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.
5 comments:
I know that I have questions about this entry, but in a rush now so just to say that your clarity is quite something. That somehow you manage to make these difficult ideas so accessible. Thanks teach'
I have a question and then a comment.
First. Though the difference between logical necessities and analytical truths is obvious, all your necessary truths strike me as tautologies. What is a tautology? Etymology (an always incomplete clue) tells us that it is a repetition. Is there a more technical definition in philosophy? All your examples of the different necessary truths are tautologies as I understand the meaning of the word. So the question is, can you give me an example of a necessary truth that isn't a tautology? As you say tautologies are all about words and say nothing interesting about the world.
This brings me on to my comment. The little (and it is very little) I know about the positivists have led me to believe that they do not allow us to say anything interesting about the world or make any propositions that are not banal (the chair is blue). You mention at the bottom of your lesson that Hume is a sceptic when it comes to knowledge. Is scepticism not the easy position to take but one of little interest. I feel as if I am being dragged (not screaming and not unwillingly of course) down into a nihilistic hole. A place where any interesting statement or indeed proposition one can make about the world, about the human condition is without meaning (not meaning in the metaphysical sense, but in the everyday sense).
If I want to read Hume or a synthesis of his thoughts, where do I go?
Dear Adam and Anonymous
you raised some difficult and some deep and meaningful questions. Let's look at the difficult one first:
In academic philosophy it is agreed that all tautologies are necessary truths. The logical notation of a tautology is p V - p (either p is true or p is not true.
So why is it then that I claim not all necessary truths are tautologies? (And this is generally agreed on, but not entirely).
The camp that holds that not all necessary truths are tautologies say this is so for the obvious reason that the set of necessary (logical) truths is larger, but encompasses) the set of smaller tautological truths. In other words tautologies is a subset of logical truths.
Yes, I am begging the question, I know. I must still give a proper reason for the above. Maybe an example of a necessary truth which is not a also a tautological truth. Here it is (and once again we must work with propositions:
"All fathers are male."
This proposition does not consist of a vacuous repetition such as "It is raining or it is not raining." This is because 'brother' and 'male' do not refer to the same thing. Yet, used in the proposition as they are, the one term being a predicate of the other, they denote a logical connection/relationship with each other. This proposition is necessarily true by virtue of the definitions of the words. But I would argue that it is not quite the same thing as a vacuous circular statement- as in the case of a tautology.
Yes?
Regarding the comment on the dismall prognosis for saying meaningful things, if capitulating to the positivist campaign:
I think the value of the positivists is how they cleared up the foundatiuons of philosophy and their assistance to the development of the sciences. I am a positivist under certain conditions. But I would never ever abandon the likes of poetry and art and music and various appeals to symbolism, metaphor and other non-literal ways of speaking. I think the human mind is made for such stuff. However, I think these lovely things should have a proper place in our speaking, and literal statements intending to describe actual things, should run the positivist gauntlet. But only those should.
On a personal level, literature and things like it has a nearly bigger place in my life than a devotion to positivism. But I still maintain that positivism and its resulting poor prognosis of what can be said meaningfully is very important for maintaining intergrity in certain types of descriptive exercises.
Apologies!!!
I must apologise for two quite large mistakes in my typing due to very early morning brain deadness.
Firstly:
In the fourth paragraph of my above comment (that starts, "The camp that holds...") I used a 'but' instead of an 'and'. And this is a devastatingly serious error concerning the internal logic of the sentence, of course. Should read "...larger, AND encompasses...".
Secondly:
I suggest the proposition "All fathers are male" and then speak, by way of explanation of 'brothers' and 'male'. Please read all words that look like 'brothers' as 'fathers' in the previous comment.
Regards
Carin
Carin, when writing my comments, I have to confess that the intensely competitive side of me wants to ask you a question that might stump you or cause some hesitation (this, I hope you realise, is a minor factor in my fascination with your subject). Anyway, I love the way you seem to glide through my issues, like a prof with a first year undergrad. Bravo.
Your example and explanation of the tautology/necessary truth has nearly shut me up. I need to take it away and masticate for a while.
Moreover, your re-affirmation of the place of philosophy in one's system of thought is both patient and succinct.
I find it difficult to remember that we are not in Ancient Greece constructing metaphysical systems. Something to do with age and old dogs..
Sorry.
Should we have a little re-cap of formal logic to help with the next steps?
Adam
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