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Evidence

In return I consider that if we tried to characterize a current state of philosophy the one and only phrase, "research of the proof" would approach better, than "research of language".

A. J. Ayer, Philosophy in the XX century

 

And having tried to define that such "proof" … we will find out that it is very complex challenge.

R. J. Collingwood, Idea of history

 

The concept "proof" is key both in an epistemologiya, and in science philosophy. Certainly, it doesn't belong only to the sphere of philosophy at all: constantly speak about proofs not only — and even not first of all — philosophers, but also the judges and lawyers, historians and scientists conducting investigations journalists and reporters, and also representatives of a set of other professions. Use this word and in the daily speech. Thus, the concept "proof" possesses stronger to - the theoretical bases, than other concepts playing so noticeable role philosophies. (Compare to him, for example, the quasitechnical term of epistemolog "epistemichesky justification".)

Nevertheless, comparing the definitions of the proof given by philosophers how this concept is often used in contexts, far from philosophy, we soon face a contradiction. We will consider before what sort not - philosophers are ready to consider subjects and the phenomena as proofs. For the forensic expert fingerprints on the gun, the blood-stained knife or the dress soiled by sperm can be the proof: the proof — it, first of all, a subject which can be put in a plastic package with a label "A material evidence No. 1". Then the lawyer will be able to make a hypothesis according to which the proof which can be used against his client, was thrown by the corrupted attendant of the law, or will hope that he will be lost by the careless official. For the archeologist — it that it is possible to dig out of the earth and carefully to forward the proof to laboratory for further research. Similarly, for the historian the proof can consist in hitherto unnoticed document which is recently found in archive or someone's private library. [1] Considering of such examples allows to conclude naturally that proofs — it, first of all, physical objects or, probably, the physical objects definitely processed. After all physical objects — it, most likely, just that it is possible to put in a plastic package to dig out from under the earth, to send to laboratory or to find among the things belonging to any historic figure.

However however this picture, it seemed natural, at least, it is hard to reconcile with historically significant philosophical definitions of the concept "proof". Russell, the greatest empiricist of the first half of the XX century, inclined to that the proof — is sensual data, the mental components of someone's condition of consciousness directly available to the one who endures them. Quine, the greatest empiricist of the second half of the XX century, held the opinion that the proof consists in stimulation of the nervous terminations. [2] Logical positivists believed that with what proofs is supported the concrete scientific theory, decides by "offers on supervision" or "legal offers" — linguistic units on appropriately limited contents; the concrete nature of these restrictions became for supporters of this point of view a subject of furious disputes. [3] According to one recent and influential research, the proof consists in totality of pro-positions [Williamson 2000] known to the individual. It agrees to another, it represents exclusively direct conditions of consciousness [Conee and Feldman 2004]. Within the modern theory of confirmation one of the leading versions of a bayesianstvo is understood as equating the proof to those belief of which we are psychologically sure. Certainly, the assumption as if sensual data, stimulation of the nervous terminations, known pro-positions or cash mental states it is possible to place in a plastic bag (or to dig out from under the earth, or to send to laboratory etc.), raises some doubts. From the point of view of the majority of daily representations and statements about proofs, deep philosophical reflections in this respect lead to especially ridiculous categorial mistakes.

Moreover, business not only that the definitions of the concept "proof" offered by philosophers are, at least at first sight, in some contradiction how it is used out of a field of philosophical reflections. As it is obvious even from the short review given above, philosophers put forward very various theories of that can act as the proof. In what the reasons of such divergences?

One of them is as follows: both in philosophy, and out of her concept of the proof often played some different roles. And though some of these roles also are complementary, others at least partly conflict with each other. Really, as we will see below, isn't obvious at all that the same concept can be used in all those situations in which the concept of the proof was at various times used. Thus, various theories about the nature of the proof could arise naturally because of the accents, in different situations placed differently. Below I will tell about some roles which the concept "proofs" had to play in various theories, and I will consider the relationship which arose between them.

 

1. The proof as that proves belief

2. Rational subjects take proofs into account

3. The proof as the conductor to truth: Sign, symptom or trace

4. Objectivity, general availability and intersubjektivnost: The proof as the arbitrator

Bibliography

 

1. The proof as that proves belief
 

Anyway, the concept of the proof is inseparably linked with concept of justification. When we speak about "proof" in epistemological sense, we speak about justification: one "proves" another just when the first strengthens a rationality or validity of the second … Strictly substandard concept of the proof — it not our concept of the proof: we don't understand him.

Dzhegvon Kim, What such "Naturalizirovannaya epistemologiya"?

 

That we wouldn't consider as the proof, it changes our idea of validity of belief or (that is frequent, but not always, consider equivalent) about that, in what is reasonable to trust. Some philosophers believe that that, in what the person has the bases to trust, entirely is defined by proofs available to him. This point of view sometimes called by "evidentsializm" can be interpreted as the thesis of a superventnost according to which the standard facts about that, in what the person has the bases to trust, follow from the facts about proofs available to him [see in particular Conee and Feldman 2004]. Thus, according to an evidentsializm, any two persons having the same proofs will meet and what to consider as reasonable opinion on any specific question.

From the point of view of an evidentsializm traditional epistemological disputes naturally become disputes on the status of various theses of a nedoopredelyonnost. Thus, the one who is skeptical about our ability to learn the outside world, will begin to claim that the proofs available to the person (understood, probably, as set of his cash feelings) don't give it to opinions on world around of advantage, daily, concordant with common sense, before the various alternatives which are put forward by sceptics (for example, a hypothesis according to which he hallucinates, without having opportunity for certain it to establish). Similarly old dispute between realists and anti-realists in philosophy of science can be understood as discussion about, whether the type of proofs available to the scientist is sufficient for justification of belief in fidelity of the theories describing in principle inaccessible to supervision: for example, electrons or quarks.

