There are no a priori truths. Discuss.

point analogous to an item of knowledge) may hold a position such that they are the cornerstones of a large structure of beliefs, giving the appearance that those points are essential. Secondly, it should be noted that there is just one web. This brings to our attention that all knowledge is, in principle, on the same level. There is no great divide between different types of knowledge. All beliefs, whether directly or indirectly (as part of a “corporate body”), interact with experience. Thus there is no room for apriority in Quine’s web.Putnam and GeometryPutnam added meat to the bones of Quine's argument. He claims that, after General Relativity, Euclidean geometry ceased to be the correct geometry to describe space, replaced by non-Euclidean geometry (specifically, Riemannian geometry). In this geometry, space may be curved and so our conception of a straight line has been revised. A straight line still means 'the shortest distance between two points'. However, this now corresponds to a geodesic (a segment of a great circle on the surface of a sphere). It is still the shortest distance between two points, but in locally curved space. We can see this revision at work in the example of two light rays approaching a star from opposite sides (Putnam, 1975c, p.174). The star's mass, according to the theory of General Relativity, bends space (technically, space-time). The two light rays approaching the star (from infinity) may have a constant distance between them as they approach. However, once they pass a certain point (where space begins to curve) they begin to converge, and yet they are still travelling in a straight line (that is, along a geodesic). This is a contradiction within Euclidean geometry. However, it also happens to be a physical actuality, according to the General Theory of Relativity. Therefore, we conclude that Euclidean geometry is wrong and the correct geometry is Riemannian. In Putnam's own words: “what was yesterday's 'evident' impossibility is today's possibility” (ibid, p.175). We have revised a system of knowledge that was considered a priori true by switching to Riemannian geometry. If we could do it once, in the case of geometry, then this shows that there is nothing about any statement (or system of statements) that allows it immunity from potential revision. Putnam and Framework PrinciplesPutnam's other contribution comes in the form of accounting for why we thought these beliefs to be a priori. Any good new theory must explain why the previously accepted theory seemed true. Thus, any theory denying apriority must explain why it seemed to be so. While Putnam does deny that Euclidean geometry was a priori, he is willing to allow that it was more resistant to revision than a simple statement such as “the cat is on the mat”. This is because a system such as Euclidean geometry formed what Putnam called a “framework principle” (1975a, p.8. In a sense, Euclidean geometry was a priori with respect to a certain framework of physics: it was good methodology to hold certain beliefs fixed and immune from revision (another example would be the idea that every event has a cause). Using this framework, science experienced extraordinary success in the form of classical physics. In this sense the revision of geometry was not a purely empirical matter. No experiment alone would have caused scientists to revise Euclidean geometry – the system as a whole was too strong to be revised in such a circumstance. Rather, what was required was an alternative theory to shift to (Putnam 1975e, p.48 and 1983a p.94). Due to its status as a framework principle, the revision of geometry was partly conceptual, partly empirical. We see examples of this resistance to revision from many areas of scientific practice. For example, Newtonian mechanics was not abandoned until the theory of Special Relativity was there to take its place, even though it was known that Newtonian mechanics failed to account for the perihelion of Mercury. However, as we have seen, this resistance to revision created only the appearance of the apriority of geometry, not apriority itself. Even though some beliefs were held to be fixed in a framework, it was still possible to revise the framework. Following this argument, objections to revisability based on sheer incredulity or the appearance of apriority hold no ground. Both are accounted for and explained by Putnam's theory. The appearance of apriority alone is not enough to differentiate between actual apriority (if it exists) and framework principles.Objections and RepliesThese arguments support the idea that we should abandon apriority. I shall now examine two arguments to the opposite effect: that revision has not taken place.Objection 1A first objection may come from a certain conception of Euclidean geometry. It might be said that geometry is not something that is either true or false at all. If one looks at Euclidean geometry, one will see that it is a formal system of mathematical and logical inferences. It is not an empirical theory. Its points are non-extended, its lines have no width. Certainly the system may have certain applications in science, but the theory itself is not a scientific one. Therefore, using a different system of geometry in our science does not show Euclidean geometry to be false (and therefore revised), because we never considered it to be true. Instead, we are to think of ourselves as having simply switched to a different formal system to describe space. Everything said here is true. However, this objection would miss the point of my