Oh hey, some papers
These are on Aristotle, specifically the Posterior Analytics and the Metaphysics.
The Inadequacy of Scientific Knowledge
In Chapter 2 of the Posterior Analytics, Aristotle lays out a theory of how we come to possess scientific knowledge. A critical aspect of this is that scientific knowledge can only be known when first explained by reasoned demonstration from two premises that are already known. In Chapter 3, he considers two opposing viewpoints centered on this aspect of his theory. One claims this theory of scientific knowledge will regress infinitely, and so we cannot begin know anything scientifically. The other view is a response to this first one, and claims that scientific knowledge can be justified if the demonstrations can be circular. Aristotle will reject this proposed solution to the infinite regress, and so must instead postulate another kind of knowing that will not lead to such a regress.
All scientific knowledge, as Aristotle defines it, requires an explanation, or rational demonstration, to proceed it before we can know it. All demonstrations take the form of a syllogism wherein all statements are all of the form “all X are Y”. As science is concerned only with general truths, these are the only kinds of statements that qualify as scientific knowledge. Additionally, the two premises must be known prior to scientifically knowing the conclusion, for it is only through explanation that we can scientifically know anything. This means that there are several prerequisites anyone must meet before they can scientifically know any given truth. If it is true that [if X and Y than Z], then we must first know that [if X and Y than Z], and must also know X and Y before we can come to scientifically know Z.
Skeptics of Aristotle’s theory of scientific knowledge might claim that on such a theory, knowledge is impossible, for reasons of it leading to an infinite reduction. Scientific knowledge is based on two previously known truths, but how can we come to know those? We already have one way of knowing, i.e. knowing things scientifically, so for that we would need to know two pairs of two truths for each premise to rationally demonstrate each one. If we sought to know Z in the example [if X and Y than Z], it has already been claimed by Aristotle that we must first know X and Y, as well as the validity of the demonstration. But to scientifically know X and Y, we would first have to know two truths for each of them. We would have to know what two truths are prior to X; call them X1 and X2. Then to scientifically know Z we must first know X1, X2, and [if X1 and X2 than X] to then scientifically know X, and similarly for Y. X1 and X2 will each require us to have prior knowledge of another two truths in order to scientifically know it, and so on ad infinitum. So before we can scientifically know anything, we must first know an infinite number of other truths. Since it is impossible to ever go through an infinite sequence of this sort, it is impossible to know anything on this account.
Another idea Aristotle presents is that of circular demonstration, which can be seen as a counter argument to the infinite regress. The circular argument claims that the posterior statements in a given explanation (i.e. the conclusion) can serve as a premise in an explanation of a term its prior to. The meanings of prior and posterior would be arbitrary here, with the most prior terms simply being the starting point of an inquiry, rather than some quality of the terms themselves. This means in all demonstrations, a set of statements will eventually reciprocate to the first statements used. For an example of what this kind of demonstration looks like, take three terms H, P, and L. Under a circular system, [if H than P, if P than L, if L than H] is archetypal for a progression of demonstrations. This is the only kind of demonstration allowed under the circular model, as any non-circular demonstration would run into the infinite regress problem.
Aristotle rejects this proposed solution, though he is overly dismissive of it. He remarks that in the case where [if H than P, if P than L, if L than H], we can reduce that by using transitivity. From the separate statements [if H than P] and [if P than L], we can see can be reduced to [if H than L]. If we take this term and further reduce it by applying transitivity to it and [if L than H], we get [if H than H]. If this is all that is required to explain something, then anything can be explained with no effort at all. In this way Aristotle claims all circular demonstrations amount to nothing more than the stating of a tautology, which is obviously insufficient to be an explanation. He has, however, sold the circular theory short. In the original series of claims, H entailed not only itself, but P and L as well. It would be inaccurate to say that [if H than H] is all that circular theory really is, as it fails to capture the other terms. If a circular explanation were to be boiled down to a single if-than statement for a given term (in this case, H), it should be [if H than HPL].