As the proof — it that gives justification, concept of the proof is closely connected with other fundamental standard concepts — for example, with concept of motive. Really, it is natural to believe that "motive to trust" and "proof" — more or less synonymous concepts, [4] and distinguishes them only that one grammatical is the estimated noun whereas the second — collective. [5]

In that measure in which that, in what we have the bases to trust, depends on proofs available to us, important is a body of evidence. Even if it is enough separately taken proof of E to prove belief in the validity of a hypothesis of H, from this doesn't follow that the one who has the proof of E, has thereby the bases to trust in H. After all he can have also such additional proof of E’ which in combination with the proof of E doesn't give the grounds to believe in the validity of H. In these circumstances the proof of E’ undermines the bases of our belief in H which would be supported with the proof of E taken separately. Thus, even if I initially have bases to believe that call you Fritz (as you so told me), further accumulation of the proofs testifying that you — the pathological liar, will lead me to doubt in validity of this belief. The concrete proof is refutable only when it in principle can be destroyed by further proofs thus; the proof which emergence of new proofs can't shake, will be incontestable. The question, whether can be any proof incontestable in this sense, remains open. [6]

After Pollock [1986], we can allocate the cutting and overturning denials. It is intuitively clear that if E is the proof of H, the cutting denial breaks evidential link between E and H. Thus, the proof assuming that you — the pathological liar, is the cutting denial of your certificate: though in usual circumstances of your words will be enough to convince me that you are called Fritz, the proof of that you — the pathological liar, conducts to a rupture of evidential communication between your certificate and the fact to which we testify. On the contrary, the overturning denial doesn't allow E to prove our belief in H, supporting a не-H more directly. Thus, the certificate received from other source and credible that call you not Fritz, but Leopold, will become the overturning denial of your initial certificate. That, how far comes distinction between the "cutting" and "overturning" denials, remains a subject for discussions.

It is important that the proof denial itself can be disproved with the advent of further proofs: later I can obtain such evidence of E" according to which you after all not the pathological liar, and everything that proved it — fabrications of your sworn enemy. In this case initial validity of my confidence that call you Fritz, will be restored. In principle, there are no limits of complexity of the relations of a denial which can exist between separate elements of a certain set of proofs. This complexity — one of the reasons of that we aren't always capable to apprehend the proof properly.

So, to prove confidence in the validity of any offer it is, not enough, that the offer was well supported with any suitable subset of the cumulative proof available to us. Important more likely how well the offer is supported with body of evidence. When evidentsialist insist that the facts about that, in what we have bases to trust, follow from the facts about our proofs, they should be understood in the sense that body of evidence which we have is important. Certainly, it leaves dug out a question of that, properly to treat the proof of E that E could be considered as part of body of evidence, and also a question of what sort of a thing it is possible to include in body of evidence. [7]

If to accept the thesis according to which the proof — it that proves belief in something, intuitive ideas of the proof, in a hypothetical situation available to the person, will form our opinion on that, in what he in such situation can have bases to trust. Certainly, it is possible to go and in an opposite direction: in that measure in which we have independent intuitions concerning that, in what the person will have bases to trust in a concrete situation, such intuitions will form idea of what proofs to the person in this situation will be available, and consequently, and opinion on more general theoretical question that such proof or that can or can't be considered as the proof. So, if somebody is firmly convinced that in circumstances of the C people can have the bases to believe in the validity of p, from this directly follows that stay in circumstances like C will be coordinated with possession of the proofs, sufficient to prove the validity of p. As we will see below (in Section 2), such general reasonings often support representation according to which our cumulative proof is settled by the feelings felt by us.

Here an example of how intuitive ideas of justification can form our idea of the proof if we accept the thesis of evidentsialist according to which changes in that, in what the individual has bases to trust, changes in the body of evidence which is available for him always reflect. The assumption is sometimes made that degree of confidence of the scientist in that, is how proved the validity of a concrete hypothesis, depends not only on character of available significant data, but also and on space of known alternative hypotheses. According to this point of view, that, how well concrete data set supports a hypothesis, is defined not only contents of data and hypotheses. (And also not only their contents in combination with basic ideas of the researcher of the world.) Rather it also depends on, whether there are in the field convincing competing hypotheses. For this reason it is sometimes rather simple to sound a convincing alternative hypothesis that degree of probability of the explanation of available data offered by the first hypothesis sharply decreased. [8]

We will review a historical example of which often think that it illustrates this phenomenon. Many organisms show the special characteristics allowing them to prosper in an environment, typical for them. According to a hypothesis of a reasonable plan, it occurs because such organisms were created by the reasonable Creator (i.e. God). The hypothesis of a reasonable plan is a potential explanation of the corresponding facts: if she is true, she can explain them. How strongly corresponding facts support a hypothesis of a reasonable plan? Quite probably on the truth that introduction of the Darvinian hypothesis challenging its validity in the XIX century considerably weakened support which was possessed by a hypothesis of a reasonable plan. That is, even if there would be no bases to prefer a Darvinian hypothesis to a hypothesis of a reasonable plan, that fact that the last wasn't the only potential explanation in the field any more, conducts to easing (at least, to some degree) trust to a hypothesis of a reasonable plan on the basis of essential reasons.

For descriptive reasons we will assume that that, in what we have bases to trust, actually depends on area of alternative hypotheses known to us: as new hypotheses, our bases for belief in earlier made hypotheses are entered change. If we agree with the thesis of evidentsialist that changes of justification are always based on changes of proofs, the complete description of the proof which is available for us in any concrete time will send to a set of hypotheses of which we for this moment know. It is an example of how intuitive judgments about that, in what certain people have bases to trust in certain circumstances, in combination with commitment to an evidentsializm, can form our theory of the proof (i.e., to matter for this purpose what exactly we call at creation of the theory the proof).

