reason recognizes a lot more than contradictions,

I believe that this insight of Bryan Caplan (about the false dilemma of Hume) provided a seed for the development of the thinking of Michael Huemer about the idea that reason recognizes a lot more than contradictions, rather it recognizes universals However I am not trying to say that Kant and Hegel, Georg Hamann, and Nelson had no value. They were, rather, trying to solve the problem of how reason recognizes universals

Yet none of the German idealists saw that the entire premise of Hume was a fallacy.

I put this important paper here because it shows something amazing. The entire basis of German idealism from Kant up until Hegel was based on this one idea of Hume. It forms the basis of the idea of Kant about the limits of pure reason. Hegel accepted this except that he tried go around it by the dialectic method. Yet none of the German idealists saw that the entire premise of Hume was a fallacy. [Hume taught Euclidean geometry and from that he decided that all human reason can do is to perceive contradiction.] Here is a link to Caplan's early material. An Enquiry Concerning Hume's Misunderstanding Bryan Caplan Tu 3-4 Phil 122 Question #1 1. Introduction Remarkably, it is possible to sum up David Hume's vital assumptions about reasoning in a single proposition: Reason does NOTHING except locate the presence or absence of contradictions. This paper will attempt three tasks: first, to show the textual support for my interpretation; second, to explain how Hume's skepticism about induction depends on this assumption; and third, to briefly argue that Hume's basic assumption is wrong. 2. Textual Support Whenever Hume wants to show that reasoning cannot support something, he uses the same argument: the alternative is not a contradiction. "The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind."1 Suppose that we try to use reason to establish any matter of fact. Hume says that our effort is futile, because the alternative is conceivable. But if the alternative is conceivable, then it is not a contradiction, because contradictions are inconceivable. But reason can refute something only if it is a contradiction. Hence, reason can never establish any matter of fact. Hume liberally repeats this argument throughout his works on epistemology. When he denies that reason justifies the law of cause-and-effect, he says, "That there are no demonstrative arguments in this case, seems evident; since it implies no contradiction, that the course of nature may change."2 The argument is the same as above: An alternative is conceivable; contradictions are not conceivable; and reason can only demonstrate that something is false if it is a contradiction. Hence, reason cannot establish the law of cause-and-effect. Hume uses the same argument in A Treatise of Human Nature. "There is no object, which implies the existence of any other if we consider the objects in themselves. Such an inference wou'd amount to knowledge, and wou'd imply the absolute contradiction and impossibility of conceiving any thing different."3 Once again, Hume notes that he can conceive of one object without a second object. Since no contradictions are conceivable, this is not a contradiction. And since reason does nothing but locate the presence or absence of contradictions, reason cannot establish a connection between any two things. Later in the Treatise, Hume makes the argument still more explicit: "To form a clear idea of any thing, is an undeniable argument for its possibility, and is alone a refutation of any pretended demonstration against it."4 Conceivability implies the absence of a contradiction, and the absence of a contradiction implies that reason has nothing to say on the matter. To cement my interpretation, let us turn to Hume's Abstract of a Treatise of Human Nature, where he repeats the argument. "The mind can always conceive any effect to follow from any cause, and indeed any event to follow upon another: whatever we conceive is possible, at least in a metaphysical sense: but wherever a demonstration takes