New on the site: Michi-bot. An intelligent assistant based on the writings of Rabbi Michael Avraham.

Questions about the model for non-deductive inferences

שו”תCategory: Talmudic studyQuestions about the model for non-deductive inferences
asked 9 years ago

peace,

I recently came across two papers from Isadora 23 and 24 that describe a mathematical model for non-deductive logic.

I have a few questions about the above articles:
1. First, I have a question about the issue itself – what difference does it make that it can be redeemed for money, when it is seemingly irrelevant to an issue that deals with personality? The problem is reinforced when, at the end of the issue, this claim of relevance is used to reject the argument from its source.

2. Regarding the model drawing – in almost all places the model is based on a diagram based on columns. (Apart from the issue of ink). Regarding the KV and the main building, it is possible to present the model for the rows as well, but when looking at the row diagrams of the equal side ski, you can see that there is no difference in them between filling 1 and filling 0. What does this say about the model?

3. Throughout the first part of the article, microscopic parameters are not used. In all places, the decision is made solely from the topological considerations of the graph. In fact, the only place where dimension also has significance (and perhaps not surprisingly) is when presenting the argument based on microscopic considerations directly.
Of course, the motivation for searching for microscopic elements that affect the result is clear, but is there an explanation for why considerations of connectivity or the number of vertices have an impact?
If we imagine two diagrams with two vertices, one with an arrow between them and an explanation that one vertex has alpha, and the other has alpha and beta, compared to a diagram without an arrow and then one vertex with alpha and the other only with beta. Why is the first diagram better? What is the intuition for this?

4. Regarding the rule that only one parameter can have a value – seemingly this rule needs to be restricted. After all, it is always possible to observe two different Qs from different places as one diagram with two binding components. In such a case, the first Q would be alpha and two alphas, and the second Q would be beta, and beta + gamma.
A restriction that seems reasonable is to claim that valence is limited to one microscopic parameter passing through one equivalence component.

5. Regarding microscopic dissection on the KV – seemingly the action of such a dissection is to cancel the arrow between the two vertices by introducing a microscopic parameter that exists on the light side and not on the severe side. But it can always be argued that in fact the opposite is true. On the severe side there is an inverted microscopic parameter and on the light side it disappears.
For example, the first qu’on could be interpreted as meaning that money provides pleasure that marriage does not, and therefore money will establish an engagement and marriage will not. But it could also be said the other way around, that marriage lacks pleasure (a formal legal act), and this is precisely what marriage (and even more so engagement) is capable of.
This cannot be done for a parent building, because it doesn’t matter who has a special parameter, the main thing is that there is no similarity (and in the diagram there are two vertices instead of one)
Maybe this is the meaning of the divination of all the dust that can only be done for the main building and not for the ku?

Thank you very much,


Discover more from הרב מיכאל אברהם

Subscribe to get the latest posts sent to your email.

Leave a Reply

0 Answers
מיכי Staff answered 9 years ago
Hello Avner, and thank you for the comments. 1. If money has the power to do something that a bill or a chuppah does not, then it is more powerful. This is a reasonable explanation for the case. Especially since the kiddush of money is learned from the field of Kinan. I didn’t understand the comment from the fraternity in Emma. 2. I think in the chapter dealing with ink we discuss the relationship between column and row considerations and show that it should give the same thing. There are subtleties there, and it’s hard to get into that here. As far as I remember, when you go over the subtleties you’ll see that there is equivalence between the presentations. 3. I think we have explained why intuitively the topological parameters are significant (we defined them a priori and only later saw that it really works. That is, there is an internal logic in their relevance to deciding inference). In principle, they all point to simplicity (expressions of Ockham’s razor). These parameters point to connections between the parts of the graph, and the more connections there are and the shorter and more directional they are, the simpler the picture. Regarding the example of the diagrams with two vertices, I didn’t understand. When there is an arrow between the points, there is one parameter (alpha and two alphas) ​​and not two (alpha and beta). Reminder that we are solving for a minimal model (the simplest). The first is better both in terms of dimension and in terms of constraints. And it is completely intuitively clear that the picture of the constrained diagram is simpler. Here it is really Occam’s razor, because without an arrow there are two parameters and two independent columns, and with an arrow there is one parameter and the columns are dependent (i.e. one is a function of the other). It’s like a straight line is simpler than a parabola (a graph with two parameters). 4. I didn’t completely understand the argument. But it’s certainly possible that there are options for additional models. From your description, I didn’t understand why the second CV has two parameters (beta and gamma). The CV diagram has only one parameter. 5. There are usually intuitive assumptions regarding the connection between the causes (or microscopic parameters) and the (halakhic) results. Pleasure adds to the ability to sanctify, not subtracts. Contrary to what one might think, we do not come to a tabula rasa conclusion, if only because of the fact that we decided which columns to include in the same table and which not. ——————————————— Asks: Hello and thanks for the answers. You’ve answered my questions a bit: 1. At the end of the issue, they try to refute the equal side by arguing that everyone has a “Bak”, and then Rav Huna rejects this by saying that money is possible “Bak” only in the mother but not in the person, and therefore it is irrelevant. It seems to me that the same argument could be made against the claim that money can redeem a second tithe. It is irrelevant because I will not forget who they are. 2. Let’s look at the following table for example (excerpt from the first KV): Embedded image 1 You can see that the line diagram of fill 0 and fill 1 are identical. Both have two points in the TL, m and h. 3. I understand why the topological consideration indicates simplicity in the graphic sense of the diagram, but if we try to think of the diagram as a parable and the collection of halachic events as a parable – then I have difficulty understanding the parable. For example, let’s look at the following diagram (I didn’t write what the relevant data table is, but one can be invented): Embedded image 2 What is important is that according to the model, it is clear that we should choose option 1 on the left (which includes an arrow between C and A) because of the constraints. But it’s not clear why – why would we prefer to say that C has a combination of alpha and beta, why is it simpler than saying that there is only beta? 4. Let’s look at the following table, it consists of two different KWs added together (this can be done from any two KWs that exist in the world) Embedded image 3 Filling in 1 in both places will give the diagram: Embedded image 4 And we see that D should take a combination of two microscopic parameters instead of twice beta. That’s a little strange. Thank you very much, and sorry for the quality of my diagrams. —————————————- Rabbi: 1. There is money in the company only in the mother and not in the husband. Identify a positive figure (it is known that there is no money in the husband). You suggested a negative interpretation that perhaps redemption is not relevant to the husband. 2. If you look in the chapter on ink (I think it’s there) you’ll see that the way the row diagram is constructed is different from the column diagram. It’s a delicate calculation, and I don’t have time to go into it now. 3. Topological simplicity is not just another tool that is concerned with expressing the complexity of the parameters. The graph and the parameters (dimension) are two different criteria. Therefore, the fact that both diagrams have two parameters does not mean that they are equivalent. The complexity of the diagram itself is also a criterion and is the decisive one. 4. On the surface, it seems to me that you are right, and that high values ​​should be allowed in one parameter in each subgraph. But this requires more thought.

Discover more from הרב מיכאל אברהם

Subscribe to get the latest posts sent to your email.

Leave a Reply

Back to top button