The proving or rationalizing role of the proof is central also in other influential epistemological theories, including also what, strictly speaking, are incompatible with an evidentsializm in the form in which he is described above. We will take, for example, a bayesianstvo. (See article about a Bayes epistemologiya.) The supporter of a bayesianstvo believes that that to trust in what for us is reasonable, depends both on proofs available to us, and on initial distribution of probability. Therefore, two individuals possessing the same cumulative proof can differ in that, in what is reasonable to believe them in a concrete situation, that they began with various aprioristic distributions of probability. But, as supporters of a bayesianstvo often focus attention on change of rational belief or on in what rational reconsideration of the belief consists eventually, the proving role of proofs in Bayes system keeps rather high situation. After all supporters of a bayesianstvo usually claim that rational changes in our belief are distinguished from irrational with that the first, unlike the last, assume proper response to again obtained evidence. [9] So, for supporters of a bayesianstvo not to a lesser extent, than for evidentsialist, the proof — it that proves needing justification.

Very significant is that fact, what even in those representations which are inclined to marginalizirovat a role of proofs available to the person in definition of the facts in which he or she has the bases to trust, the facts about proofs available to such person usually aren't considered absolutely not having any value. We will take, for example, relayabilistsky theories of epistemichesky justification [Goldman 1979, 1986]. In the purest and simple look the relayabilizm claims that the status of separate belief as reasonable or unreasonable is defined by that, is or not psychological process as a result of which there is this belief, reliable, i.e. the leader to truth. At such formulation the concept of the proof doesn't play any role in the relayabilistsky description of justification. In particular, the status of concrete belief as reasonable or unreasonable depends on, whether the corresponding process of formation of belief, but not from any proof which the person sharing belief can possess that is related to a question of reliability (or even, actually, from any proof which the person sharing belief can have that has a direct bearing more on the validity of the belief is actually reliable). So, the one who actually authentically predicts the future, will have the bases to adhere to the belief created on the basis of his predictions even if the cumulative proof which is available for him persistently assumes that (i) he has no ability to predict the future, and that (ii) the corresponding belief are false [BonJour 1985, Chapter 3]. However in response to such examples relayabilist usually seek to reconcile the representations with the intuition prompting that such predictor has no bases to defend reliability of the "belief received in the reliable way" in the face of the available proofs, and for this purpose seek to modify the simple relayabilistsky description [see Goldman 1986: 109–112]. The felt need to modify initial, simpler description, probably, is the testimony of resilience of idea according to which the proof which is available for us matters for justification of our belief — even if we consider essential and other factors.

 

2. Rational subjects take proofs into account
 

The reasonable person — is the one who correctly uses reason: and it in addition means the correct assessment of a strength of evidence.

Ayer, Probability and proof

 

In that measure in which we are rational in the belief, power of belief usually corresponds to reliability of available proofs. And if we are rational, we will refuse belief searches of proofs for which were vain.

Quine and Ullian, Network of belief

 

The wise man correlates the belief to proofs.

David Yum, Research about human understanding

 

Rational subjects usually take proofs into account. If we are rational, are inclined to react to available proofs adequately: in any concrete time our views precisely reflect character available to us for this moment of proofs, and usually are sensitive to the changes happening to proofs during time, or readiness to react to these changes. Certainly, rationality — not a guarantee of the validity. Really, in a concrete situation the available proof can mislead us — for example when this proof is deceptive. But to be mistaken doesn't mean to be unreasonable. In that measure in which we consider the available proofs, we are reasonable, even when we are mistaken. [10]

The previous remarks though border on banality, naturally assume existence of the model describing our practice of attribution of belief. According to this model, attributing you belief, I have to attribute, other things being equal, to you the belief in the validity of p only in case proceeding from the body of evidence which is available for you for you would be reasonable to believe in the validity of p. It is the key idea standing behind widely known version of the principle of trust (Principle of Charity). According to this point of view, I have the bases to draw conclusions about of what you are convinced, on the basis of my knowledge of your epistemichesky situation. Thus, if I know that proofs available to you resolutely testify that today it is going to rain, (other things being equal), I have to attribute to you conviction that today it is going to rain. On the other hand, if I know that, agrees to the proof of a rain which is available for you today will definitely not be, I in the same way have to attribute to you the corresponding belief. Though in a concrete case of belief of usually reasonable subject can disperse from the proofs which are available for him, such cases represent an exception. For lack of any reason to believe that the concrete case is a such exception, we can draw conclusions about the content of belief of other people on the basis of information on character of the proofs which are available for them. We by default assume that the person shares those belief which for him are natural for dividing, considering the available proofs.

Above we noted that we can be mistaken in a concrete case, following the proofs which are available for us: even if p — is right, our proofs can mistakenly specify that it not so. When the available proofs mislead, following them, we usually come to the false conclusion. As a rule, we consider such cases exclusive. Whether there are possible worlds where such is norm? We will imagine the careful and judicious person, consistently and to honestly following proofs leading him to some belief. In our world this line of conduct conducts to cognitive success — at such person will be rather a lot of true and few false belief. (Or, at least, he will be much more successful, than those who isn't capable to follow proofs and instead forms the belief hasty or in a random way.) Now we will look at the same person in the world subject to the Cartesian spiteful demon — to the being seeking to mislead inhabitants of the world of rather true nature of this world: though she resolutely differs by nature our world, from the point of view of his inhabitants these worlds are absolutely indistinguishable as the demon tries to make so that endured by people of sequence of feelings subject to him were qualitatively identical to what they endure in our, not illusory world. In the world operated by the Cartesian demon, our careful and judicious person with not smaller sequence and integrity than in our own world, is guided by those reasons which he considers relevant. However because of regrettable circumstances, his belief reflect absolutely wrong picture of world around. Considering, what his belief concerning world around are incorrect, whether it is possible to consider them as less reasonable, than in our world? Whether is he though a little less rational? Many philosophers claim that his belief are equally well proved, and that he is equally rational in both worlds [see, for example, Cohen 1984 and Pryor 2001]. Most likely, idea that the person, whose main tendencies and intellectual habits remain invariable, less rational it becomes simple because it appeared in less favorable circumstances, causes strong intuitive resistance. However, as Villyamson [2000] insistently emphasized, agreeing that he is equally rational in "favorable" and "adverse" circumstances, we inevitably incline to the concept of the proof according to which the proofs which are available for us are consolidated to subjective, not factive conditions of consciousness. After all if rationality — is ability correctly to react to the available proofs, judgment as if the person is equally rational in favorable and adverse circumstances, apparently, will demand that in both cases he had identical proofs in favor of his belief. But, according to a hypothesis, the only thing, as in favorable, and in adverse circumstances is the candidate for a proof place inspiring trust — these are not factive conditions of consciousness of the observer. Thus, the judgment as if the person in both cases is equally rational, in combination with idea of rationality as about ability adequately to react to the available proofs, apparently, compels us to recognize that proofs of this person even in favorable circumstances are limited to not factive conditions of his consciousness. So the requirement that in favorable and adverse circumstances of people I had the same proofs, apparently, supports that Villyamson calls "the phenomenal concept of the proof". [11]

