What is the relation between a priori and tautologies?

Question

I have just started learning Epistemology. I am not sure about the relation between a priori and tautologies.

My textbook has given definitions for a priori and tautology.

A priori: knowledge which is dependent on the meaning of words, not sense experience.

Tautology: a formula that is always true on any interpretation of its terms and sense experience is not required.

I think if I want to prove not all tautologies are priori, I can try to find examples based on ‘sense experience’. This is to say according to the definitions, priori can not connect with sense experience, and though sense experience is not compulsory for tautologies, sense experience can still exist in tautologies.

E.g. Honey is sweet. We know honey is sweet, as we have tasted it, which is sense experience. However, I think this sentence is a tautology, because this is true all the time. However, at the same time I also have another contradictory idea: honey is defined as ‘a sweet, viscous food substance made by honey bees and some related insects’. I think this means at the time I write down this sentence, everything has already been defined and hence does not need sense experience.

Answer 1

All tautologies are a priori truths, but not all a priori truths are tautologies.

For example the ontological argument for God's existence was considered an a prior proof by Anselm and Clarke but few people today would call it a tautology.

A second historical example comes from metaphysics which has considered the principle of cause and effect to be an a priori truth. But the epistemological certainty granted to cause and effect was debunked in the eighteenth century by David Hume and later by Quantum theory (cf. scientist Edward Dougherty's book The Evolution of Scientific Knowledge: from Certainty to Uncertainty. Read the first five chapters to cover all of this, but the specific passage that quantum theory debunks our notion of cause and effect can be found on pp.77-78. The book is free in pdf format from SPIE press.)

As for the example of Honey:

Let P be: Honey is sweet.

I can construct a truth table and assign T and F to P and thus there is a truth-value assignment where P is false and therefore it is not a tautology.

Let R be: ~(Q ^ ~Q)

In classical logic R is a tautology. There is no truth-value assignment you can give where R is false.

As a tip: with logical syntax, validity, and tautologies: it doesn't matter what the empirical truth of a statement is, only if it is possible for the statement to be true.

Example: Paris is the Capital of the United States.
This is a false statement, but it is not logically false - it is possible to assign this statement a truth-value of T on a truth-table.

Honey is sweet: can be assigned both T and F values. That is all that matters when evaluating if a statement is logically true.

Answer 2

Firstly, the word 'tautology' has a somewhat different meaning in logic from the way it is used in ordinary English. Its common meaning refers to a needless repetition of words in a sentence, such as "completely unique", or, "4 p.m. in the afternoon". In logic, it refers to a sentence that naively speaking comes out true always and everywhere. Logicians commonly use model theory to account for the truth of sentences, and in the terminology of model theory we would say that a tautology is true in every interpretation, which roughly speaking means it remains true no matter how you swap out the names and predicates that are present in the sentence, as long as you hold the logical constants the same. So, for example, "it is not the case both that Fred is an engineer and Fred is not an engineer" is a tautology because you can swap the name Fred for Jane, or 'engineer' for 'gorilla', or anything else you like, and the sentence remains true. What you cannot swap out are 'not' and 'and' because those are logical constants.

So, although in ordinary English, saying, "This honey is sweet," would probably elicit the response, "Well, duh," in the technical sense, "honey is sweet" is not a tautology because if we swapped 'honey' for 'garlic' it would be false.

That said, your textbook definition, "Tautology: a formula that is always true on any interpretation of its terms and sense experience is not required," should not really refer to sense experience. "A formula that is always true on any interpretation" is better. It is confusing to mention sense experience because 'tautology' has to do with logic not epistemology. A tautology is a tautology no matter how you come to learn it or what you think its truth is grounded in. There are in fact several different accounts of how we know logical truths to be true and some appeal to an empirical basis. Bear in mind also that there are many logics. "P or not P" is a tautology of classical logic but it is not a tautology of intuitionistic logic.

Your textbook definition of a priori is also open to criticism. You give it as "A priori: knowledge which is dependent on the meaning of words, not sense experience." This definition confuses a priority with analyticity. A priority has to do with knowledge. A proposition is knowable a priori if it can be known independently of experience or empirical evidence other than whatever experience is necessary to understand the language it is expressed in. Analyticity is concerned with the claim that some propositions are true in virtue of the meanings of their words, or in virtue of linguistic conventions, or in virtue of some terms containing others, or in virtue of the proposition being reducible to a logical truth with the help of definitions. The reason it is common to confuse a priority with analyticity is because the logical positivists proposed to explain away a priori knowledge as nothing more than knowledge of analytic propositions. The logical positivists have gone, but some of their ideas hang around like the unpleasant smell of yesterday's cooking. A priori knowledge, if there is such a thing, is not defined in terms of analytic propositions, if there are such things.

To return to your question. 'Tautology' is a logico-linguistic term, 'a priori' is an epistemological term, and for good measure 'necessary' is a metaphysical term. Be careful not to confuse them. Whether tautologies are knowable a priori will depend on your preferred account of the epistemology of logic. Most people tend to think of logic as knowable a priori, but not all. Whether all a priori knowledge is of tautologies is almost certainly false.

Answer 3

• Litterally a tautology is an "auto -logy", that is a sentence in which the same ( auto-) is said ( -logy) of the same. In other words, a tautology is an " identical proposition" as said Leibniz ( either an actually identical one, such as "Theft is theft" or virtually identical one, such as 2+2 = 4 , which can be reduced, by analysis, to 4=4, using the definitions of number 2, number3, number 4 and the properties of addition).

Note :the t- in tautology is here for euphonic reasons

• So in the general sense a tautology is a proposition that is true in virtue of logic alone, that is, in virtue of the principle of non- contradiction ( equivalent to the principle of identity).

• Nowadays tautologies are considered as only a species of logical truths. Logical truths belonging to predicate logic are not called tautotogies. Only logical truths of sentential logic are technically called " tautologies" .

• Kant raised the question : are all a priori truths tautologies in the broad sense, that is " analytic propositions" ( propositions in which the predicate is contained in the subject term, in virtue of logic; for example " all bodies - material entities - are spatially extended") .

• His answer ( in the Critique Of Pure Reason) was that there are true propositions which are (1) a priori (2) though synthetic ( hence, not tautologous, nor vacuously true). For example :" the shortest way between 2 points is the straight line" or " everything that happens is linked to something else thet precedes it in time according to a law".

Note : you may have a look at the book by Schwartz called Possible Worlds ( legally and freely downloadable at the author's personal page)