place, the contrary is impossible, and implies a contradiction. There is no demonstration, therefore, for any conjunction of cause and effect."5 As always, his argument flows from the conceivability of an alternative, to the absence of a contradiction, to the forced silence of reason on the question. "What is demonstratively false implies a contradiction; and what implies a contradiction cannot be conceived."6 Hume could hardly be more explicit. In all three works, he uses precisely the same argument. And this argument rests on a crucial assumption about reason and reasoning: namely, that reason does nothing except locate the presence or absence of contradictions. While Hume may be open to interpretation on some points, the textual support for my claim is quite solid: it spans at least three of his epistemological works, and appears repeatedly in each. The next section explains in detail why this assumption about reasoning matters. 3. The Crucial Assumption Let us formally state the argument that Hume uses above in order to see why his assumption crucially supports his view that we never have any reason to believe any matter of fact. 1. The alternative to any matter of fact is conceivable. 2. If something is conceivable, then it is not a contradiction. 3. Reason does nothing except locate the presence or absence of contradictions. Therefore, reason has nothing to say about any matter of fact; if a proposition concerns matters of fact, reason can neither support nor refute it. It is hard to doubt premises #1 and #2. We can indeed conceive of alternatives to any matter of fact. And it seems like a basic feature of a contradiction that it is inconceivable. (Try to conceive of a circular square. Now try to conceive that gremlins exist. Notice the difference?) Premise #3 is therefore the crucial step in the argument -- and Hume's most central assumption about reasoning. How does the above argument relate to Hume's argument that we never have any reason to believe any unobserved matter of fact? I shall briefly but formally state Hume's argument against induction, then see how it relates to his central assumption about reasoning. 1. All knowledge comes either from observation or reason. 2. Knowledge of unobserved matters of fact can't come from reason, because the alternative to any matter of fact is conceivable and therefore implies no contradiction. 3. Knowledge of unobserved matters of fact can be derived from knowledge of observed matters of fact only if the law of cause-and-effect is known. 3a. Reason cannot establish the law of cause-and-effect, because the alternative is conceivable and therefore implies no contradiction. 3b. Observation alone cannot establish the law of cause-and- effect, because this is itself an unobserved matter of fact, so the argument would be circular. Therefore, we never have any reason to believe any unobserved matter of fact. Let us now cross-examine these two formal arguments, and see why Hume's assumption about reason (premise#3 in the first argument) is crucial for his second argument to work. Interestingly, it is actually used twice in the second argument - in premises#2 and 3a. Premise #2 claims that we cannot come to know about unobserved matters of fact just by reasoning about them. Why? Because the contrary to every matter of fact is conceivable, conceivable things are not contradictions, and reason does nothing except locate the presence or absence of contradictions. Premise #3a claims that we cannot come to know the law of cause-and- effect just by reasoning about it. Why? Because the contrary of the law of cause-and-effect is conceivable, conceivable things are not contradictions, and reason does nothing except locate the presence or absence of contradictions. So Hume's basic assumption about reasoning is absolutely crucial at both steps. Suppose someone had a different theory of reasoning. Hume's argument would fall apart. A critic could accept everything else that Hume says, but claim that reason does more than merely locate the presence or absence of contradictions. Perhaps we use reason