The Necessary, The A Priori And The Analytic: Are These Just Three Expressions For One Thing?

The necessary, the a priori and the analytic: are these just three expressions for one thing? Necessity, a priority and analyticity are different and are not just three expressions for one thing. This can be shown in two ways: By demonstrating that they must be defined differently as there are subtle differences between the three, and also by showing that they could not possibly have the same meaning anyway as they do not have the same extension. Part of the difficulty in discerning whether these three expressions are for one thing arises from the fact that they are difficult to define in their own right. Frege proposes that an analytic proposition is one that can be proved using only logical laws and definitions, for instance if one takes the logical law "No unmarried men are married" and the definition "Bachelors are unmarried men" one can see that the proposition "No Bachelors are married" is analytic. However, Quine takes issue with this definition of analyticity, arguing that analyticity cannot be defined without the definition presupposing the notion of analyticity. The second part of Frege's definition, that definitions are used to prove analytic statements, leads Quine to question what makes something a satisfactory definition, and concludes that a definition is satisfactory is the defined and defining terms are synonymous- if the definition did not have to be satisfactory to prove a necessary truth, this would enable us to 'show' that false statements are necessarily true. However, it is not sufficient to say that two terms being interchangeable within a sentence without a change of truth value makes then synonymous. The problem with this is apparent when first order logic is applied. For Fx and Gx, if the predicates F and G have the same extension, then when exchanging F for G in the sentence Fx the truth value will not change. However, two predicates may have the same extension accidentally, for instance if F stands for "is a creature with a heart" and G stands for "is a creature with kidneys", the two are interchangeable but do not have the same meaning. To solve this difficulty, Quine says that terms are cognitively synonymous if they are necessarily interchangeable (although for this condition to be added a language more complex than first order logic is required). However, the term "necessary" cannot itself be satisfactorily defined without an appeal to analyticity. Quine then erroneously argues that this means that there is no real distinction between analytic and synthetic statements. Leaving aside the fallacy of assuming that because a distinction may not be defined to one's preferred standards it does not exist, the flaw in this argument is in demanding a non-circular definition of analyticity- it seems Frege's definition has aided our understanding of the concept of analyticity without being non-circular. This certainly seems preferable to Kant's rather more vague definition of analytic statements as "those which attribute to the subject no more than is already conceptually contained in the subject concept", in which Quine would takes issue with the terms "conceptually contained" and "concept", which are themselves in need of explanation. "Concept" is particularly problematic as it implies a subjective rather than objective view of A- it is plausible that I may have a slightly different conception of an object than someone else. Necessity is equally controversial to define. It is widely agreed that analytic statements are necessary. Kripke defines a necessary proposition as "true in all possible worlds". However this could appear to raise problems for the definition of analyticity which I have favoured. Essentially, Frege's definition is dependent on our linguistic conventions; that words which are synonymous with each other have arisen in our language. However, one could imagine a possible world in which our linguistic conventions were otherwise. On further analysis, this is not a real problem. All this shows is that our linguistic conventions are not necessary; however it is plausible that within a different linguistic system in another possible world, statements can still be judged to be analytic in virtue of these alternate conventions. Therefore it is possible to accept both Frege's definition of analyticity and Kripke's definition of necessity. It also seems to be preferable to do so, due to the problems raised if, due to the fact that analytic statements are necessary, we equated necessity with logical laws and definitions. It can be argued that objects can be described in such a way that propositions appear necessary when they are not. Kripke gives the example of "Nixon won the election". If we choose to define "Nixon" as "the man who won the election in 1968" then the statement, according to this definition, is necessary. Although it is not particularly problematic to say that this proposition is analytic, we would object to its necessity. To avoid this, we