We will consider also as the above-mentioned principle of trust supports such idea of the proof when it is applied to the world operated by the Cartesian demon. Attributing the individual of belief in adverse circumstances, we attribute to him exactly the same belief which would attribute, be he in favorable circumstances. After all if the illusions created by the demon and really can't be distinguished, inability to find them can be hardly called inability to rational thinking. Attributing the individual who is in adverse circumstances the belief dictated by common sense, we act according to the principle of trust: eventually, they are represented just by those belief which even absolutely rational (though not infallible) the being will share in the circumstances. But if the belief dictated by common sense are not less reasonable and when sharing them is in adverse circumstances, the proofs testifying in their advantage which the individual has, have to be in adverse circumstances not less powerful, than in favorable. Really, it is natural to describe adverse circumstances as the world in which the proofs which are available for the individual systematically mislead him. Well to play a role of the spiteful demon (we could think), it is most important to throw skillfully misleading proofs. If to follow intuition, the demon misleads the victims, playing on their rationality as he abuses dependence of their belief on the misleading proofs. (Really, those who is dogmatically committed to favourite theories even in the face of the proofs which are undoubtedly disproving them, apparently, will be to a lesser extent subject to manipulations of the demon.) But the demon deceives, creating at the victims the misleading feelings. From here temptation it is simple to identify proofs and feelings: and again the phenomenal concept of the proof ahead looms.

As Villyamson if we insist, as in favorable emphasizes, and in adverse circumstances we have the same proofs, thereby resolutely we sweep aside many theories of the proof which differently would seem the very promising:

The assumption that in successful and unsuccessful circumstances we have the same proofs, imposes on the proof nature serious restrictions. It is incompatible with representation according to which the proof consists of the offers similar corresponding to truth that usually act as the proof in scientific theories … for the same reasons [it] doesn't allow my proof to include the perceptual states partly differing from each other in communications with world around. Regardless of degree of usefulness of my epistemichesky situation, it is considered that I have exactly so many proofs, how many would be in the situation described by sceptics however unusual and freakish she wasn't. Stimulation of a retina and a condition of a brain approach not better as in epistemicheski adverse situations they will also change in a way, imperceptible for me, [2000:173].

In view of her obvious consequences for the theory of the proof, the idea as if in favorable and adverse circumstances we have the same proofs, demands further research. And again, existence of deep distinction between an innocent mistake on the one hand, and irrationality or unreasonableness — with another, doesn't cause disputes. Usually such mistake doesn't mean irrationality, even when she is rather widespread and meets everywhere. Nevertheless, it is worth asking, to what degree we can rely on this distinction. In what degree it is possible to be mistaken in conclusions about the world surrounding us, remaining thus absolutely rational? Or whether more likely rather serious mistake under doubt will substitute at some point our ability to form rational belief concerning this world around?

Here a reasoning from which follows that rather serious mistake and really is capable to undermine our ability to come to rational belief concerning world around. Quite convincing the assumption seems that mostly (if not entirely) the value which in our eyes has rationality of belief, depends on communication between rationality of belief and their validity (though the concrete nature of such communication, undoubtedly, is represented exclusively knotty problem). Then can disturb us that the idea according to which even ideal, absolute rationality can coexist harmoniously with entirely or partly wrong idea of world around, threatens to weaken so strongly communication between rationality of belief and their validity that will become unclear why the last has to be important from the point of view of the first. We will tell the same in relation to the proof: it seems convincing that we take proofs into account substantially (if not entirely) because we assume that between such behavior and detection of truth there is a communication. Then that the idea according to which scrupulous following to the available proofs is compatible with entirely or partly wrong idea of world around, threatens to make not clear why it is good to follow the available proofs when we want to find rather true, than wrong belief can disturb us.

However this point of view not so is incontestable. In general, value x can consist that with his help it is possible to receive y even if there are conditions in which, relying on x, we aren't able to receive y at all (or even we stir it to emergence). Thus, can happen so that the value of concrete medicine consists that it is capable to cure wonderfully some illness even if in certain circumstances it can aggravate it. In the same way may be that we attach significance to following to the available proofs for the purpose of receiving true belief even if we understand that there are circumstances in which — if to us won't carry to them to appear — to arrive so means to remove this purpose or to interfere with her achievement.

