A little bit of philosophy: Lesson 4: Oh so logical and oh so positive

Let us try again. My apologies to my more discerning readers for the previous post on the positivists.

Same introduction: One thing is certain, if only simple lessons are intended, I should find it an easier task to speak about the positivists than any other theoretical movement in philosophy. And this is exactly the way the positivists would have liked it- the outcomes of their doctrine being comparatively minimalist and their campaign aimed at simplicity.

It should, however, be cautioned that, as within all specialised schools of thought, there exists disagreement, so by no means must the following very superficial explication of positivist theory be taken as the unequivocal conclusions reached by all positivist theorists themselves. But then it has never been claimed that the writings posted to this blog set out to forward a deep and thorough analysis of anything, even though its author makes every attempt to be careful in her summaries and as precise as possible in her representations of others’ thoughts.

Inspired by Hume’s explanation of only two types of truths, the necessary and the contingent, the logical positivists maintained that only propositions which are either necessarily true/false (true by definition) or are contingently true/false (can be shown to be true/false by the certain matters of fact) can have any sort of meaning. And here, I hope, the astute reader will notice that ‘meaning’ has suddenly become a new character in our play.

For the positivist the most effective way of addressing the problems of philosophy is first to address and resolve the problems with philosophy. The problem with philosophy, dear reader, is that it at times sets out to do things which it is not adequately positioned to do. The positivists took offence and devised a plan to clean up the foundations of philosophy. The strategy was to take the products of philosophy, the foundational propositions which comprise the premises and conclusions of the arguments of philosophers, and to scrutinise them for their efficacy. The hypothesis was that if the propositions themselves are without meaning, are vacuous statements with no bearing on the world which they attempt to denote, then the arguments themselves will never take hold (except on our imaginations maybe).

And it is because of this method of the positivists that the author has employed, as from lesson one, the methodology of making propositions, which are linguistic objects aimed at conveying meaning and the component parts of philosophical arguments, the objects of our study.

Taking this proposition: “God is good.”

The logical positivists maintained, in short, that each component part of a proposition must be reducible to observable data. Complex concepts and ideas are permissible if and only if their component parts are grounded in simple observational, or sensory, data and that the particular suggestion around the relationship between the various sensory objects to which the proposition is making reference, can also be verified empirically. So if, for instance, a causal relationship is being referred to the causal relationship must, itself, be observable and not just the objects presumably in the causal relationship. (And we know from one of our previous lessons that it is impossible to observe causality. At most we get some sort of inductively inferred correlation always up for refutation.)

Let us take a look at what happens in a proposition such as: “God is good.”

If the claim is that an object ‘X’ has the property of being ‘Y’ then it is not only a semantic requirement that ‘X’ and ‘Y’ be traceable- in principle- but that the claimed relationship of ‘X’ to ‘Y’ be traceable.

Is there any observational data which the term ‘God’ could be referencing? It seems, by the very definition of ‘God’ this is not possible. God is above the sensory. This is logically (and conveniently) required for god to be what he is. We see that the term ‘God’ is not illogical in itself, of course, but is certainly not empirically traceable to an object in a material reality. And ‘good’? The property of goodness is, evidently, not traceable either. People sometimes think that they have traced such a property (and it makes no difference whether it be ‘good’ of the aesthetic kind or the ‘ethical’ kind), but this is questionable for someone like a positivist.

For the sake of good sportsmanship, let us give the proposition the little head start it does not deserve. Let us assume that ‘God’ and ‘good’ are traceable objects and properties. The term ‘is’ still requires the one be a property of the other. However, if it were possible to track ‘God’ in the sense that the positivists require, I suggest, it is doubtful that it will be found that he is ‘good’- in the same manner as something, for instance, being green colour. Taking everything we know about god, his abilities and sentiments, I doubt if I would like to describe him as good.

Thus, if the statement, hypothetically, were to have meaning, at best it seems to turn out false. And at worst it is meaningless.

I take a stand here: The proposition is doomed to one of semantic barrenness and so are all propositions like this. At least those propositions which are intended by the speaker to be taken seriously in the literal sense. And, so, dear reader, we get to the positivist campaign against metaphysics in philosophy. But this is for the next time.

A little bit of philosophy: Lesson 3: Hume's Fork and the demise of Knowledge

A little recap before we continue: We now have established two ways in which propositions can be true. They can either be necessarily true or they can be contingently true. A proposition which is necessarily true is so by virtue of the meaning of the words which make up the proposition such as “All blue things have a colour.” A proposition which is contingently true is so by virtue of a certain state of affairs obtaining in the world, such as “It is raining outside” being true by virtue of it actually raining outside. If it happens to be the case that it is not raining outside then, of course, the proposition will be false.

Hume, on looking at these two options for truth, decided that the prognosis is poor for knowledge about reality. The reason for this is that necessary truths do not give us much information about the world and contingent truths can always be overturned by emerging evidence.

Necessary truths come in three forms which are slightly different from each other.

Necessary truths: The propositions we have been looking at are called logical necessities. It is a logical necessity that all bachelors be unmarried men because this is what the term ‘bachelor’ implies by definition. However, it is not true that all unmarried men be bachelors. Some unmarried men are so because they are divorced or widowed. So the proposition, “All bachelors are unmarried men”, does not express an ‘if and only if’ sort of statement. In other words, it is not saying that all bachelors are unmarried men if and only if all unmarried men are bachelors. The proposition is only true in one direction. The same is true for “All blue things have colour.” This statement is not necessarily (but it may be, if the world makes it so- only by accident though) true in the opposite direction, because it simply is not the case that all things which have colour must be blue.

