Does the inference lead to knowledge?

Many of the things we believe in are formed not on the basis of personal experience or testimony, but in the process of inference. Are we allowed to see these beliefs as information?

Much of our information originates from our senses and testimony. So, for example, we know that the new neighbor has a bushy beard because we saw him, or because another neighbor told us so. We also saw that our belief that the new neighbor has a thick beard is considered knowledge because he does indeed have such a beard (our belief is true) and because the source of our information is reliable in this context, whether it was our sense of sight, or whether it was the other neighbor, who is known to us as a reliable and serious person ( our charter is justified).

However, many of our arts are formed indirectly through various inferences: if I open my eyes after a night's sleep and see light through the blinds, I conclude that it is already morning (if I don't see light, I turn over to the other side and continue to sleep); If I hear barking under my window, I conclude that there is a dog there (perhaps the new neighbor's); If yesterday was Wednesday, I conclude that today is Thursday; and so on and so on.

No one told me that the morning had come and what I saw through the shutters was light, and not the morning itself; No one told me that there was a dog under the window of my house, and my sense of hearing recognized the barking of a dog, not the dog itself; No one told me that today is Thursday, and my senses certainly did not provide me with this information (I did not glance at the date on my watch); And these examples are just one of many. In fact, we are consolidating a huge amount of art based on different types of assumptions, and the question arises whether it is justified to see the various assumptions as a basis for knowledge. We will examine this question below.

a priori and a posteriori

It is customary to distinguish between knowledge whose formation requires information about the world, and therefore it is called a posteriori or empirical knowledge, and between knowledge that can be formulated without such information, and which is called a priori knowledge. For example, we know for sure that no bachelor is married without having to check the marital status of all the bachelors, based on the definition of the term "bachelor".

Claims based on definitions of concepts are called analytic claims, and since their truth derives from the definitions of the concepts, our knowledge of them is a priori, that is, we do not need information about the world to know them.

Claims whose truth is not based on conceptual definitions alone are called synthetic. For example: "All windows are closed". Our same knowledge is based on empirical information (the state of the windows must be checked), and is therefore a posteriori (note: Kant believed that a priori synthetic sentences also exist, but we will not deal with this issue here).

We are also able to know the results of arithmetic operations without any information about the world, and therefore our arithmetical knowledge is also a priori, as is our other mathematical knowledge (we do not have to be able to reach them ourselves; the very fact that in principle it is possible to reach them without information about the world is what gives have the a priori status). Since in mathematics we sometimes rely on basic assumptions (axioms), the truth of the other sentences in the specific mathematical field depends on the truth of the basic assumptions. Nevertheless, we are allowed to speak here about an a priori justification of the sentences: they logically follow from the basic premises, and our ability to perform logical moves that lead to the proof of the mathematical sentence without relying on information from the world gives these moves an a priori status (in contrast, justification based on information from the world is empirical justification ).

Logic allows us to make a priori moves even when they are based on a posteriori assumptions: for example, given that Ronan was in Yaakov Memorial on a certain date and at a certain time (based on empirical information), we can conclude with complete confidence (and without additional empirical information) that he was not at that time in Tiberias, And this is based on the fact that the same person cannot be in two different places at the same time (this is the power of an alibi). Of course, it is possible that our assumption of origin is false, and Ronen was not at all in Jacob's memory at the time mentioned, however, if the assumption is true, our conclusion is also true, and we concluded it not on the basis of additional empirical information; Therefore, its justification is a priori (however, our knowledge of the conclusion is empirical because it is based on another empirical knowledge: Ronen's whereabouts at the time in question).

It seems, then, that it is possible to formulate information on the basis of a justified inference and on the basis of assumptions that are themselves considered information: if I know that Ronan was at the Yaakov memorial yesterday at 13:00 p.m., I also know that he was not in Tiberias at that time (so that if Ronan is suspected of a jewelry robbery which took place yesterday at this time in Tiberias, a solid alibi will lead to a change in the direction of the investigation).

Below we will examine the two main types of inference in use, and we will see to what extent, if at all, they are indeed justified moves that are capable of leading to knowledge.