On other way Villyamson who is in detail explaining went that we shouldn't believe as if in favorable and adverse circumstances we have the same proofs. For his argument the following contradiction is central: even if we accept the phenomenal concept of the proof, it doesn't allow us to defend the intuitions meant by it which, apparently, first of all and do this concept attractive; from this it follows that the phenomenal concept of the proof eventually isn't well motivated. As we saw, the desire to keep intuition according to which rather consistently arguing person in adverse circumstances can be reasonable in the belief (actually not less reasonable, than so consistently arguing person in favorable circumstances) appears because of what we sweep aside any concept of the proof according to which our proofs could consist from we (will tell) true pro-positions or the facts about the outside world. After all the one who conducts a reasoning in adverse circumstances, isn't capable to distinguish the facts of the outside world; however he is capable to distinguish the facts of his own feelings. Thus, representation as if the proofs which are available for us are limited to our feelings, apparently, motivated idea that our proofs (regardless of what else statement about them is true), have to be that we always — at least, in principle — are capable to take adequately into account. But it is considered that our feelings — it that we are always capable to take adequately into account. Villyamson claims that this last course of thought is wrong: in practice we aren't always capable to estimate adequately our feelings. Really, according to Villyamson, it is impossible to formulate such uncommon condition about which we could always know that it is observed. Thus, idea as if the proof can be such that we are always capable to know that it is, isn't true. Therefore, to insist that in order that x could become part of the proof, it has to be such that we were always capable to know, whether includes our proof x, means to build in the theory of the proof an element desired, but wrong and impracticable. To put it briefly: "That the proof wouldn't represent, we can not always know, whether we have it" [2000:178, italics of the author].

Having rejected the phenomenal concept, Villyamson suggests to consider that the proof which the person has, consists of all pro-positions known to him and only of them. [12] Villyamson very sophisticated develops this simple and clear idea; here we will be engaged only in how the theory resulting from her acceptance interacts with that rational subjects consider proofs available to them. Certainly, one of direct consequences of idea that the proof consists from this that is known to the subject, is that the subject in favorable circumstances differs from the subject in adverse circumstances — moreover, significantly differs — in what proofs are available to him. When in favorable circumstances the subject learns that the knife is blood-stained as sees the blood-stained knife, the corresponding pro-position becomes part of his cumulative proof. On the contrary, when in adverse circumstances the demon forces it to endure the same feeling (or, at least, feeling, qualitatively indistinguishable from him), and he comes besides to the belief, the corresponding pro-position isn't part of his cumulative proof as she isn't true and, therefore, isn't part of the sum of his knowledge. As in favorable conditions logically conceiving subject will know much more, than so logically conceiving subject in adverse conditions, the first will have much more proofs, than at the second. And if both of them have same belief, apparently, that for the subject which is in favorable circumstances it will be much more reasonable to share these belief. [13] As far as it is problematic? We should distinguish between two different intuitions which can be had about the subject in adverse circumstances. The first consists that in adverse circumstances he has in accuracy the same proofs, as subject in favorable circumstances. Probably, we will lose not so much, having refused her — if at all though we will lose something. The second intuition is as follows: when in adverse circumstances the subject takes the feelings in all good faith and forms belief concerning world around as usual, these belief won't become simply unreasonable as it would be if, for example, the subject accepted the same belief at random or for lack of any reasons so to arrive. It is much heavier to refuse this intuition, apparently. However it is doubtful that we will be able to keep her if we accept the point of view according to which our proofs consist of our knowledge. Let's imagine again the subject in adverse circumstances in which the demon causes visual feeling as if before him there is a blood-stained knife. Without having the bases to doubt that this feeling is true, the subject in the regular way forms belief that on a knife there is a blood. Intuitively this belief on the most smaller measure is better proved, than it would be in the absence of the corresponding visual feeling. Assuming that our proofs consist of pro-positions known to us, we can ask: what known pro-position — or pro-positions — proves this belief in that measure in which it in general is reasonable? The pro-position according to which on a knife there is a blood, is false and consequently, isn't part of our knowledge. Probably, the proof of belief of the subject that the knife is blood-stained, is a true pro-position (i) it seems that the knife is blood-stained, or a true pro-position, according to which (ii) my feeling such is as though the knife was blood-stained. [14] However some philosophers claim that in typical cases of perception we don't form belief about by what things are presented to us or about as what things appear in our experience of perception: it is rather, as reaction to our feelings, we simply form belief about what the world around is. [15] If this is so, provided that the knowledge demands belief, the pro-positions similar (i) and (ii) aren't known as aren't a belief subject. Therefore, if this model is right, that, considering that our proofs consist only of known pro-positions, belief of the conceiving being that the knife is blood-stained, apparently, is completely deprived of the bases. [16]

According to the phenomenal concept of the proof, only our feelings can be proofs. According to Villyamson's concept about the proof as knowledge, feelings can't be considered as the proof — at best, the proof includes any pro-positions known to us about our feelings. However even if we reject the phenomenal concept of the proof, we can adhere to representation that proofs are among feeling as our feelings can affect and often influence that, in what we have bases to trust, regardless of, whether there are at us belief of rather feelings. Thus, idea of the proof less rigid, than Villyamson's theory or the phenomenal concept, could allow to include in him both our feelings, and available to us knowledge on the ground that belief of the rational subject will depend as that he knows, and from the feelings endured by him. Question of, whether our feelings — unlike our belief concerning our feelings or our knowledge of our feelings can — directly to participate in process of justification of belief about world around, causes many disputes among the philosophers dealing with problems of perception; we in detail won't sort it here.