Aristotle’s mischaracterization of circular demonstration is regrettable, but there are still very strong grounds for rejecting it, because it can never give a sufficicient account of how we come to know something scientifically. For any term like H, we will need to know L before we can know it, because of the statement [if L than H]. But to know L, we must first know P, because of the statement [if P than L]. And to know P, we must know H; [if H than P]. This means that it is impossible to come to know anything by itself, but only as groups. In order to scientifically know H, P, or L we must come to know them all simultaneously; otherwise, we cannot know any of them for the reason above. Knowing P and L are is not merely insufficient for knowing H, it is impossible to know P and L without knowing H because to know P requires knowing H, and knowing L requires knowing P. This means that a requirement for coming to know H is knowing H; this clearly falls far short of an account of the acquisition of knowledge. The notion that it is required to know H before you know H is nonsense if interpreted to mean the H is known before H is known. A more charitable interpretation might be a claim that knowing H is what it is to know H, which does absolutely nothing to account for how one can go from not knowing H to knowing H. This may be what Aristotle was getting at, but was too hasty in dismissing circular demonstration to remark on.
After rejecting circular demonstration, this leaves Aristotle with the infinite regress problem to solve. He recognizes that if all knowledge is scientific, and requires demonstration consequently, there would indeed be no way to know anything. What he does is posit another kind of knowledge, one that we can no without demonstration, which will serve as the foundational premises for rational demonstration. This gives an end to the regression, because non-demonstrative knowledge will have no need for prior explanation, and thus not regress.
Search for the Genus of a General Science of Being
In Metaphysics Book IV, Aristotle begins by asserting that there is in fact a general science that studies being itself; in other words, it investigates the things that are in so far as they are things that are. There is a problem with this claim, however, because we seem unable to define the genus associated with this science. Aristotle has claimed in the Posterior Analytics that every science has a genus, the single thing that a particular science investigates. But there is seemingly no satisfactory candidate for a genus of the general science of being, and unless one is given, Aristotle would be at fault for asserting such a science. He does in fact address this concern in Book IV, and explains how there can be such a genus, so that we can proceed confident that there is indeed a general science of being.
The only obvious candidate for a genus here is a genus of “being”; however, on close inspection, this will fail to be a genus at all. According to Aristotle, for every science, there is an associated genus that is the field of the specific science. Change is the genus of physics and earth is the genus of geology. So too must a science of being have a specified genus, or else it is not a science at all. But all genera must be each a single thing, because each science has by definition one thing it studies. There could be no science with both motion and light as its genus, for instance, because those are two genera, with two different kinds of investigations, concerned with two different sets of qualities. Now, a science can study multiple things, but only in so far as they fall within a single genus. An example would be zoology, which studies many things, but only in so far as they are animals (the genus). With these criteria, it is impossible for a genus of being to exist, because according to the Categories, there are 10 different kinds of being, which are all irreducible. Since Aristotle denies there being a single thing “being”, and a genus is always a single thing, being cannot be a genus. And since all sciences require a genus, and being is not a genus, there can be no general science of being. At best, there could be 10 specific sciences of being, but that will not amount to a general science of being, which is what Aristotle wants.
Aristotle seems to be logically committed against a general science of being, but there are some finer points that will open the way for this science without denying his previous works about being (Categories) or science (Posterior Analytics). The argument above has two major premises: that A, every science has an associated genus and that B, being is not a genus. These are both things Aristotle affirms in other works, and it would be wrong to say he has changed his mind about either of these to accommodate the Metaphysics. Rather, there is a hidden premise to this argument; it is not a valid one without it. It supposes that if being is not a genus, then there is no genus for a science of being. In other words, being must be the only candidate for a genus of the general science of being. It is this premise that Aristotle can deny, and by presenting something besides being that can serve as a genus, he can hold to a general science of being. Aristotle will argue that the genus that is sought here is the genus of substance.
The choice of substance as a satisfactory genus initially seems a strange choice, because substances are not the only things that are, as established in the Categories. Aristotle claims in Chapter 5 that only primary substances and their species and genera are substances. Those are the things not said-of nor present-in (e.g. a man or a wolf) and the things said-of and not present-in (e.g. the species homo sapien or canis lupus) respectively. There are also the things that are present-in substances, such as pieces of knowledge or a color that are not themselves substances. These will not be covered under the genus substance, and as such, substance fails to be a genus of all the things that are. Underlying this perceived fault is the relationship between a science and its genus. The claim is here that there can only be a general science of being if the things it studies all fall under its genus. More generally, the principle is that Q is a science that studies a subset of things {a. . . z} if and only if all the members of {a. . . z} fall under a single genus. Of all the things that are (the subset of things a general science of being studies) not all of them are substances. Aristotle must now explain how non-substances can be included in a science with substance as its genus.
