On the Limits of Philosophy

[Petros Agapetos]

The material world may not be real

There are certain questions to which philosophy cannot give conclusive answers. Among these questions are the question of the existence of the physical world and the problem of the justification of induction. As one looks at blue light, the blueness one perceives is in the mind, yet the physical object, the light of frequency ‘blue’, belongs to the domain of the physical world and has physical properties, such as having a certain frequency and being located in time and space as well as being determinate, public, and persistent in nature. While objects which are perceived by the mind, the blueness of the light, have the properties of sense data, they are indeterminate, private, and instantaneous, and belong to the domain of the mind.

If two things have different properties and belong to domains of a different nature, they are distinct. Therefore sense data (blueness) and physical objects (light of frequency blue) are distinct. Any attempt to verify the existence of public and persistent objects by the testimony of other conscious agents who perceive the physical objects would be circular because it would presuppose that those conscious agents exist in the first place and aren’t merely the result of sense data alone. Therefore there can be no non question begging deductive argument for the existence of blue light by the mere sensation of blueness that one sees when looking at blue light.

No contradiction arises from the supposition that sense data are as they are yet physical objects, like light of frequency blue, do not underlie them, and sense data are perceived in such a way as to create the illusion that they are coming from an external world while in reality they could merely be correlated with collections of sense data induced in the mind. The mind being a pattern seeking entity infers to the best possible explanation for the determinate, public and persistent apparent nature of physical objects, namely that they exist. The belief that the material world exists harmonizes our experience of sense data and is an instinctive belief that cannot be definitively demonstrated by any deductive argument. There is a genuine limitation in the ability of philosophy to give an answer to the question of the existence of the material world. It is naïve to suppose philosophy could give us a definitive answer.

[Petros Agapetos]

On the Problem of Induction

A similar question can be raised about the principle of induction. If one lets go of an object on Earth from a certain distance from the ground, we can infer by induction that it will fall with an acceleration of 9.8 m/s2 due to the applied force of gravity on Earth. This law of nature has been observed and understood by scientists, and it is inferred that this law will hold for any object at any time in the future. This is an inductive inference, which infers a general truth ‘all objects will accelerate at 9.8 m/s2’ from observed instances in which the law holds true.

The principle of induction infers from past instances of a law applying to the next instance that this law will apply, and thereby generalizes to all instances that the law will apply. The justification for making the inductive inference is based on the assumption that the future will resemble the past, which is inferred from the observation that in the past, the future has resembled the past, that is, past futures resembled the past. Any attempt to appeal to the uniformity of nature implicitly assumes that the future will be like the past.

One cannot infer, without begging the question, that in the future the future will be like the past from the fact that in the past the future has been like the past, since this inference already makes use of induction, it assumes that past futures will be like future futures, which once again reduces to inductively inferring that the future will be like the past. Past experience cannot serve as evidence for the truth of the principle of induction. No amount of past instances of an object accelerating at downward can guarantee that in the future the same object will accelerate downward at the same rate.

Any attempt to prove the future will be like the past from the fact that in the past the future has been like the past invokes the very principle that is to be justified and demonstrated. Appeal to observation cannot rationally justify the expectation that the law of gravity will always apply. Any appeal to inductive inference to justify the use of an inductive inference would assume that the use of inductive inference is justified and therefore be circular and beg the very question and hence not be completely or ultimately justifiable. Therefore there can be no inductive justification for inductive inference.

In addition to there not being any inductive way to justify the principle of induction, there can also be no deductive way to justify induction because an inductive inference by its very nature is ampliative or knowledge inducing: the truth of the conclusion contains more information than the premises, and the truth of the premises does not guarantee the truth of the conclusion in an inductive argument. It is logically possible that the future does not resemble the past. Therefore there can be no deductive justification for making an inductive inference. Since the principle of induction cannot be justified neither inductively nor deductively, therefore there can be no rational justification for the principle of induction.

The principle of induction is at best an inference to the best explanation. It is an innate instinctive expectation that is not epistemically justified upon close rational examination, yet it is firmly believed because of the nature of the (human) mind to be predisposed to building models of reality with predictive capability in order to learn and make sense of the world. The use of inductive inferences can thereby be considered ‘reasonable’ even though it is not demonstrated to be ultimately justifiable.

There is a genuine tension between what the mind tends to believe by virtue of its nature and what can be demonstrated to be true. While the existence of the material world cannot be proven definitively and the use of inductive inference cannot be justified rationally, the mind tends to operate under certain basal assumptions: that the universe exists, that we can learn about it, and that models with predictive capability are more useful than models without. Insofar as these fundamental beliefs are assumptions rather than demonstrated truths, there is a genuine limitation of philosophy to give ultimate and conclusive answers.