to directly justify our beliefs about unobserved matters of fact. Or perhaps we use reason to justify the law of cause-and-effect (major premise), coupled with our knowledge of observed matters of fact (minor premise), to justify our beliefs about unobserved matters of fact (conclusion). In either case, Hume's problem of induction dissolves. Only if reason is as weak as Hume says would his skepticism about induction follow. But Hume never proves the weakness of reason. Instead, he accepts the weakness as a basic premise, claiming that no one denies it: "[W]hatever we conceive is possible, at least in a metaphysical sense: but wherever a demonstration takes place, the contrary is impossible, and implies a contradiction. And this is a principle, which is generally allowed by philosophers."7 Since his conclusions differ so radically from those of earlier philosophers, Hume should have considered that they might not accept the same conception of reason. At the very least, he should have argued for his position, instead of just asserting that, "To form a clear idea of any thing, is an undeniable argument for its possibility, and is alone a refutation of any pretended demonstration against it."8 But is it? Only if we accept Hume's view of reason in the first place, according to which reason does nothing except locate the presence or absence of contradictions. How would Hume convince someone who didn't already agree? I don't think that he could. 4. An Alternative Conception of Reason Consider the claim: Circular arguments are invalid. Think about it for a while. You can see that it is true -- but how? Even though Hume himself uses this principle in his argument, we could never justify it on his principles. The denial is not a contradiction. We can at least conceive that "Some circular arguments are valid" is true. But at the same time, this principle is not a mere matter of fact. Once we grasp the principle, we see that it is true always and everywhere; moreover, we grasp it by the mere operation of thought. Or consider the claim: The argument ad hominem is a fallacy. Again, the denial is not a contradiction; yet we grasp that it is universally true with the mere operation of thought. I think that these two claims are convincing counter- arguments to Hume's conception of reason. Reason does more than merely discover the presence of absence of contradictions. Frequently, we justify necessary truths just by thinking about them; and sometimes, the opposite of these necessary truths is still conceivable and hence not a contradiction. What is so amazing about this claim? It just turns out that Hume underestimates the power of reason when he limits it to locating the presence or absence of contradictions. I probably won't convince anyone in so brief a presentation. But at least let me raise some doubts in the minds of convinced Humeans. Hume claims that reason cannot justify the law of cause- and-effect. I think that it plainly does. We grasp that "Circular arguments are invalid" and "The argument ad hominem is false" by the pure operation of thought, even though their opposites are conceivable and hence not contradictions. I say that we justify the claim "Every effect has a cause; the same cause always produces the same effect" in exactly the same manner. Namely, we think about the claim; and if we are sufficiently intelligent, open-minded, and intellectually honest, we immediately see its truth. 5. Conclusion Hume assumes that reasoning can do nothing except locate the presence or absence of contradictions. Moreover, his argument that we never have any reason to believe any unobserved matter of fact crucially depends on this unproven assumption. For if reason could do something more than locate the presence or absence of contradictions, we could use reason to justify our claims about unobserved matters of fact. Reason might directly give us a reason to believe unobserved matters of fact; or, reason might give us a reason to believe the law of cause-and-effect, which coupled with immediate observations would give us a reason to believe unobserved matters of fact. I have not proved that this alternative conception of reason is correct. But we should at least consider it. Not only do the examples in the section four tend to support it; but it is also the most likely escape route from the long list of absurd conclusions Hume's premises imply. No one accepts Hume's conclusions in practice; it is time to question his theory as well. Notes 1: David Hume, An Enquiry Concerning Human Understanding, pp.15-16. 