What Aristotle does here is provide another criteria for the things that can be studied by a science, one that will include non-substances as a subject of the general science of being. In addition to those things that fall under their genus, a science can also study things that are in reference to their genus. It expands the principle in the last paragraph into this: Q is a science that studies a subset of things {a. . . z} if and only if all the members of {a. . . z} fall under a single genus or are in reference to the genus. In the case of the science of being, this would mean it could study not only substances, but also the things that are present in them, by means of referencing the substances they are present in. It isn’t clear immediately why we should accept this expanding of domains of study, but Aristotle presents us with an example of a science who’s existence is agreed upon, and shows how it also requires this expanded theory in order to make sense as a science. Specifically, it is the science with the genus health. Obviously, the things that fall under health are states of a body, in as much as they are healthy or unhealthy states. But the science goes far beyond that, and studies various herbs and diets, in order to improve health. In this case, the study of health would be pointless if the questions of what improves/worsens health was not answered, and yet that necessitates the study of many things that are not health by any means, but they are studied in reference to health.
There are a final few objections to Aristotle’s explanation at this point, but they are all weak. One could argue that even though the things that are present-in substances can be referenced to substances, this treatment will only study them in the ways that relate to substances. This will omit study particular to these things, when any general science of being should study all the things there are exhaustively. The answer to this is simply that things present-in substances cannot exist without these substances, and as such, they can have no qualities independent of substances. Studying them in relation to substances will in fact be an exhaustive study, because they have no independent existence from substances. Another complaint could be leveled that health science is a practical discipline whereas a general science of being is a theoretical one, and this somehow makes them unsuited for comparison. But health science fits in to the definition of a science in the Posterior Analytics, which is precisely what Aristotle is attempting to do with a science of being. How “down to earth” it is shouldn’t matter as long as it is a proper science.
Many of these problems are not made explicit in the Metaphysics, and so it can be easy to misunderstand Aristotle and think he has changed his mind or denied principles put forward in his earlier works. Quite the opposite, he has refined these ideas and made them more clear in order to make a strong argument for the existence of a general science of being. There is no reason to think then that anything in the body of Aristotle’s work is not compatible with the core thesis of Metaphysics Book IV.
The Inadequacy of Scientific Knowledge
In Chapter 2 of the Posterior Analytics, Aristotle lays out a theory of how we come to possess scientific knowledge. A critical aspect of this is that scientific knowledge can only be known when first explained by reasoned demonstration from two premises that are already known. In Chapter 3, he considers two opposing viewpoints centered on this aspect of his theory. One claims this theory of scientific knowledge will regress infinitely, and so we cannot begin know anything scientifically. The other view is a response to this first one, and claims that scientific knowledge can be justified if the demonstrations can be circular. Aristotle will reject this proposed solution to the infinite regress, and so must instead postulate another kind of knowing that will not lead to such a regress.
All scientific knowledge, as Aristotle defines it, requires an explanation, or rational demonstration, to proceed it before we can know it. All demonstrations take the form of a syllogism wherein all statements are all of the form “all X are Y”. As science is concerned only with general truths, these are the only kinds of statements that qualify as scientific knowledge. Additionally, the two premises must be known prior to scientifically knowing the conclusion, for it is only through explanation that we can scientifically know anything. This means that there are several prerequisites anyone must meet before they can scientifically know any given truth. If it is true that [if X and Y than Z], then we must first know that [if X and Y than Z], and must also know X and Y before we can come to scientifically know Z.
Skeptics of Aristotle’s theory of scientific knowledge might claim that on such a theory, knowledge is impossible, for reasons of it leading to an infinite reduction. Scientific knowledge is based on two previously known truths, but how can we come to know those? We already have one way of knowing, i.e. knowing things scientifically, so for that we would need to know two pairs of two truths for each premise to rationally demonstrate each one. If we sought to know Z in the example [if X and Y than Z], it has already been claimed by Aristotle that we must first know X and Y, as well as the validity of the demonstration. But to scientifically know X and Y, we would first have to know two truths for each of them. We would have to know what two truths are prior to X; call them X1 and X2. Then to scientifically know Z we must first know X1, X2, and [if X1 and X2 than X] to then scientifically know X, and similarly for Y. X1 and X2 will each require us to have prior knowledge of another two truths in order to scientifically know it, and so on ad infinitum. So before we can scientifically know anything, we must first know an infinite number of other truths. Since it is impossible to ever go through an infinite sequence of this sort, it is impossible to know anything on this account.
