INTRODUCTION
Formal argumentation plays an important role in philosophy. Many philosophers defend their views using formal arguments. While formal arguments are helpful in clarifying the logical connections between different propositions, there are certain limitations to them. In this article, I highlight one of their limitations and explain why formal argumentation is not an adequate method to settle disputes between competing philosophical positions. The article is based on the work of Graham Oppy, a prominent philosopher of religion.The article summarises a part of Graham Oppy’s paper titled “What derivations cannot do” . We end the article with an explanation of an alternative methodological approach defended by Graham Oppy.
FORMAL ARGUMENTS
Before proceeding further, it is important to present a rough sketch of what a formal argument is. Roughly, a formal argument is a set of propositions which aims to establish a conclusion. The conclusion of a valid formal argument is a logical consequence of the set of propositions. The set of propositions are called the premises of the argument. The premises includes both assumptions and sub-conclusions. Assumptions are those propositions which are not derived from other propositions in the argument and sub conclusions are intermediate propositions which are derived from the assumptions.
With this in mind, let us consider what happens when two people argue about a proposition? Suppose there are two persons P and Q and they are arguing about a proposition C. P believes C and Q believes ~C(not C). In order to persuade Q, P presents an argument to support C. The argument will typically include some statements and the conjunction of those statements entails the conclusion C if the argument is valid. Now the question is what role does this argument play in the dispute. To evaluate that, we need to consider the set of total beliefs of both P and Q. Suppose P believes in a set of propositions which includes p1,p2,.....,pn, q1,q2,......,qn and C. And Q believes in the set of propositions which includes p1,p2,.....,pn and ~q1,~q2,.., ~qn and ~C. Both P and Q share the beliefs in the propositions p1 to pn. However, P believes in q1 to qn and C whereas Q believes in ~q1 to ~qn and ~C. Now, let's discuss the argument presented by P to support his conclusion.The argument will contain some propositions which will logically entail the conclusion. Will the argument be successful against Q? The argument will work if and only if the premises contained in the argument are members of the set of propositions Q believes. So in order for the argument to succeed, P needs to take premises from either p1 to pn and from ~q1 to ~qn and show that some of the premises from Q's worldview logically entails C. Because Q believes ~C, Q needs to revise his worldview to make it internally consistent . Q can take two route in this case. Either Q will revise his belief in at least one of the premises in the argument or Q will revise his belief regarding C. This is the only role formal arguments can play in debates and discourses. That is to show that someone’s beliefs are internally inconsistent. In other words, only successful formal arguments are reductio of someone else’s views. The argument by itself doesn’t tell us anything about which belief we ought to revise. Q is in his epistemic rights to keep his belief in ~C even if the argument is a successful reductio of his worldview, Q can choose to revise his belief in the premises rather the conclusion. This is one of the limitations of formal arguments. It shows that formal arguments by itself doesn’t tell anything about belief revision. Moreover, the only successful role we ascribe to formal arguments is a very minor role because the best pictures around any philosophical issues is mostly internally consistent. For example, in the debate between theists and atheists on the existence of God, it is safe to assume that there are certain theistic worldviews and certain atheistic worldviews which are internally consistent. This means formal arguments can play no role in assessing between these internally consistent worldviews. In that case, devising formal arguments for one worldview or against the other worldview seems fruitless.
AN ALTERNATIVE METHODOLOGICAL APPROACH
In this section I provide a rough sketch of an alternative methodological approach defended by Graham Oppy. The approach involves comparing the best articulation of different competing theories in terms of their explanatory power and commitments. Here a theory means a set of sentences closed under entailment. This alternative method essentially involves three steps, first is articulation. We ought to articulate two competing theories in as much as detail as possible, we ought to present a precise and detailed sketch of two competing theories. Secondly, we ought to check whether the competition theories are internally consistent. An internally inconsistent theory is ought to be rejected. Thirdly, if two competing incompatible theories T1 and T2 are internally consistent, then we need to compare them based on their explanatory power and commitments. We ought to prefer a theory which maximises explanatory power and minimises commitments. A theory has a higher explanatory power if the theory predicts the data more accurately than the competing theory where the data is the set of propositions which both parties agree to. The commitments of a theory mainly involves three types of commitments: ontological, ideological and theoretical. A theory has a fewer ontological commitments if it commits to a fewer entities or a fewer types on entities. A theory has a fewer ideological commitments if the theory has a fewer undefined primitive terms. A theory has a fewer theoretical commitments if the theory has a fewer fundamental principles where the fundamental principles of a theory are sentences of that theory which are not derived from other sentences of the theory. The theory which fares best in the comparative assessment along these dimensions is the theory we ought to believe.
CONCLUSION
While formal arguments can be immensely useful in certain contexts, they are not the ultimate arbiters in settling philosophical disputes. This post outlines one of its limitations. It is important to acknowledge their limitations in order to prove our philosophical discourse. I hope this post helps you to gain an important insight into the nature of formal arguments.
BIBLIOGRAPHY
1)OPPY, G. (2015). What derivations cannot do. Religious Studies, 51(3), 323–333. http://www.jstor.org/stable/43658390
The Limitation of Formal Argumentation