would have to impose some sort of restriction on how we define terms, an obvious one being that a term must be defined using only its essential rather than accidental properties, and then we start to commit ourselves to the idea of essences. This problem doesn't arise with the possible worlds definition. In thinking about a counterfactual situation, there is no need to define "Nixon", it can simply be asked whether "this man" could have lost the election in any possible world, to which the answer is clearly yes. As it has been shown that we cannot define both necessary and analytic statements under the definition "provable using only logical laws and definitions" it is starting to be apparent that the two are not the same thing. Analyticity, as it can be defined in this way is semantic, whereas necessity, as it must have some relation to the actual state of affairs is metaphysical. Attempts to argue that the three are not equivalent have also been made by demonstrating that the terms do not have the same extension. It is often assumed that necessary, a priori, and analytic all apply to one group of statements, whilst contingent, a posteriori and synthetic apply to another. However arguments have been made against this straightforward division. Kant has argued that it is possible to have a priori synthetic propositions, namely those of mathematics, however I would suggest that this is simply a result of his definition, which I believe to be inadequate. Kant argues that in statements such as "7 + 5 = 12", the concept of 12 is not conceptually contained within 7 + 5, making the statement synthetic. However, since knowing the truth of the proposition "7 + 5 = 12" is not dependent on empirical evidence, this means that it is knowable a priori. However, this is an error since the idea of conceptual containment reduces the complex notion of analyticity to something much more like self-evidence. Since many of us would simply argue instinctively that it appears that the concept of 12 is conceptually contained in the concept of 7 + 5, this becomes much more apparent if we take a complex proposition such as "The Square of the hypotenuse of a right angled triangle is equal to the sum of the squares of its other two sides". When I think of the concept of a right angled triangle, Pythagoras' theorem admittedly is not apparent, and therefore not part of my immediate mental concept when asked to think of the triangle. However, this does not mean that the statement is not analytic. On an application of logical laws and rules of geometry (all a priori) I would eventually arrive at Pythagoras' theorem. In fact, Pythagoras' theorem is conceptually contained within the concept of a right angled triangle; however my faculties are not sufficient to be able to see this prima facie. The statement is analytic- Kant has wrongly presumed that if something is not conceptually contained within a concept prima facie, it is not conceptually contained within it at all. He then seems to have generalised from mistake in the case of more complex mathematical propositions, and assumed that simple mathematical propositions are also 'synthetic' when in fact, for example, when presented with the concept of 7 + 5 the concept of 12 is evident prima facie. Additionally, if we do accept that the proposition is a priori synthetic, then Kant argues that we link 7 + 5 and 12 by some sort of intuition. This is incredibly problematic for a number of reasons, for instance, surely intuitions can be faulty? If this were the case it would be possible to know a priori a synthetic statement that is false. Therefore, in this case, Kant has not shown that a priori synthetic statements are possible and it has not yet been shown that the three terms are not co-extensional (although by any means, failing to show that the three terms are not co-extensional does not imply that they are the same thing- as Quine would point out it may be an accident of extension). An argument from Kripke that the three are not co-extensional seems to hold better. He argues that there are propositions that are necessary but cannot be known a priori. A priority is not equated with necessity, but rather a necessary a priori proposition is one that is both necessary and can be known to be necessary independent of empirical enquiry. An example of a necessary a posteriori proposition is "Hesperus is Phosphorus" or "the morning star is the evening star"- an astronomical discovery found the two to refer to the same celestial body, meaning that the proposition is necessarily true- it appears even to be analytic, as its truth depends on the definitions of Hesperus and Phosphorus and the logical law of identity. However it could not have been known that Hesperus and phosphorus refer to the same object without this empirical enquiry. It may then be asked to what extent we need a posteriori knowledge of definitions in order to know that any proposition is necessary- to know that "Bachelors are unmarried men" would we need some a posteriori knowledge of the usage of the term