a contingent proposition? Because it could be, or might have been, false. If we say
Tony Blair is not the Prime Minister.
what we say is indeed false, but not necessarily false. It might have been true. It is not necessarily true, but it is contingently true.
Thus, in the tradition which sturdily accepted the idea that propositions are either a posteriori and therefore possibly false, or a priori and necessarily true, Kant came along with his synthetic a priori. Analytic necessary truths were so because of the meaning of terms and were therefore not synthetic in nature. Kant, however, came along and said that not only are there necessary analytic truths, but also a priori necessary truths that are also synthetic or about the world. They are not synthetic because they are derived from experience, however. They are synthetic for two reasons:
i)There necessary truth is not a question of meanings.
ii)They are necessary truths about the world but not derivable from the world.
In the Kantian lingo, then, synthetic a priori necessary truths are transcendental. They are about the world and applicable to it; but not derivable from it. Instead they are transcendental in the sense that they express the
conditions of all possible experience.
For example, there are synthetic a priori truths about the nature of space, time and causality. Their forms are necessary conditions of all possible experience. We cannot experience anything at all without these ‘forms of sensibility’. They are the frames, as it were, in which all empirical phenomena must be contained.
One of the most interesting, and to some extent counter-intuitive, facts about Kant’s synthetic a priori is that he took mathematical truths to be examples of them. That is,
mathematical truths are neither analytic nor empirical.
They are knowable a priori, but not because of the meanings or identities of the terms used within them. Take:
7 + 5 = 12
In that equation we learn something more about 7 + 5 other than that which is only derivable analytically. That is,
the number 12 is not contained in 7 + 5.
7 + 5 = 12 is not a mere identity or a Wittgensteinian tautology. We may think that 12 is contained in 7 + 5, but that is only because we have already learnt that 7 + 5 equals 12. So it has a quasi-analytic feel to it.
Hume and the empiricists, on the other hand, believed that mathematical propositions are only analytical in nature, not synthetic. This is because they also believed that all acceptable propositions must fall under two types:
i)Relations of ideas
and
ii)matters of fact.
They saw mathematics in terms of relations of ideas. Clearly they are not matters of fact. Kant said that they are neither solely relations of ideas nor matters of fact. They are synthetic and a priori. They were necessary and applicable to experience and the world.
Metaphysically, synthetic a priori truths tell us what must be the case about the world if we are to experience it at all. Synthetic a priori truths express the transcendental necessities that the empirical world must adhere to if we are to have any kind of knowledge of that world. They constitute the form or structure of all possible experience. If the world were not as our synthetic a priori truths say it is, then if it were so, we could not experience it at all. Thus Kant’s synthetic a priori truths are like Wittgenstein’s Tractatuslogical forms or structures that the world must adhere to if we are to describe it in any natural language. It is not the case that we derive these fundamental logical truths about the world from the world. Instead we apply them, non-consciously, to the world in order to make it describable at all. The world could be different, Wittgenstein conceded. If it were, we would not be able to describe it. It is even possible that our logical truths impose incorrect or false frames or forms on the world in order to make it describable. Thus Wittgenstein’s Tractatuslogic is Kantian in the sense that we can correlate
transcendental and a priori truth→ the world
with
logical truths and forms →the world.
In both instances the arrow points from one thing to the world, not from the world to the explananda. Many other philosophers, on the other hand, have stressed the point that they think the arrow points in the inverse direction: from world to logic or from world to transcendental synthetic a priori truth. The world somehow imposes itself on our logic or transcendental truths. We have such truths because they match or replicate the necessities in the world itself. Logical or transcendental necessity simply reflects the necessities of the world that they are then taken to represent or explicate. These necessary features are the universal laws of nature, the essential character of kinds and individuals, the necessity of causal relations, and so on. For both Kantians and metaphysical realists, necessities are much more than being merely analytic. They express truths about the nature and features of the world and give us the means required to describe and experience it.
Kant also argued for the idea that all a priori truths must be strictly universal in nature as well as necessary. Indeed these two requirements are mutually related:
universal truths are universal because they are necessary.
necessary truths are necessary because they are also universal.
Only if a truth were universally applicable could it also be deemed necessary. The very fact that they are universal also shows us that they must be necessary:
Their necessity comes from their universality. Only universal things can be necessary. Only necessary things can be universal.
