem. (Godfrey-Smith 2003) It points to the suspicion that there is something insidious about introducing new terminology that cripples the process of formalising confirmation.
Despite this seemingly crippling problem, not all hope is lost for the logical empiricists. While, it might be true that modifications of terminology from “green” to “grue” would have negative implications. However, it is worthy to note that scientific terminologies are seldom defined in such manners. It is important to note that modifications of definitions in predicates should not be done frivolously. Moreover, scientific definitions are often highly resistant towards such modifications. In other words, it is essential to point out the distinction between ordinary and scientific language.
Godfrey-Smith, Peter. 2003. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press. 2006.
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