argument. I am not claiming that Euclidean geometry is no longer internally consistent. I am not disputing the logical validity of Euclidean geometry as a formal system. Given the axioms of Euclidian geometry, its statements necessarily follow. However, it is precisely its application that I am discussing. I am questioning the truth of the axioms. Apriority is a concept tied up with the world and confirmation. If a statement is a priori true then it is still true of the world, even if it is not true by the world. An a priori statement is considered to be one that cannot be contradicted by the way the empirical world is. This concept requires that our statement is considered true (taking truth in a realist sense), not just logically valid. Therefore, to assert the internal logical validity of Euclidean geometry does nothing to defend it from the idea that it is not a priori true. It is a non sequitur. Objection 2The second objection is related to the first and attacks the idea of revision itself. The claim is that when we change from Euclidean geometry to Riemannian geometry we have not revised Euclidean geometry at all. Rather we have changed the meanings of the terms involved. When we are talking about a “straight line” in Riemannian space we are talking about an entirely different entity to a “straight line” in Euclidean space. Therefore we have not revised the notion of “straight line” – we are just using a different one. The appearance of revision comes only from the fact that we have used the same word for both concepts. The interesting thing about this argument, and one of the ways it fails, is that it is not empirically neutral: if we decide that 'meaning change' has taken place then it has testable physical consequences. Putnam gives an example of this in his essay “Philosophy of Physics” (1975a, p.89). We can use a notion of 'place' (measurable by volume) in both Euclidean and Riemannian geometry. In Euclidean geometry, because space is infinite, we can say that there are an infinite number of 'places' of a given size. In a Riemannian space of high curvature, space is finite, and so there will be only a certain number of 'places'. Thus we can say that, in a Riemannian universe (a universe perhaps not unlike our own), given a suitably long amount of time, we can visit each and every place. However, if we maintain that there has been a 'meaning change', then the Euclidean sense of 'place' is independent of the new sense, and so we can apply the Euclidean version of 'place' to our new Riemanniean world, if we so choose. If we do so we will find that there are more (Euclidean) 'places' out there that we have not visited. Further, these 'places' are non-physical and inaccessible. The Riemannian places, plus those extra “ghost entities” we have posited, will “fill out a Euclidean world” (ibid). So the idea of 'meaning change' forces us to adopt certain theoretical baggage, at least in some cases. There is no evidence to support these “ghost entities”. Further, they needlessly complicate our space. Finally, as they are non-physical and inaccessible they are falsifiable. These considerations should, I hope, convince us to rid ourselves of “ghost entities” and reject meaning change.There is a further, more fundamental, problem with 'meaning change', which is that it leads one into nonsense. If one claims that “straight line” and “geodesic” are two different ideas, and that in 'meaning change' we have changed from the one to the other, there are many conceptual problems involved. If a geodesic is not a straight line, then in a Riemannian space a straight line is not 'the shortest distance between two points', which is a geodesic. There are two problems with this as an objection to my argument. Firstly, it is self-defeating. If one holds that a straight line is no longer “the shortest distance between two points” then one has been forced to revise one of the truths that was held to be a priori in order to escape the non-Euclidean properties of geodesics. In either case some kind of revision has taken place. Secondly, if “straight line” does not mean “the shortest distance between two points”, then what does it mean? There is no way to make sense of the idea. No matter what path one selects as your non-geodesic 'straight line' in Reimannian space, that path will “not look straight when one is on it, will not feel straight, as one travels along it, and will measure longer, not shorter” than the geodesic (Putnam, 1975c, p.176). Further, there is no “non-arbitrary” method for calling any one non-geodesic path your 'straight line' over any other path! Clearly the idea of 'straight line' being an independent idea to 'geodesic' is nonsense. It forces one to give up on geometry entirely.ConclusionIn this essay I have presented the contradiction of the apriority and the revision of a priori knowledge. I have outlined the case for naturalistic confirmational holism over “first philosophy” and shown why we should consider the rise of non-Euclidean geometry to be evidence for the claim that there are no a priori truths. I have displayed how this thesis accounts for our epistemological intuitions regarding apriority and explains them in terms of Quine's “web of belief”. I have also considered some replies to this theory, most importantly the objection from 'meaning change'. Finding these objections inadequate, I conclude that revision has taken place and that the only way to dissolve the contradiction is to abandon the concept of a priori truth. BibliographyGrice, P. and Strawson, P. 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