The problem which recently acted on the foreground is connected with distinction between proofs of the first order and proofs of higher order [Christensen 2010, Feldman 2005, Kelly 2005, 2010, Lasonen-Aarnio 2014]. Intuitively it seems that the proof of the first order of E has a direct bearing on a certain target pro-position or a hypothesis of H. The proof of higher order — this proof about character of E or about abilities and tendency of the subject is rational to react to E. We will assume that the qualified meteorologist attentively studies available meteorological data and draws a conclusion that tomorrow it is going to rain. Here meteorological data (E) — it the proofs of the first order concerning a hypothesis (H) that tomorrow it is going to rain. Now we will consider that fact that the meteorologist came to a conclusion that tomorrow it is going to rain, on the basis of E. This fact — the proof of higher order, as this proof about the contents and value of basic meteorological data of E. In particular, if our meteorologist is usually competent of the assessment of the important proofs, that fact that on the basis of E she drew H conclusion, is the proof of an epistemichesky pro-position that E supports H. Moreover, in many cases that fact that the meteorologist drew H conclusion on the basis of E, will be considered as the proof not only an epistemichesky pro-position that E supports H, but also and the hypothesis, i.e. that tomorrow it is going to rain. It seems especially obvious in a case when the third party has no access to basic meteorological data of E (or she can't competently estimate the proof), but she knows that the meteorologist on their basis came to a conclusion that tomorrow it is going to rain. In these circumstances it makes to the third party sense, having learned about the meteorologist's conclusions, with bigger confidence to wait for a tomorrow's rain. In effect, in these circumstances we perceive that fact that the meteorologist drew a conclusion that tomorrow there will be a rain as some kind of replacement of meteorological data to which we have no access or which we can't adequately estimate [Kelly 2005]. Here the proof of the proof (for H) itself becomes the proof for H [Feldman 2005]. The main conclusion is that proofs of higher order sometimes serve as proofs which have to affect not only our belief concerning proofs of the first order, but also concerning the world.

However other cases can cause questions. For example, suppose, that the second qualified meteorologist estimates available meteorological data of E and comes to own conclusion about probability of a tomorrow's rain. Then she learns that the first meteorologist on the basis of the proof of E drew a conclusion that tomorrow there will be a rain. Whether has to consider the second meteorologist opinion of the colleague as the additional proof of a hypothesis, what tomorrow it is going to rain? Or it will be, in effect, the wrong double accounting of the initial proof [Kelly 2005, Matheson 2009]? Or we will ask more general question: in what, actually, conditions the proof of the proof (for a certain pro-position) is the proof of this pro-position [Fitelson 2012, Feldman 2014]? Questions of the nature and value of proofs of higher order are a subject of active research work.

 

3. The proof as the conductor to truth: Sign, symptom or trace
 

Situation in which I could tell rightfully that I have a proof of that fact that a certain animal — a pig, is a situation when, for example, an animal not on a look, but I can see a set of the traces similar to traces of a pig round its shelter. If I find some buckets of a pork forage, it will be the additional proof, and grunting and a stench will even better confirm my guess. But if then the animal leaves the shelter, and it can be considered, the sense assembled of proofs won't become; his look isn't one more proof of that before me a pig — now I simply see that it quite so.

J. L. Austen, Sense and sensibiliya

 

There isn't enough proofs, My God! There isn't enough proofs!

Bertrán Russell's answer to a question that he would tell if after death I appeared before God, and that would ask him why during lifetime he was a non-believer

 

If E is the proof of a certain hypothesis of H, thanks to E this hypothesis with bigger probability it will be true: in such circumstances of E confirms H. On the other hand, if E testifies against H, because of E hypothesis of H with smaller probability will be true: E disproves H. Verification — a limit case of confirmation: the proof verifies a hypothesis in this sense only in that case when it finalizes that the hypothesis is true. On the other hand, falsification — a limit case of a denial: the proof forges a hypothesis only in that case when it finalizes that the hypothesis is wrong. A question of, whether full verification or falsification in such understanding is possible then, remains, at least, a little inconsistent. [17]

Possibly, there are some pro-positions, the validity or which falsehood we grab absolutely directly, directly. We will take, for example, such simple arithmetic truth, as 2 + 2 = 4. Traditionally such truth is considered as "axiomatic"; allegedly for their knowledge it is enough only understanding. If truthconditional value of any pro-position was such obvious, we, probably, wouldn't feel an urgent need for proofs or wouldn't need them at all. On the contrary, the main function of the proof consists in making obvious that in the absence of the proof that wouldn't be.

Usually we rely on the proof when differently access to truth for us is complicated. Recognition of that fact that Earth round, apparently, depends on, whether there are at us proofs of it while recognition of that 2 + 2 = 4, doesn't demand proofs. Of course, it is possible to argue, whether it is difficult to get in certain cases access to truth and whether, therefore, our ability to comprehend truth in these cases depends on proofs. The common sense prompts that we often without special problems comprehend the facts about world around by means of sensory perception; probably, partly therefore from the point of view of common sense it is represented at least very strange if not simply wrong, to say that the one who face to face faces with a pig, thereby has strong evidence that an animal before him — a pig. (Though, undoubtedly, also in a similar situation will claim strange that we have no proofs of that this animal — a pig.) On the contrary, according to the majority of izvod of a traditional epistemologiya, our access to similar truth is always problematic; questions doesn't cause more likely recognition of that fact by us that our feelings represent the world organized definitely. Therefore the majority of izvod of a traditional epistemologiya interprets relationship between our feelings and belief of rather physical world by analogy to relationship between the proof and a hypothesis when sensory perception assimilates to not deductive conclusion that both are subject to mistakes. (The words of Austin provided above, certainly, contradict it.)

As a rule, the proof plays a role of the intermediary in relation to our attempts to build the world picture corresponding to truth: we seek to believe that is true, adhering to the belief supported with proofs, and we seek to avoid belief that doesn't correspond to truth, refusing the belief which aren't supported with proofs. This situation is well summarized by Blanshar:

"The only thing is possible the rule" — we — "could tell it, of course, to believe that is true, and not to believe that is false". And, certainly, it would be the rule if we could know that is true, and that — is false. But all complexity that we don't know it and often we can't know. So than then to be guided? … The ideal consists in trusting in that degree in which we it are allowed by proofs: no more, but also not less [1974: 410–411].

Really, the assumption, as ability of the proof to prove belief (Section 1), and that fact that rational subjects take proofs into account (Section 2), depend on communication between the proof and truth, it seems quite convincing.