Deduction

An argument is a collection of claims, one of which, the conclusion, should follow from the others, the premises. An argument is called valid if in any situation where its premises are true, its conclusion is also true. Thus, for example, the argument: "All politicians are honest people, and an Israeli Israel is a politician, therefore an Israeli Israel is an honest person" is a valid argument. The fact that the premises of the argument are false (and perhaps the conclusion as well) does not harm the validity of the argument, because its validity stems from the fact that in any situation (however imaginary) in which the premises are true, the conclusion is also necessarily true.

Such an argument, whose conclusion necessarily follows from its premises, is called a deductive argument, and is characterized by the fact that its validity derives not from its content, but from its structure. The structure of the argument is: "All A is B, and C is A, therefore C is B", and any content that is attached to this structure cannot change the fact that it is valid. For example: "All Greeks are mortal, and Socrates is Greek, therefore Socrates is mortal."

There are different types of valid structures, and all of them allow deductive logical moves, in which the conclusion is drawn from the premises with absolute certainty. So, on the face of it, it seems that if the premises of such an argument are known to us, then we can say that its conclusion is also known to us. For the most part, when the logical move is simple, this is indeed the case, but sometimes it is possible to conclude something from a collection of assumptions only through complicated logical moves, and even if in such a case the truth of the premises necessarily entails the truth of the conclusion, it is possible that a person who knows the premises of the argument, does not will be able to carry out the logical process and draw the conclusion that follows from them (a clear example of this is Fermat's theorem, which even among professional mathematicians are unable to understand its proof, let alone prove it in practice).

Hence, another condition for forming knowledge through deduction is the ability of that person to carry out the logical process and reach a conclusion. An example of this is mathematical theorems that many mathematicians suspect are correct, but the way to prove them has not yet been found. Such sentences, even if they are true, cannot be said that those mathematicians know them, but only that they believe in their correctness. However, when such a sentence is proven deductively (with a mathematical proof), then anyone who is able to understand the proof, his belief in the correctness of the sentence is justified on the basis of that proof, and therefore he indeed knows that the sentence is true. But even others, those who are not familiar with the complicated proof, can know this on the basis of the reliable testimony of the experts in the field.

Induction

An argument is called inductive if its premises lead to a conclusion with high probability, but not with absolute certainty. For example, the argument "Ronen goes for a run every morning, so this morning he also went for a run" is an inductive argument. Although it is very likely to assume that if the premise of the argument is true, so is its conclusion, but this is not absolute certainty. If until today (in the last weeks, in the last months, and maybe for years) Ronan went for a run every morning, although it is likely that he will not deviate from his habit today, there is still a possibility that due to an unexpected event (illness, for example) Ronan will stay at home this morning. If so, would we like to say that our belief that Ronan went for a run this morning based on the inductive logical process is considered knowledge? Well, if Ronen didn't go for a run, then we certainly don't know it for the simple reason that our belief is false. However, if Ronen did go for a run, our belief is true, and the question arises whether it is also justified?

On this matter, opinions differ among epistemologists (those who deal with the theory of knowledge), but the position is generally accepted that just as an inductive argument can have varying degrees of logical strength (has Ronen used to go for a morning run only recently, or has he been doing it for years without skipping a day?), so The justification of the logical course can also have different degrees; And in order for the conclusion of the move to be considered knowledge (on the basis of knowledge of the assumption), the justification must be of a relatively high degree. So, for example, if I believe that Ronan will behave as he has been doing for years and go for a run this morning as well, and he will indeed do so, I can say that I know it. On the other hand, if he only started his training a week ago, then even if I believed it would turn out to be true, then there is doubt as to whether it can be considered real news.
conclusion

If so, the real agreement, which is formed through a process of reasoning on the basis of other knowledge, is also considered knowledge, and this is provided that the process of reasoning is deductive or inductive with a high degree of logical strength. On the other hand, if the logical process is inductive with a low degree of logical strength, there is doubt as to whether it is possible to see the conclusion in terms of knowledge (in the extreme case, when the conclusion does not derive from the premises at all, it is nothing more than a successful guess, and then surely it is not knowledge, but only a true belief ).

Those epistemologists who require as a condition for knowledge that the true belief be formed in a reliable manner, indeed consider deductive inference and often also inductive inference with a high degree of logical strength as a reliable procedure for forming information. If so, not only are our true arts empirically justified in terms of knowledge, but also many of our true arts are a priori justified through a correct Hiski move.

About the author: Dr. Marius Cohen teaches philosophy at Ben-Gurion University

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