Bibliography: The Problems of Philosophy Bertrand Russell, Watchmaker Publishing 1929

[Petros Agapetos]

The Problem of Deduction Explained

There are general deductive principles which are foundational to rational thought. Among these are 1) Modus Ponens and the three ‘Laws of Thought’ or ‘Logical Absolutes’ – 2) The Law of Identity, 3) The Law of Non-contradiction, and 4) The Law of Excluded Middle. These are basic deductive principles which appear to be self-evident truths which are known a priori and are not able to be neither proved nor disproved on the basis of experience nor through rational inquiry, and may be taken to be true by definition. Modus ponens or ‘affirming the antecedent’ is a deductive inferential pattern which is of the form:

Argument MP
Premise 1. If P (is true) then Q (is the case)
Premise 2. Since P (is true)
Conclusion MP. Therefore Q (is the case)

In order for Argument MP to be valid, it must be impossible for Premise 1 (‘If P then Q’) and Premise 2 (‘P’) to be true while Conclusion MP to be false (i.e. not Q). Making ‘If P then Q’ and ‘P’ true implies ‘Q’ by modus ponens, which cannot be ‘not Q’. A contradiction would arise if the premises were granted true yet the conclusion were false. Therefore, the Argument MP, which represents modus ponens, is valid.

An example of modus ponens:
Premise 1. If Socrates is a man, he is mortal.
Premise 2. Socrates is a man.
Conclusion. Therefore Socrates is mortal

What makes an argument valid is its form. Validity is the notion that the truth of the conclusion is guaranteed by the truth of the premises, such that the truth of the premises is preserved in the conclusion. If the premises of a valid argument are true, then the conclusion will follow inescapably. It is impossible to define validity without the use of modus ponens.

Argument V
Premise 1. If it is impossible for ‘If P then Q’ and ‘P’ to be true while Q to be false, then Argument ‘MP’ is valid.
Premise 2. ‘P’ is true and ‘If P then Q’ is true imply ‘Q’
Premise 3. The truth of ‘P’ and ‘If P then Q’ do not imply Q is false
Conclusion. Argument MP is valid.

Notice that the inference that allows one to conclude that Argument MP (modus ponens) is valid makes use of modus ponens in order to reach that conclusion. Modus ponens is entailed in the very definition of validity. In order to prove that the use of modus ponens is justified, one would have to argue that:

Argument J
Premise 1’. If ‘P’ and ‘If P then Q’ imply ‘Q’, therefore modus ponens is justified.
Premise 2’. ‘P’ is true
Premise 3’. ‘If P then Q’ is true
Premise 4’. ‘P’ and ‘If P then Q’ imply ‘Q’ (by modus ponens)
Conclusion J. Therefore, Q is true: modus ponens is justifiable.

Notice that accepting Premise 1’ as true is equivalent to assuming the validity of modus ponens. Premise 4’ establishes ‘Q (is true)’ by making use of modus ponens, by following Argument MP: ‘If P then Q’, since ‘P’, therefore ‘Q’. Argument J which is meant to demonstrate the justifiability of the use of modus ponens follows the inferential pattern of affirming the truth of the antecedent (‘P’ and ‘If P then Q’ imply ‘Q’) such that “whatever follows from a true proposition is true” [P*,52]. By stating as a premise that which needs to be demonstrated one commits the fallacy of begging the question. Thus, the ‘proof’ that modus ponens is justified assumes the validity of modus ponens by employing it, which implicitly presupposes the use of modus ponens is justified. Any attempt to prove that modus ponens is justified is bound to make use of the very deductive inference that is to be demonstrated to be justifiable. Therefore there can be no deductive justification for the use of modus ponens that is non-circular and hence doesn’t beg the question. Modus ponens can also not be proved to be justifiable inductively, because to offer a sound deductive argument is to guarantee the conclusion of the argument, while a strong inductive argument merely establishes that the conclusion is probably likely to be true but does not guarantee it, which is what is required for a deductive argument. Inductive inferences do not suffice to demonstrate the reliability of modus ponens, since they are too weak. Since modus ponens cannot be justified neither deductively nor inductively, any justification of modus ponens is bound to be epistemically circular, and therefore cannot be ultimately proved to be justified without begging the question.

Modus ponens is certain, ubiquitous and inescapable, yet we can neither prove nor disprove it. “The truth of the principle is impossible to doubt and its obviousness is so great that at first sight it seems almost trivial”. [P*, 52] The source of the justification of this principle seems to be our innate epistemic feeling of certainty, which appears to be distinct from logic. We have direct a priori knowledge of general principles about which we can have the same degree of certainty that we grant to our direct knowledge by acquaintance (i.e. sense data, memories, etc.).2 The Laws of Thought are among the general deductive principles which are self-evident and are known a priori without the need of any justification, which are arguably as certain as modus ponens, and can neither be confirmed nor disconfirmed on the basis of experience nor through rational inquiry.