2: ibid, p.22. 3: David Hume, A Treatise of Human Nature, pp.86-87. 4: ibid, p.89. 5: David Hume, Abstract of a Treatise of Human Nature, pp.13- 14. 6: ibid, p.17. 7: ibid, p.14. 8: A Treatise of Human Nature, op. cit., p.89.

בבא קמא בדף כ"ג. הרמב''ם לפי הגר''א

כשחזרתי מהים עלה בדעתי מדוע הרמב''ם (לפי הגר''א) קבע שר' יוחנן שינה את דעתו, וקובע שנזק על ידי שריפה חייב בגלל נזק על ידי רכושו, לא נזק על ידי גופו. הסיבה היא השקלא וטריא של הגמרא בבא קמא בדף כ"ג. אביי שאל, אם צודק ר' יוחנן שנזק על ידי אש הוא בגלל "חיציו" {נזק ישיר על ידי גופו}, אז למה נזק לטמון (דברים נסתרים) לא יהיה אחראי? והוא ענה, היה שם חומה, והיא נפלה (לא בגלל האש), ולא הספיק לתקן אותו לפני שפרצה השריפה. אז זה מקרה של אי יכולת לעשות שום דבר כדי לעצור את הנזק הזה (אונס) . [למרות שבדרך כלל אנו אומרים שאדם תמיד עלול לגרום נזק, עדיין נזק באמצעות רכושו (או אפילו בשריפה שהיא חמורה יותר), העובדה שהמצב אינו בשליטתו גורמת לו שהוא ללא אחריות. לאחר מכן רבא שאל, אם כן, אז גם על דברים גלויים אינו צריך להיות אחראי. הגמרא עונה ר' יוחנן מחזיק נזק מאש נחשב חיציו וגם רכושו; ועניינו שהוא חייב בדברים פתוחים, אבל לא חייב בדברים נסתרים הוא במקום שהייתה התרשלות. זה יהיה דומה למה שיהיה אם הוא שכח לנעול את השור שלו בלילה, והוא יצא וגרם נזק.] אני חושב שהגמרא רואה בחומה מקרה של אי יכולת לשנות כלום (אונס) . אבל בלי חומה בינו לבין שכנו, אם זה יהיה "החצים שלו", אז הוא יהיה אחראי גם לדבר גלוי וגם נסתר. [כדי לגרום לו לא להיות אחראי לדברים נסתרים, הגמרא צריכה להמציא תרחיש שבו היה קיר. אחרי הכל, חיצים עוברים הרבה מעבר לחומות. ולכן הרמב''ם קבע שאין אנו חושבים עוד שר' יוחנן מחזיק ב"חיציו" אלא כדי להטיל עליו אחריות בכל חמשת מיני הנזק שחייב אדם בהם במקרה של נזק מגופו. מלבד זאת, הוא אחראי רק לנזק שנגרם על ידי רכושו.רק תחשוב. הגמרא אמרה כשהייתה חומה, "נגמרו החצים שלו". לכן, כדי למצוא דרך שחיציו לא יגמרו, היה על הגמרא לחלץ את החומה, ולהכניס עצלות והזנחה פשוטה. בשלב זה, מדוע שחצים יסתיימו? ברור שלא

the Gemara on page 23 in Bava Kama. Rambam according to the Gra.

As I was walking back from the sea it occurred to me why the Rambam held that Rava held that R. Yochanan holds that damage by fire is obligated because of damage by his property, not damage by his body. The reason is in the questions and answers of the Gemara on page 23 in Bava Kama. Abyee asked, if R Yochanan is right that damage by fire is because of “his arrows” {direct damage by his body}, then why would damage to hidden things not be liable? The abyee answered, there was a wall there, and it fell (not from the fire), and he did not have time to repair it before the fire broke out. So it is a case of not being able to do anything to stop that damage. [Even though we normally say a person is always liable to do damage, still damage by means of his property or (or even with fire which is more serious), the fact of the situation being totally out of one’s control makes him not liable. Rava then asks, if so, then even for open things he should be not liable. The Gemara answers R Yochanan holds damage by fire is considered “his arrows” and also his property; and our case where he liable for open things but not liable for hidden things is where there was neglect similar to what would be the case if he forgot to lock his ox up at night, and it went out and cause damage.] I think that the gemara considers a wall to be a case of not being able to change anything. but with no wall between him and his neighbor, if it would be “his arrows” then he would be liable for both open and hidden thing. [To get him to not be liable for hidden things the gemara has to come up with scenario where there was a wall. After all, arrows go far beyond walls. so the Rambam held that we no longer think