Why the attention to proofs could become a promising way of achievement of adequate idea of the world? One concepts of the proof with bigger readiness answer this question, than others. So, we will take the theory according to which proofs consist of the facts. If any true pro-position doesn't contradict any fact, we receive the direct basis not to trust any pro-position which contradicts our proof as only among those pro-positions which will be coordinated with the proof, there can be pro-positions corresponding to truth subsequently. The same is right and for the concept of the proof offered by Villyamson as knowledge: in that measure in what any known pro-position is true, the contradiction to the proof will cause a contradiction to any truth. In other words: if the proof consists of the facts or known pro-positions, no body of evidence can disprove truth. We will notice that it not so for concepts of the proof according to which the proof consists of our belief, either feelings, or pro-positions of which we are psychologically sure: that the pro-position won't be coordinated with one of my belief, or with the maintenance of one of my feelings, or with a pro-position in which I am psychologically confident, doesn't guarantee that it is false.

Probably, the basis of concept of the proof is idea of something, acting as a reliable sign, a symptom or a trace of that, the proof of that it something is. Telling to Jan Hakinga's words it "the proof of the thing specifying out of the limits" [1975:37]. So, the smoke — this proof of fire, characteristic rash on mucous membranes of cheeks and language — the proof of that the person is sick with measles, and an unpleasant smell — the proof of that egg became rotten. Apparently, here we have to be guided by direct correlation: the reason for which the smoke is considered a sign of fire, but not approaching rain, is that a smoke — a reliable sign or a symptom of the first, but not the second. At first sight, the idea of the proof as reliable sign supports inclusive idea of what sort of a thing and the phenomenon can be considered as proofs; according to inclusive representation, both mental, and not mental objects, events and states because it seems can be among those that similar to essence can perfectly enter the corresponding relations with other objects, events and states.

We will consider the statement

(1) Characteristic rash is the proof of that the person is sick with measles.

If we are guided by probably his most natural reading, the validity of this statement — the empirical discovery made by medical science. It was at a given time revealed that rash on mucous membranes of cheeks and language is a reliable symptom of measles that, most likely, was true how this discovery was made. Here the relation of the proof is understood as the relation which has or doesn't take place regardless of the fact that someone knows about his existence or has some belief concerning him. [18] In that degree in which we seek to gain an adequate impression about the world, the knowledge of cases of such relation (roughly speaking, the knowledge of what elements of our world are usually connected with other elements of our world) could seem just to that we look for. When the relation of the proof is interpreted thus, his research will be coordinated with research of the world.

Similarly, statement

(2) The smoke is the proof of fire

the statement (1) is submitted the possessing same empirical status, as, and the main difference consists that the second fact is known to much bigger number of people.

If the proof is understood thus, no wonder, that studying of proofs — good strategy for this purpose who is anxious with construction to the corresponding truth of a picture of the world: if characteristic rash is a reliable symptom of measles, to the person seeking to have right belief concerning what people are sick with measles, obviously, it is necessary to pay attention at whom from them characteristic rash is observed. Thus, when we understand expression "E — the proof of H" as more or less synonymous to expression "E — a reliable sign of H", communication between the proof and truth seems easily provided and rather direct.

Certainly, in spite of the fact that existence of rash and really is a reliable symptom of measles, the one who doesn't know about it, won't be able to draw a conclusion that the specific patient is sick with measles even if he knows that she has a characteristic rash. The one who knows that rash on mucous membranes is the proof of existence of measles, can make to patients the diagnosis which the person who isn't knowing about this symptom isn't able to put. In general, in what degree we are capable to receive new data on the basis of concrete proofs, usually depends on what knowledge we already have. This fact is well-known to philosophers of science, and the historians who are also tempted in philosophy paid attention to it. [19]

We will assume, we know that at a certain patient rash on mucous membranes of cheeks and language is observed, but we don't know about communication between such rash and measles. Moreover, suppose, that this ignorance isn't result of the irrationality which is earlier shown by us or a nerazumiya: it is rather, at us it was never simple opportunities to learn about communication of such rash with measles. Whether there is at us in these circumstances a proof of what the patient has measles? In one sense it is necessary to answer a question in the affirmative: we have such proof though we also aren't capable to understand it. However this idea — that in such circumstances we have the proof — conflicts to representations according to which the proof usually proves belief, and rational subjects take proofs into account. Think of a moment when we learn that from the patient rash. Considering that we don't know about communication between this rash and measles, it will be necessary to feel bigger confidence at all that the patient has measles. Moreover, considering our ignorance, apparently, that we will show nerazumy if with bigger confidence we diagnose measles, having learned that the patient rash, and that the basis shared on it, will have no reasonable belief as if the patient is sick with measles.

It means that the concept of the proof used in such statements as "the proof, as a rule, proves belief" and "rational subjects consider the available proofs", it is impossible to identify simply with concept of the proof as reliable sign. Let's call the proof about which there is a speech in the first case, standard, and about what to be told in the second — indicative. Though the standard concept of the proof can't be identified simply with indicative, it is possible to expect that they will be closely connected as, whether we have standard proofs, often depends on, whether it is known to us that one thing is the indicative proof another.

The reflection about a role which reasons of the basic theory is played in definition of what will be reasonable reaction to new information, convinced some that it is easier to understand standard concept of the proof in terms of three-dimensional, but not two-dimensional communication. According to this representation, judgments of a look "E — the proof of H" (when they are understood as more or less synonymous to judgments of a look "E does more reasonable belief in H") usually represent an ellipsis of judgments of a look "E — the proof of H taking into account the basic theory of T". Thus, if your basic theory includes the statement that rash on the mucous — a reliable symptom of measles, that fact that in a concrete case such rash is observed, will become for you the standard proof of that the patient has measles (i.e. will give to you the grounds to trust in it). On the other hand, if my basic theory of such statement doesn't include, rash on mucous membranes of cheeks and language won't become for me the standard proof of that the patient has measles (i.e. won't give to me the grounds to trust in it).