And one way in which we come to realise their universal status is that we need not consult the world to determine their nature. They can be deduced a priori. We could not, in other words, experience any kind of universality or necessity and thus such things must be knowable a priori. In this Kant agreed with the empiricists who also rejected universal truths and necessary relations. However, unlike the empiricists he did endorse universal and necessary truths. But such things came only from the nature of the transcendental mind and its concepts. They impose universality and necessity on the world. This is a prime example of Kant’s fusion of rationalism and empiricism. He agreed with the empiricists in that we do not, and cannot, derive universal and necessary truths by observing the world. Unlike the empiricists he did not reject them. This time he is at one with the rationalists. Universalities and necessities, according to traditional rationalists and realists, are derivable from the necessary and universal features of the world. Kant, however, said that such things are imposed, non-consciously, on the world by the transcendental ego. This was not realist enough for many of Kant’s rationalist contemporaries. It is still too subjectivist or idealist for the likes of, for one, Tom Nagel. Even though Kant accepts universal and necessary truths, they are still merely and only a product of mind. It makes no difference whether the transcendental ego is universal. It is still the case that the mind is seen to impose universality and necessity on the world. The rationalists and realists, on the other hand, want their universal and necessary truth to come from the world – whether that is the concrete or abstract world.
What are the examples of Kantian synthetic a priori truth? This is one example:
i)Nothing can be red allover and green all over at the same time.
This necessary and universal truth is synthetic because it is applicable to objects and colours in the world. It is not analytic because we cannot analytically conclude from the sentence
This ball is red all over.
the conclusion that
This ball is also green all other.
is false. It is not, therefore, simply a question of meanings. It is a worldly necessary fact that a ball cannot be both green all other and red all over. Empiricists will argue that we do derive that consequence from the meanings of the words contained in the sentence
This ball is green all over.
It is a conceptual fact, or a fact about words and meanings, that if we say that a ball is red all over, we cannot also say that this same ball at this same time is green all over. We need not consult the world to see the conjunction as analytically self-contradictory. Now take this:
Every event has a cause.
To the Kantian, we do not conclude from many observations of events that every event must have a cause. Instead causation is a ‘form of sensibility’ imposed on the world by the mind. We need the form of causality in order experience at all. Causality is not a feature of the world as it is in itself. It is a feature, instead, imposed on the world by the transcendental ego. Here again the empiricist would say that the above is merely an analytic truth not a metaphysical one. That is, ‘contained’ in the concept [event] is the subsidiary concept [causation], etc. If we talk about an un-caused event, we are speaking meaningless words that are analytically self-contradictory. Every event has a cause because we make this true, and necessarily true, simply by means of our words, concepts and meanings. We make the necessity conventionally.
However, Kant would argue that there is no contradiction involved in saying
This event, here and now, was not caused.
That statement cannot be true, according to Kant, but this is not because it states or contains within it a logical contradiction. It is false because the mind makes it the case that every event is determined by a cause of some kind. This necessity is metaphysical, not logical. It is a necessary and universal truth of all experience that every event is perceived to have its own cause. We may as well add here that
Event B was caused by the discontinuous and distant cause A.
This again is metaphysically impossible according to Kant’s Newtonian position on space and causality. To say the above is not to utter a logical contradiction. It is simply to deny or reject a universal and necessary synthetic a priori truth about the world. It is metaphysically false, but not logically contradictory.
Right up to the logical positivists, empiricists believed only in analytic necessities. And right up to, and beyond, Mach and Einstein, Kantian notions about the necessary and universal features of the world were prevalent in both science and philosophy. Indeed Kant believed that Newtonian mechanics and Euclidean geometry simply expressed, mathematically and scientifically, the truth about our a priori impositions on the world. Kant believed that space must be Euclidean and objects and causality must also abide by Newtonian mechanics and Newton’s belief in absolute time and absolute space. In that sense science proved Kant wrong with its non-Euclidean geometries and non-Newtonian mechanics. However, it is often said that Kant is still, after all, correct, because we can still apply Euclidean geometry and Newtonian mechanisms to phenomenal space – that is, to the objects and causations we experience in time and space. Einsteinian relativity and quantum indeterminacy do not apply to the everyday-sized objects as perceived in phenomenal space. The world to the perceiver, not the physicist or theoretician, is still Kantian in that it is a world of space, time, discrete objects, causal relations, substances and properties, etc. All the Einsteinian and quantum exceptions, as well as those of Whitehead’s ‘process philosophy’, are still not applicable to the world of experience. We do not experience curved space, relativistic time, quantum affects and processes, in phenomenal space. In that sense, such things may as well be untrue or remain ignored.