that R Yochanan holds with “his arrows” except to make him liable in all the five kinds of damage that one is liable for in a case of damage by his body. Besides that, he is liable only for damage by his property. Just think. the Gemara said when there was a wall "his arrows were finished". So, to find a way that his arrows would not be finished, the Gemara had to extract the wall, and put in simple laziness and neglect. At that point, why would arrows be finished? Clearly not. I want to explain why the Gra wrote that only way to understand the subject on page 23 of Bava Kama is like the Rif and Rambam, that is that the Gemara decided that R Yochanan does no longer hold with his arrows except in so far as it makes him liable in another four types of damage. But in all other aspects, he holds like reish lakish that damage by fire is because of damage by mean of his property. The reason is this. Neither Abaye nor Rava had any problem with the idea that if one is liable because of his arrows that would extend beyond one’s own domain. The only question was it should even more liable for damage to hidden things. But then Abaye said the scenario is when there was a wall and so his arrows were finished. But Rava objected and said that then he wouldn’t be liable even for open things. So Rava decided the case is when there was no wall. But again, if there is no wall, then he should be liable for his arrows alone. There is no need to make him more liable because of damage by mean of his property. It was already perfectly fine for him to be liable for all damage done on another domain just from his arrow alone. so in short, the give and take questions and answers of Abaye and Rava make no sense unless you say that Rava held that R Yochanan hold his arrows are liable because of his money alone. His arrows would be finished if there was a wall there or if it fell and he had no time to repair it. But with no wall, there is no finishing of his arrows ------------------------------------- As I was walking back from the sea it occurred to me why the רמב''ם held that ר’ יוחנן changed his mind, and holds that damage by fire is obligated because of damage by his property, not damage by his body. The reason is in the questions and answers of the גמרא בבא קמא on page 23. אביי asked, if ר’ יוחנן is right that damage by fire is because of “his arrows” {direct damage by his body}, then why would damage to טמון hidden things not be liable? HE answers, there was a wall there, and it fell (not from the fire), and he did not have time to repair it before the fire broke out. So, it is a case of not being able to do anything to stop that damage(אונס) . [Even though we normally say a person is always liable to do damage, still damage by means of his property or (or even with fire which is more serious), the fact of the situation being totally out of one’s control makes him not liable. The רבא then asks, if so, then even for open things he should be not liable. The גמרא answers ר’ יוחנן holds damage by fire is considered “his arrows” and also his property; and our case where he liable for open things, but not liable for hidden things is where there was neglect. THAT WOULD BE similar to what would be the case if he forgot to lock his ox up at night, and it went out and caused damage.] I think that the גמרא considers a wall to be a case of not being able to change anything(אונס) . But with no wall between him and his neighbor, if it would be “his arrows”, then he would be liable for both open and hidden thing. [To get him to not be liable for hidden things the גמרא has to come up with scenario where there was a wall. After all, arrows go far beyond walls. so the רמב''ם held that we no longer think that ר’ יוחנן holds with “his arrows” except to make him liable in all the five kinds of damage that one is liable for in a case of damage by his body. Besides that, he is liable only for damage by his property. Just think. the גמרא said when there was a wall "his arrows were finished". So, to find a way that his arrows would not be finished, the גמרא had to extract