bachelor? A response to this is that for a proposition to be true a priori, we do not need to arrive at it a priori, we may arrive at it a posteriori as long as it is theoretically possible for us to know it a priori. But if it is feasible that one may not come to know that "Bachelor" is synonymous with "unmarried man" or that "Hesperus" is synonymous with "Phosphorus" a priori (presumably as one is not familiar with the correct definitions), how can we distinguish that the former is theoretically possible to be known a priori but the latter not? Could "Bachelors are unmarried men" be a posteriori too? This could be argued because "bachelor" and "unmarried man" are synonymous due to linguistic convention- one could argue that knowledge of linguistic convention is a posteriori, however if this were the case many statements that would generally be recognised as analytic (including those of maths and geometry) would be a posteriori, which seems counter intuitive. The distinction is that the proposition that "Hesperus is Phosphorus" is not necessary in virtue of being dependent on linguistic conventions as its truth is in fact contrary to linguistic conventions. The general linguistic use prior to the discovery was that "Hesperus" and "Phosphorus" referred to different objects, and they were used linguistically as such. Considering only this conventional use, the obvious statement to arise would be "Hesperus is NOT Phosphorus". "Hesperus is Phosphorus" is theoretically not capable of being known a priori, as this would require that linguistic convention to have previously always been otherwise. To know the necessary truth we must know that the linguistic convention has been faulty- the correction cannot come only from definitions, as this would mean that our linguistic conventions had always been self-contradictory. Therefore the correction must be based on empiricism, meaning the proposition must be known a posteriori. Kripke's assertion that there are necessary a posteriori truths therefore holds. The three terms have been shown not to have the same extension. Another argument from Kripke that the terms are not co-extensional also serves to demonstrate the difference in meaning of the terms. He argues that not only are there necessary a posteriori propositions, there are also a priori contingent truths. Take the propositions "Stick S is one meter long at a given time", where stick S is a meter rule. This can be known a priori as we have determined the reference of "a meter" to be "stick S". We are using Stick S as the standard by which to judge if something is a meter long, therefore we know a priori that it is itself a meter. However it is not an analytic and therefore necessary truth, as Stick S is not the meaning or definition of a metre, although in this case it fixes the reference. It is clear that stick S could have been a different length in another possible world, so the proposition is contingent. The reason that a priority and necessary are then not co-extensive is due to the fact that they are dealing with entirely different issues. To say that we know that "Stick S is one meter long at a given time" a priori is to say something about the epistemological statement of the proposition- that we are epistemologically capable of knowing it a priori, as we have fixed the reference ourselves. However, to say that "Stick S is one meter long at a given time" is contingent is to say something about its metaphysical status. Since a priority is an epistemological consideration and necessity a metaphysical consideration they are clearly not the same thing. Therefore, it has been shown that the three are not co-extensional as it is possible to have necessary propositions that are only knowable a posteriori and contingent propositions knowable a priori. This does not demonstrate that analyticity is different from either a priority or necessity (although it cannot be equivalent to both) - presuming that Kant's argument fails that is. This is shown by the fact that analyticity and necessity cannot be satisfactorily defined by the same definition. Additionally these considerations reveal that the three refer to different considerations; Necessity is a metaphysical concept, analyticity a semantic concept and a priority an epistemological concept. Therefore the three terms are not the same thing. Bibliography Quine, Two Dogmas of Empiricism Miller, A., Philosophy of Language, (Oxon: Routledge, 2007) Smith, P., An Introduction to Formal Logic (Cambridge: Cambridge University Press 2003. 2009) Ayer, A.J., 'The a Priori", in Language, Truth and Logic. 2nd ed. (London: Gollancz, 1946) Hume, D., Enquiry Concerning Human Understanding, edited by P. H. Nidditch (Oxford: Oxford University Press, 1999) Kant, I., 'Introduction', in his Critique of Pure Reason, translated by N. Kemp Smith (London: Macmillan, 1929) Bennett, J., Kant's Analytic (Cambridge: Cambridge University Press, 1966) Kripke, S., Naming and Necessity Grayling, A., An Introduction to Philosophical Logic. 3rd ed. (Oxford: Blackwell 1997)