Another idea Aristotle presents is that of circular demonstration, which can be seen as a counter argument to the infinite regress. The circular argument claims that the posterior statements in a given explanation (i.e. the conclusion) can serve as a premise in an explanation of a term its prior to. The meanings of prior and posterior would be arbitrary here, with the most prior terms simply being the starting point of an inquiry, rather than some quality of the terms themselves. This means in all demonstrations, a set of statements will eventually reciprocate to the first statements used. For an example of what this kind of demonstration looks like, take three terms H, P, and L. Under a circular system, [if H than P, if P than L, if L than H] is archetypal for a progression of demonstrations. This is the only kind of demonstration allowed under the circular model, as any non-circular demonstration would run into the infinite regress problem.
Aristotle rejects this proposed solution, though he is overly dismissive of it. He remarks that in the case where [if H than P, if P than L, if L than H], we can reduce that by using transitivity. From the separate statements [if H than P] and [if P than L], we can see can be reduced to [if H than L]. If we take this term and further reduce it by applying transitivity to it and [if L than H], we get [if H than H]. If this is all that is required to explain something, then anything can be explained with no effort at all. In this way Aristotle claims all circular demonstrations amount to nothing more than the stating of a tautology, which is obviously insufficient to be an explanation. He has, however, sold the circular theory short. In the original series of claims, H entailed not only itself, but P and L as well. It would be inaccurate to say that [if H than H] is all that circular theory really is, as it fails to capture the other terms. If a circular explanation were to be boiled down to a single if-than statement for a given term (in this case, H), it should be [if H than HPL].
Aristotle’s mischaracterization of circular demonstration is regrettable, but there are still very strong grounds for rejecting it, because it can never give a sufficicient account of how we come to know something scientifically. For any term like H, we will need to know L before we can know it, because of the statement [if L than H]. But to know L, we must first know P, because of the statement [if P than L]. And to know P, we must know H; [if H than P]. This means that it is impossible to come to know anything by itself, but only as groups. In order to scientifically know H, P, or L we must come to know them all simultaneously; otherwise, we cannot know any of them for the reason above. Knowing P and L are is not merely insufficient for knowing H, it is impossible to know P and L without knowing H because to know P requires knowing H, and knowing L requires knowing P. This means that a requirement for coming to know H is knowing H; this clearly falls far short of an account of the acquisition of knowledge. The notion that it is required to know H before you know H is nonsense if interpreted to mean the H is known before H is known. A more charitable interpretation might be a claim that knowing H is what it is to know H, which does absolutely nothing to account for how one can go from not knowing H to knowing H. This may be what Aristotle was getting at, but was too hasty in dismissing circular demonstration to remark on.
After rejecting circular demonstration, this leaves Aristotle with the infinite regress problem to solve. He recognizes that if all knowledge is scientific, and requires demonstration consequently, there would indeed be no way to know anything. What he does is posit another kind of knowledge, one that we can no without demonstration, which will serve as the foundational premises for rational demonstration. This gives an end to the regression, because non-demonstrative knowledge will have no need for prior explanation, and thus not regress.
Search for the Genus of a General Science of Being
In Metaphysics Book IV, Aristotle begins by asserting that there is in fact a general science that studies being itself; in other words, it investigates the things that are in so far as they are things that are. There is a problem with this claim, however, because we seem unable to define the genus associated with this science. Aristotle has claimed in the Posterior Analytics that every science has a genus, the single thing that a particular science investigates. But there is seemingly no satisfactory candidate for a genus of the general science of being, and unless one is given, Aristotle would be at fault for asserting such a science. He does in fact address this concern in Book IV, and explains how there can be such a genus, so that we can proceed confident that there is indeed a general science of being.