the wall, and put in simple laziness and neglect. At that point, why would arrows be finished? Clearly not. I want to explain why the גר''א wrote that only way to understand the subject on page כ''ג of בבא קמא is like the רי''ף and רמב''ם , that is that the גמרא decided that ר’ יוחנן does no longer hold with his arrows except in so far as it makes him liable in another four types of damage. But in all other aspects, he holds like ריש לקיש that damage by fire is because of damage by mean of his property. The reason is this. Neither אביי nor רבא had any problem with the idea that if one is liable because of his arrows that would extend beyond one’s own domain. The only question was it should even more liable for damage to hidden things. But then אביי said the scenario is when there was a wall and so his arrows were finished. But רבא objected and said that then he wouldn’t be liable even for open things. So רבא decided the case is when there was no wall. But again, if there is no wall, then he should be liable for his arrows alone. There is no need to make him more liable because of damage by mean of his property. It was already perfectly fine for him to be liable for all damage done on another domain just from his arrow alone. so, in short, the give and take questions and answers of אביי and רבא make no sense unless you say that רבא held that ר’ יוחנן hold his arrows are liable because of his money alone. His arrows would be finished if there was a wall there or if it fell and he had no time to repair it. But with no wall, there is no finishing of his arrows

בבא קמא כ''ב וכ''ג

הייתי בחוף הים וחושב שאפילו אם נלך עם הגר"א שכתב שהרמב"ם סבור שרבא מחזיק שר' יוחנן מסכים עם השיטה של ריש לקיש שחובת תשלום נזק אש היא בגלל נזק על ידי רכושו (לא על ידי חיצים שלו) שעדיין זה לא מספר לנו כלום על המשנה עם הכלב והפחם. אתה בכל מקרה צריך לומר את הסיבה לריש לקיש שעל שאר הערימה לא חייב כי זה כוחו של כוחו. אבל זה רק זורק את השאלה צעד אחד אחורה. נניח שהכלב זרק את הפחם על הערימה. האם אין אנו אומרים שאנו הולכים בהתחלה של נזק? וכך בעצם הכריע הרמב''ם בהלכה. {זה כמו רבה שאם זורק כלי ולפני שהוא מגיע לארץ ונשבר, מישהו אחר שובר אותו בעודו באוויר. הראשון הוא חייב, לא השני.} עם זאת, אולי זה כל העניין של ריש לקיש? שנלך על תחילת הנזק, ולכן גרירת הפחם או השלכתו על הערימה תהיה אחראית כי זה הכוח הראשון. ואז שאר הערימה הוא כוח הכוח שלו. אז זה יסביר את הרמב''ם. זה גם עוזר לר' יוחנן שאמר שהוא אחראי לכל הערימה שהכלב צריך להניח עליה את הפחם. יכול להיות שהוא מסכים שאם הכלב יגרור אותו לאורך הערימה או יזרוק אותו על הערימה זה יהיה כמו ריש לקיש שהאזור הזה חייב בחצי נזק, (אבל לא נזק מלא כי זה לא דרכו הרגילה של כלב לזרוק גחלים. אבל אדם שזורק כלי יהיה אחראי מלוא נזק שלם.) אבל ר' יוחנן מחפש דרך לקבל חוק המשנה שאת החובה של חצי הערימה כולה תהיה חצי נזק. בסיכום, החליט הרמב''ם שהחוק כמו ריש לקיש. בעל הכלב חייב על הלחם נזק מלא, ועל מקום גרירת הפחם הוא חייב חצי נזק כי אנו הולכים עם תחילת הגורם נזק כמו רבה; ועל שאר הערימה, הוא אינו חייב כי זה כוחו של כוחו.-----------אני רוצה להסביר מדוע כתב הגר"א שרק הדרך להבין את הנושא בדף כ"ג בבא קמא היא כמו הרי"ף והרמב"ם, כלומר שהגמרא החליט שר' יוחנן אינו מחזיק יותר בחיציו אלא במידה שזה גורם לו להתחייב בעוד ארבעה סוגי נזק. אבל בכל ההיבטים האחרים, הוא סבור, כמו ריש לקיש, שנזק אש נובע מפגיעה על ידי רכושו. הסיבה היא זו. לא לאביי ולא לרבא הייתה שום בעיה עם הרעיון שאם אדם אחראי בגלל החיצים שלו זה ירחיק מעבר לתחום שלו. השאלה היחידה הייתה שהיא (אש) צריכה להיות אחראית אפילו יותר, היינו בנזק לדברים נסתרים. אבל אז אביי אמר שהתרחיש הוא כשהייתה חומה וכך החיצים שלו גמרו. אבל רבא התנגד ואמר שאז הוא לא יישא באחריות אפילו לדברים גלויים. אז רבא החליט שהמקרה הוא כשאין חומה. אבל שוב, אם אין חומה, אז הוא צריך להיות אחראי גם בגלל חיציו בלבד. אין צורך להטיל עליו אחריות רבה יותר בגלל נזק באמצעות רכושו. זה כבר היה בסדר גמור עבורו להיות אחראי לכל הנזק שנגרם בתחום אחר רק מהחץ שלו בלבד. אז בקיצור, השאלות והתשובות של תן וקח (שקלא וטריא) של אביי ורבא אינן הגיוניות אלא אם כן אתה אומר שרבא קבע שר' יוחנן מחזיק שאש אחראית רק בגלל הרכוש שלו. חיציו יגמרו אם היה שם חומה או אם היא נפלה ולא היה לו זמן לתקן אותה. אבל בלי חומה, אין גימור של החיצים שלו

Bava Kama page 22 and page 23.