Analytical truths: These are the sorts of propositions which are, let us say, true in both directions. Propositions such as “A mammal is any animal which gives birth to live young, not eggs, and feeds its young on its own milk”. This proposition expresses a logical equivalence or an analytical truth. In other words, it is true in both directions: Any thing which gives birth to live young, not eggs, and feeds its young on its own milk will have to be a mammal. Definitions are often, but not always, analytically true. The good ones are, at least. All analytical truths are necessary truths but not all necessary truths are analytical truths.

Tautological truths: Quite simply, these are circular statements or phrases. They are obviously true as in “That is either true or false” or “He is either dead or alive” or phrases such as “over exaggeration” and “descend down”. All tautologies are necessary truths but not all necessary truths are tautologies (but, naturally, this is debated, dear reader).

Contingent truth, as we now know, is the sort of truth which is made so by the world. But more importantly, by our access to the world, and by our evidence that we have of certain things being the case or not. But, as we know from experience, this is up for grabs all the time. This is because the evidence for the facts we think we have about the world changes as science does its work and as our observational data changes shape. These sorts of truths, as interesting and helpful as they are to us, are not stable. They are not truths that are settled by the rules of reasoning, but by a dynamic world and an evolving tradition in empiricism.

So, says Hume, we have on the one hand stable logical truths which tell us nothing about reality and much about words and, on the other hand, we have truths which say a lot about reality but which can be overthrown around every and any corner. In effect, the latter, maybe, say too much. Or, more than they really are entitled to.

Thus, for Hume, the only decent position to obtain, regarding the possibility of knowledge, is one of skepticism.

Next lesson: Onto the logical positivists and meaning.

A little bit of philosophy: Lesson 2: Two truths

Now that we do to some extent understand what Hume said about cause we need to see what he has done with truth. The task, dear reader, is to try and predict what Hume's notions on truth might have for the possibilities of knowledge. That is, if we accept that our concept of truth has any bearing on our concept knowledge. Just keep such things in the back of your mind while you read on below.

To help us along on this particular journey to understanding what some theories in meaning are saying today: We are not studying the objects in the world anymore (no more metaphysics!) and we have done done done with meta-ethics too. Our proper and correct objects of investigation are the sorts of things that language yields: propositions being a particular favourite of mine and so appropriate for what we have set out to achieve in these few lessons. So, from now on I shall be giving you a proposition at the outset of various parts of any lesson. It is my wish that you do not forget to apply the lesson thereto and to nothing else. You may then have fun applying the lesson to other objects of the same category. If you are not certain whether your chosen object (proposition) is of the same category, I am always at the end of the comment-line.

It seems proper and correct that we pay credence to contingent truth as it has, after all, given us science and common sense. We start thus with this old dame:

Contingent truth

The proposition in question: All chairs are blue.

We have something someone asserts. This being "All chairs are blue." And then we have the conditions which would make such an assertion true. What could these be? It would simply have to be the case that all and every chair in existence must be blue in colour in order for the assertion above to obtain the truth value: true. Do you agree? So we have quite simply a condition which must obtain in the world in order for the assertion made about the world to be either true or false. The assertion would be false if it were found that even one chair is not blue or that the only objects which are blue are not chairs.

How would we find out if this were the case? In other words, how would we find out if the truth conditions for this proposition do, indeed, obtain? We would have to investigate the nature of reality. We would have to see what the world yields regarding the colour of all chairs. The investigation would be of the sensory kind. In science this is called empirical investigation and at the end of such an investigation things can turn out either in favour, or not, of the object under investigation. In other words, the world can turn out to either verify or falsify the proposition in question.

The point is that we need to go looking for the conditions which would settle the truth.

This is contingent truth. It is the sort of truth which is defeasible. Because new conditions can always turn up and overthrow what was previously thought to be true. It could be assumed, that every chair has been found and, as they are all blue, it could be thought that it is justified to take the proposition as true. But then one day, after having been buried deep underneath the soil of an old castle for instance, a red chair could turn up during an excavation. And suddenly the proposition is made false. And this is exactly how science does its work. Very tentatively. As it should.

Necessary truth

The proposition in question: All bachelors are unmarried men.

We have an assertion: "All bachelors are unmarried men" and then we have the conditions which would make such an assertion true. What could these truth conditions be, dear reader? Yes, naturally it would have to be the case that each and every bachelor, on finding such a thing, would have to have two qualities; being a man and being unmarried. You have learnt much I can see. These would have to be the conditions in the world for this statement to be true.

So, what then is different to contingent truth, you ask. It has to do with how we know whether every bachelor is indeed an unmarried man. The claim here is that we need not rise from our armchairs in order to establish if this really is the case. Such as with trying to find out if all chairs are blue, and then still being for ever uncertain whether this really is so. No. With objects such as "All bachelors are unmarried men" we simply know this to be true by definition. Because being a bachelor means that you are unmarried and that you are a man. There is no other way of being a bachelor, unlike the possibility of being a chair and not being blue. We say, that bachelors by necessity have to be unmarried and a man, but that chairs do not, necessarily, have to be blue. This is a matter of contingency.

Regarding the troublesome question of how I know whether the conditions obtain so needed to make the bachelor proposition true. I know this by definition. I know that if I were ever to find an object called a bachelor this object will be unmarried and a man. If this were not the case it could not be called a bachelor. There is, therefore, a necessary relationship between the concepts "bachelor", "unmarried" and "man".

And such truths are what Hume called logical truths. Definitions are logical truths, analytical truths are logical truths and correct mathematical equations are logical truths. They are truths which are not defeasible in any way. Because they have to do with logical equivalence of some type or another. And there are different types. But this is for another day.

Do you think you have an example of a defeasible necessary truth? Let's hear about it then.

Next lesson: What does this distinction mean for knowledge?