The only obvious candidate for a genus here is a genus of “being”; however, on close inspection, this will fail to be a genus at all. According to Aristotle, for every science, there is an associated genus that is the field of the specific science. Change is the genus of physics and earth is the genus of geology. So too must a science of being have a specified genus, or else it is not a science at all. But all genera must be each a single thing, because each science has by definition one thing it studies. There could be no science with both motion and light as its genus, for instance, because those are two genera, with two different kinds of investigations, concerned with two different sets of qualities. Now, a science can study multiple things, but only in so far as they fall within a single genus. An example would be zoology, which studies many things, but only in so far as they are animals (the genus). With these criteria, it is impossible for a genus of being to exist, because according to the Categories, there are 10 different kinds of being, which are all irreducible. Since Aristotle denies there being a single thing “being”, and a genus is always a single thing, being cannot be a genus. And since all sciences require a genus, and being is not a genus, there can be no general science of being. At best, there could be 10 specific sciences of being, but that will not amount to a general science of being, which is what Aristotle wants.
Aristotle seems to be logically committed against a general science of being, but there are some finer points that will open the way for this science without denying his previous works about being (Categories) or science (Posterior Analytics). The argument above has two major premises: that A, every science has an associated genus and that B, being is not a genus. These are both things Aristotle affirms in other works, and it would be wrong to say he has changed his mind about either of these to accommodate the Metaphysics. Rather, there is a hidden premise to this argument; it is not a valid one without it. It supposes that if being is not a genus, then there is no genus for a science of being. In other words, being must be the only candidate for a genus of the general science of being. It is this premise that Aristotle can deny, and by presenting something besides being that can serve as a genus, he can hold to a general science of being. Aristotle will argue that the genus that is sought here is the genus of substance.
The choice of substance as a satisfactory genus initially seems a strange choice, because substances are not the only things that are, as established in the Categories. Aristotle claims in Chapter 5 that only primary substances and their species and genera are substances. Those are the things not said-of nor present-in (e.g. a man or a wolf) and the things said-of and not present-in (e.g. the species homo sapien or canis lupus) respectively. There are also the things that are present-in substances, such as pieces of knowledge or a color that are not themselves substances. These will not be covered under the genus substance, and as such, substance fails to be a genus of all the things that are. Underlying this perceived fault is the relationship between a science and its genus. The claim is here that there can only be a general science of being if the things it studies all fall under its genus. More generally, the principle is that Q is a science that studies a subset of things {a. . . z} if and only if all the members of {a. . . z} fall under a single genus. Of all the things that are (the subset of things a general science of being studies) not all of them are substances. Aristotle must now explain how non-substances can be included in a science with substance as its genus.
What Aristotle does here is provide another criteria for the things that can be studied by a science, one that will include non-substances as a subject of the general science of being. In addition to those things that fall under their genus, a science can also study things that are in reference to their genus. It expands the principle in the last paragraph into this: Q is a science that studies a subset of things {a. . . z} if and only if all the members of {a. . . z} fall under a single genus or are in reference to the genus. In the case of the science of being, this would mean it could study not only substances, but also the things that are present in them, by means of referencing the substances they are present in. It isn’t clear immediately why we should accept this expanding of domains of study, but Aristotle presents us with an example of a science who’s existence is agreed upon, and shows how it also requires this expanded theory in order to make sense as a science. Specifically, it is the science with the genus health. Obviously, the things that fall under health are states of a body, in as much as they are healthy or unhealthy states. But the science goes far beyond that, and studies various herbs and diets, in order to improve health. In this case, the study of health would be pointless if the questions of what improves/worsens health was not answered, and yet that necessitates the study of many things that are not health by any means, but they are studied in reference to health.
There are a final few objections to Aristotle’s explanation at this point, but they are all weak. One could argue that even though the things that are present-in substances can be referenced to substances, this treatment will only study them in the ways that relate to substances. This will omit study particular to these things, when any general science of being should study all the things there are exhaustively. The answer to this is simply that things present-in substances cannot exist without these substances, and as such, they can have no qualities independent of substances. Studying them in relation to substances will in fact be an exhaustive study, because they have no independent existence from substances. Another complaint could be leveled that health science is a practical discipline whereas a general science of being is a theoretical one, and this somehow makes them unsuited for comparison. But health science fits in to the definition of a science in the Posterior Analytics, which is precisely what Aristotle is attempting to do with a science of being. How “down to earth” it is shouldn’t matter as long as it is a proper science.
Many of these problems are not made explicit in the Metaphysics, and so it can be easy to misunderstand Aristotle and think he has changed his mind or denied principles put forward in his earlier works. Quite the opposite, he has refined these ideas and made them more clear in order to make a strong argument for the existence of a general science of being. There is no reason to think then that anything in the body of Aristotle’s work is not compatible with the core thesis of Metaphysics Book IV.