I have been at the sea shore and thinking that even if we go with the Gra who wrote that the Rambam holds that R Yochanan changed his mind, and he goes with the idea of Reish Lakish that the obligation of paying for damage by fire is because of damage by his property (not his arrows) that still does not tell us about the Mishna with the dog and coal. You anyway have to say the reason for Reish Lakish that the rest of the stack is not liable because it is force of his force. but that just throws the question one step back. Let’s say the dog threw the coal on the stack. Don’t we say that an animal that steps on a vessel and it rolls away and get broken, that we go by the beginning? And that is in fact how the Rambam decided the law. {Thi I lie Raba that if one throws a vessel and before it reaches the ground and is broken, someone else breaks it while it is still in the air. The first one is obligated, not the second one.} However, maybe that is the whole point of Reish Lakish? that we go by the beginning of the damage and o dragging the coal or throwing it on the stack would be liable because of that is the first force. then the remainder of the stack is force of his force. so that would explain the Rambam. This also helps R Yochanan who said to be liable for the whole stack the dog needs to place the coal on it. It might be that he agrees that if the dog dragged it along the stack or threw it on the stack that would be like Reish Lakish that that area is liable half damage. But R Yochanan is looking for a way to get the obligation of half damage to be applied to the whole stack, not just the place the coal landed. In summery the Rambam decided the law like Reish Lakish. The owner of the dog is liable for the bread full damage, and for the place where the coal was dragged, he is liable half damage because we go by the beginning of the cause of damage like Raba; and for the rest of the stack, he is not liable because that is force of his force. I am thinking that this explains Reish Lakish and the Rambam, but the sugia on page 23 is still blurry to me. The nice thing about this approach is that it uses the insight of the Gra to explain the Rambam, and also the inight of the Tosphot that we still need the idea of force of his force. _____________________________________________________________________________ I have been at the sea shore and thinking that even if we go with the גר''א who wrote that the רמב’’ם holds that ר’ יוחנן changed his mind, and he goes with the idea of ריש לקיש that the obligation of paying for damage by fire is because of damage by his property (not his arrows) that still does not tell us about the משנה with the dog and coal. You anyway have to say the reason for ריש לקיש that the rest of the stack is not liable because it is force of his force. but that just throws the question one step back. Let’s say the dog threw the coal on the stack. Don’t we say that an animal that steps on a vessel and it rolls away and get broken, that we go by the beginning? And that is in fact how the רמב’’ם decided the law. {This is like רבה that if one throws a vessel and before it reaches the ground and is broken, someone else breaks it while it is still in the air. The first one is obligated, not the second one.} However, maybe that is the whole point of ריש לקיש? that we go by the beginning of the damage and so dragging the coal or throwing it on the stack would be liable because of that is the first force. Then the remainder of the stack is force of his force. so that would explain the רמב’’ם. This also helps ר’ יוחנן who said to be liable for the whole stack the dog needs to place the coal on it. It might be that he agrees that if the dog dragged it along the stack or threw it on the stack that would be like ריש לקיש that that area is liable half damage, (but not full damage because it is not the normal way of a dog to throw coals. A person throwing a vessel however would be liable full damage.) But ר’ יוחנן is looking for a way to get the obligation of half damage to be applied to the whole stack, not just the place the coal landed. In summery the רמב’’ם decided the law like ריש לקיש. The owner of the dog is liable for the bread full damage, and for the place where the coal was dragged, he is liable half damage because we go by the beginning of the cause of damage like רבה; and for the rest of the stack, he is not liable because that is force of his force.

Mathematics was for me a big challenge. It took for me a long detour to get a grip on Math and Physics. I had to go the rout of the approach in the Gemara Tractate Avoda Zara page 19 which says that the main thing in learning is to say the words in order from the start of the book until the end and then review. I found that this helped me to get started with math and physics. And from my own experience I try to recommend this approach to others who like me may not be particularly talented in these areas and yet still realize their importance. But Isaac Rosten told me that an essential part of this approach is the review part. After you finish the book or chapter, then you need to review four times. This approach does not work without the review part.