Here's another topic to which you could respond:
In some way, the "second division" of the line is supposed to be the same type of division for both the visible and the ineligible sections. In what way is "reasoning from first principles to conclusions" like looking at images? In what way is "reasoning toward first principles" like looking at the objects themselves?
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When looking at images, you look at the objects that make the image. In a waty, this is related to reasoning from first principles to conclusions because the objects are the principles, determining the image or plainly just looking at it is a conclusion assuming that the objects are true, or right where they're supposed to be. Looking toward the objects are like the fist principle because they're the fundamental things that make up the image(i think i already explained this).
the simal;arity betwween the reasoning of the first princeiples is that if you see a image of a object then you can only form a opinion about the object because you you do not experience the whole of the said object and reasoning from first pricipal is the same in the way that both are things that you can opine about. the reason that to reason from frist prinibal which is somthing that you assume to be true and then taking that and fromit forming a concultion, this is to opine because it assumes somthing which may be untruth to be truth.
When you reason from a principle to a conclusion, you have to start with an opinion , because you really don't know anything about that certain topic, so you have to inference. From the opinion you reason every step from then on based on that first principle. This is like looking at an image beacuse when looking at an image, you can't really say much about a certain thing because some things can't be known ( what the object feels like, etc...). So you have to make inferences and from then on you can make your own rules based on that image.
When you reason toward the first principle, everything that is necessary is known and from there you prove the steps to reach a certain goal. This is like looking at the objects because when looking at the objects, you can know everything about that object, because your looking right at the object. So you're starting with all the information that you need and you reason off from there.
The "second division" of the line for both the visible section and the intelligible both describe the same thing. In the visible section, it represents reflections and images of objects, while in the intelligible section it represents facts and knowledge. Reasoning with first principles is like looking at images and assuming things about the actual object, because you must take an inference gained by looking at the image and use it to formulate ideas and characteristics of the actual object itself. This is similar to using a postulate, which isn't proved, but inferred, to find a theorem, which is always true. Reasoning toward first principles is like looking at the object itself and reasoning certain things about it based on facts about the object.
Well to begin with a proper definition for objects/images and "objects"/"images" is needed. For the visible, an image is when your looking at something indirectlt or not exactly at the object itself, (E.g:a reflection or photograph). An object is the object itself and no "replica" of the object.
For the Intelligible, an "image" is something that is assumed to be true and your trying to reason from the object, axiom, and reach a conclusion (E.g:Math or science). While the "object" itself is the axiom and you don't need to assume that it is true because it is already true.
Now we can proceed by saying that "reasoning from first principles to conclusions" is like looking at images because you assume that the image is true (opinion) and you reach your conclusion with that opinion. But arguing toward the axiom (first principle) helps bring out the truth of the "object".
The 2nd division of the line is the same type of division for both the visible part of the line and the intelligible part of the line. The 2nd division divides the two parts each into 2 new parts, objects and images. In this analogy, looking at images is like reasoning from first principles to conclusions and looking at objects is like reasoning towards first principles.
Looking at images is like reasoning from first principles to conclusions because when looking at an image, a shadow or a vague figure is shown. The figure shown would have some and only some properties that represent the properties of the actual object. In this case, the shown properties would be like the first principles and the actual object would be the conclusion. So, when a person looks at the shadow or figure, he or she would conclude or opine about the actual object. Now, the conclusion would be based on the properties shown or the 1st principles. An example of this whole thing would be a person seeing a shadow or figure in the shape of a circle. Now based on the property - circle like, the person would conclude that the object producing this shadow or figure is a circular object.
When looking at objects, it is like reasoning towards first principles. This is because when one sees an object, one would know all about that object. The truth is revealed when the object is seen. So, when seeing the object, one would examine and understand the properties of the object and thus, would be reasoning towards the 1st principles for the 1st principles are the properties of the object.
Intelligible visible things seem like learnable things but passed trough you. For example we all know a line is straight and is 180 degrees. But if you just draw a line and say that its a line without any measurement to pinpoint its accuracy, it is a visable thing from the original object or 1st principal. It will always be a reflection of the original thought but still be a true way by how you see it.
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