[Petros Agapetos]

The Laws of Thought
1. The Law of Identity: Something is what it is: A is A.
2. The Law of Non-contradiction: Something is not what it is not: A is not ‘not A’. Nothing can both be and not be [P*,53]
3. The Law of Excluded Middle: Everything is either A or not A, and it cannot be neither or both. Nothing can be both A and not A, or neither A or ‘not A’; it must be either A or ‘not A’. Everything must either be or not be [P*,53].

These laws are known a priori, i.e. independent of experience through the senses; knowledge of the truth of these principles is non-empirical. Russell argues that certain general principles must be granted before any attempt to demonstrate their reliability becomes possible [P*, 52], and that deductive reasoning appears to comport with these principles [P*, 53]. We shouldn’t expect to be able to prove these three “Laws of Thought”, since they are self-evident tautologies that are true by their very definition; they are logical absolutes. Russell believes that there is some knowledge that experience does not suffice to prove, but it merely makes us aware of the fact that the truth of such knowledge is manifest without requiring any proof from experience [P*, 54] Among such knowledge is the knowledge that something is whatever it is (the Law of Identity), and it is not whatever it is not (the Law of Non-Contradiction), and it is not neither or both what it is and what it is not (the Law of Excluded Middle), and that whatever follows from a true antecedent proposition is true itself [P*,52].

One could object to Russell’s view that the “Laws of Thought” and modus ponens are self-evident truths by raising sufficient amount of doubt to question their truth. Consider the statement “This statement is false”. If it is true that the statement is false, then it is false. If it is false that the statement is false, then it is true. There is an internal contradiction. Therefore, the statement ‘this statement is false’ seems to contradict the Law of Non-contradiction and the Law of Excluded Middle since the statement can be both true and false. Similar doubts can be raised about the reliability of modus ponens based on its epistemic status. Since modus ponens is not able to be proved neither deductively nor inductively, its justifiability must not be ultimately provable. Any deductive attempt to prove that modus ponens is justifiable will be circular and thus beg the question, while any inductive attempt would fall short of fulfilling the task because of the limitations of inductive inferences which do not guarantee the truth of the conclusion of an argument. It can be argued that, granting that modus ponens is self-evident is not justified based on the fact that there is no non-question-begging justification for its use. Thus, it may be argued that it is irrational or illogical to rely on modus ponens while not having a proper theory of knowledge justifying its use.

It can be argued by Russell and those who subscribe to his view regarding knowledge of general principles that The Laws of Thought and modus ponens are basic foundational principles that are the pillars of rational thought, and as such they do not require external justification or proof. Offering any valid argument in which the conclusion follows from true premises makes use of modus ponens, this includes arguments that question the reliability or justifiability of the use of modus ponens. It is impossible to argue modus ponens is not justified without making use of modus ponens. Modus ponens is a rudimentary inferential rule which forms the basis of valid deductive reasoning. To justify the use of these principles without appeal to the rules of rational thought may be an impossible task to undertake. It may be naïve to suppose that a rule of inference as basic as modus ponens or general principles as rudimentary as the Laws of Thought should have non-circular justification. In order to prove that modus ponens is valid, one must make use of the notion of validity, which itself entails modus ponens in its definition. Demonstrating validity requires deductive inference affirming the truth of the premises which leads to the truth of the conclusion for a sound argument. In order to demonstrate validity one must make use of modus ponens. Since it is impossible to prove modus ponens is valid without making use validity, it is impossible to demonstrate modus ponens without employing modus ponens. It is an impossible task to justify the use of modus ponens rationally, since it is an elementary principle of rational thought itself. Attempting to doubt the validity of modus ponens seems like an impossible task. It is impossible to doubt a principle which is valid by definition and is in fact an essential element of the notion of validity itself. Therefore, the only rational option available to the rational agent is to accept that it is justified as a brute fact of rational thought which cannot be doubted, proved, nor disproved.

1. Problems of Philosophy Bertrand Russell, Watchmaker Publishing 1929 [P*, #]
2. Class notes, Week 9, Pt1

[Petros Agapetos]

What do you think of my essays in Metaphysics and Epistemology?

[Petros Agapetos]

Do you think there is a limit to the scope of answers that philosophy can generate?
What boundaries of philosophy do you see?
Is there any question you can come up with that you think philosophy cannot solve?

[Petros Agapetos]

What do you think of my writings on the discipline of philosophy?