Representation that the status of E as standard proof of H depends on the basic theory, immediately forces to ask about the status of the most basic theory. If our basic theory consists from there is nobody a set of pro-positions, what it for a set? Whether there will be it a set of pro-positions known to us? Or more likely a set of pro-positions of which validity we are convinced? Or, probably, pro-positions the belief in which is proved? It seems, what E can be considered as the proof of H taking into account a set of pro-positions in which we trust, but not what make the content of our knowledge (or on the contrary) — what of them define, whether is E proof of H in the sense that if we have E, it will prove our belief in the validity of H? Or they can't define it at all? There are delicate and difficult questions; in Christensen's work [1997] they attentively are considered and clear up.

To the word about the theory of confirmation. Though the philosophy somewhat long since was interested in a problem of in what situations the proof increases chances of the theory to be true, during a positivism era research of this relationship reached the new level of systematicity and severity.

Hempel [1945] and Karnap [1950] distinguished two different "concepts" of confirmation: "classification" or "qualitative", on the one hand, and "quantitative" — with another. If not to go into details, the classification concept is used when we take out simple judgment about, whether supports this proof a concrete hypothesis (i.e. we answer this question "yes" or "no"). Thus, so far as concerns judgments of a look "the hypothesis of H is confirmed by the proof of E", we deal with classification concept. On the other hand, the quantitative concept is necessary for removal of numerical judgments about in what measure the hypothesis is supported by this proof (for example, "the hypothesis of H is confirmed by the proof of E in R degree"). [20] Formal theories were developed for an explanation of both concepts. Hempel [1945] developed the concept of qualitative concept whereas Karnap [1950, 1952] concentrated on the quantitative. At this time philosophical research of interrelation between the proof and the theory, probably, for the first time got a form of normal science and became the discipline full of technical problems, riddles and paradoxes which expected decisions were considered as business of future researches. [21] Here sources of the modern theory of confirmation presented by a bayesianstvo in all its variety [see, for example, Jeffrey 1965, 1992, 2004, Horwich 1983, Howson and Urbach 1993] and his rivals are hidden (for example, the "self-confirmed" model of confirmation of Glimur [1980]).

Though Karnap's idea of the theory of confirmation was eventually rejected, [22] quantitative approach which was defended him had impact on development of a question subsequently. In particular, the special attention to attempt to understand confirmation from the point of view of quantity laid a way to more and more frequent use of mathematics (and it is concrete — calculations of probability) in philosophical research of proofs. The idea that calculation of probabilities allows to understand the confirmation relation, is central for the bayesianstvo dominating in the modern theory of confirmation. Here we won't consider in detail this approach. [23] Instead we will simply pay attention to the explanation of concept of the proof offered them. At the beginning of this section we noted that the proof confirms the theory only in case thanks to the proof the theory with bigger probability is true; the proof refutes the theory only when because of it it with smaller probability is true. Bayesianstvo without changes accepts these banalities and offers the following probabilistic explanation of that to E means to be the proof of H:

E is the proof of H in only case when, when Probability (H/E)> Probability (H). [24]

That is, E is the proof of H only if the probability of H on condition of E is higher than unconditional probability of E. Thus, that fact that on a knife is the suspect's blood, is the proof of a hypothesis that the suspect committed murder, in only case when, when probability of that the suspect committed murder, will be higher provided that on a knife there is his blood, than if it not so.

In the same way

E is the proof against H in only case when, when Probability (H/E)
That is, E is the proof against H only in a case when the probability of H on condition of E is less, than unconditional probability of H. Thus, that fact that on a knife isn't present fingerprints of the suspect, is the proof against a hypothesis that the suspect committed murder, in only case when, when probability of that the suspect committed murder, is lower for lack of his prints on a knife than if they are. In this probabilistic model the verification (understood as final confirmation) will assume the probability of a hypothesis equal 1, whereas falsification — the probability equal 0.

This simple probabilistic model of the proof and confirmation is attractive and natural. Really, her traces can be found in the Anglo-American right. [25] However it is impossible to tell that she wasn't exposed to criticism. Akhinshtayn [1983] insists that it is possible to increase probability of the statement, without providing proofs of this statement. For example, information that the seven-time Olympic champion in swimming Mark Spitz went to float, increases probability of that Mark Spitz just drowned; however, according to Akhinshtayn, the first can hardly be considered as the proof of the validity of the second. [26] According to the course of the reasoning offered in Goodman's [1955] work, the concept of confirmation, key for science, shouldn't be understood as direct increase in probability. We will take, for example, generalization: "All trifle in my pocket — jitneys". If I get one coin from a pocket, I will look at it and I will find out that it is a jitney, probability of that generalization is true, no doubt, will increase as now I one potential denial have less. But Goodman insists that such supervision doesn't confirm generalization as this supervision shouldn't increase our confidence that not studied coin any other yet from my pocket is a jitney. (According to Goodman though supervision can also increase probability such "casual generalizations" as "All coins in my pocket — jitneys", they can't confirm them as can confirm "zakonopodobny generalizations".)

In general, the idea that calculation of probabilities furnishes the clue to understanding of concept of the proof, causes in philosophers of science more approval, than in supporters of a traditional epistemologiya. In the following and the last section we will address to a row on what philosophers of science also paid special attention, the subjects which became significant as a result of philosophical judgment of a role of the proof in scientific practice.

 

4. Objectivity, general availability and intersubjektivnost: The proof as the arbitrator
 

Is credible … this or that belief isn't simple, and that this belief is received as a result of process which, be the proof by other, so inevitably would lead to opposite belief.

Blanshar, Reason and belief

 

It is natural to believe that the concept of the proof is closely conne