No Object Can Go Anywhere

Source

Michael Huemer

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Original Reconstruction

1. To reach point B, the object must complete the series, [1/2, 3/4, 7/8, …].

2. [1/2, 3/4, 7/8, …] is an infinite series.

3. It is impossible to complete an infinite series. For:

   1. To complete a series, one must reach its end.

   2. An infinite series has no end.

   3. It is not possible to reach the end of a series that has no end.

4. Therefore, the object cannot complete the series [1/2, 3/4, 7/8, …]. (From 2, 3)

5. Therefore, the object cannot reach point B. (From 1, 4) But point B can be any arbitrary point (separated from A); therefore:

6. No object can go anywhere. (From 5)

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Commentary

The first thing I will do is trace the logic backward, per rule P2.

• 6 follows 5

• 5 follows 1 and 4

• 4 follows 2 and 3

Notice how premise 1 is not needed in the first argument. 4, the first conclusion, only follows 2 and 3. This suggests that premise 1 should be moved down right before 5, per rule P1.

It now looks like this.

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1. [1/2, 3/4, 7/8, …] is an infinite series.

2. It is impossible to complete an infinite series. For:

   1. To complete a series, one must reach its end.

   2. An infinite series has no end.

   3. It is not possible to reach the end of a series that has no end.

3. Therefore, the object cannot complete the series [1/2, 3/4, 7/8, …]. (From 1, 2)

4. To reach point B, the object must complete the series, [1/2, 3/4, 7/8, …].

5. Therefore, the object cannot reach point B. (From 3, 4) But point B can be any arbitrary point (separated from A); therefore:

6. No object can go anywhere. (From 5)

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Now that I have moved the premise down, I noticed that the terminology sounds a bit odd because there is no mention of “the object” in the new premises 1 or 2, even though it appears in 3. So what I am going to do is reword the propositions a bit. Specifically, I will insert “for an object” into premise 2 and replace mentionings of “the object” with “an object.” I will also replace “one” in 2a. with “an object.”

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1. [1/2, 3/4, 7/8, …] is an infinite series.

2. It is impossible for an object to complete an infinite series. For:

   1. To complete a series, an object must reach its end.

   2. An infinite series has no end.

   3. It is not possible to reach the end of a series that has no end.

3. Therefore, an object cannot complete the series [1/2, 3/4, 7/8, …]. (From 1, 2)

4. To reach point B, an object must complete the series, [1/2, 3/4, 7/8, …].

5. Therefore, an object cannot reach point B. (From 3, 4) But point B can be any arbitrary point (separated from A); therefore:

6. No object can go anywhere. (From 5)

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Next, I will switch premises 1 and 2, per rule L1, because 2 is broader. We now have this.

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1. It is impossible for an object to complete an infinite series. For:

   1. To complete a series, an object must reach its end.

   2. An infinite series has no end.

   3. It is not possible to reach the end of a series that has no end.

2. [1/2, 3/4, 7/8, …] is an infinite series.

3. Therefore, an object cannot complete the series [1/2, 3/4, 7/8, …]. (From 1, 2)

4. To reach point B, an object must complete the series, [1/2, 3/4, 7/8, …].

5. Therefore, an object cannot reach point B. (From 3, 4) But point B can be any arbitrary point (separated from A); therefore:

6. No object can go anywhere. (From 5)

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Premise 1 contains a nested list, which I like, but I will make a couple of adjustments. Specifically, I will rephrase 1c such that it reiterates premise 1, and I will remove “For:” in premise 1.

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1. It is impossible for an object to complete an infinite series. For:

   1. To complete a series, an object must reach its end.

   2. An infinite series has no end.

   3. Therefore, it is impossible for an object to complete an infinite series. (This follows 1a. and 1b.)

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Next, I noticed that proposition 5 contains a conclusion and an additional premise. I think splitting them up will be better. According to rule C1, propositions should be combined if doing so does not negatively affect flow or dialectical usefulness. Having a conclusion and an additional premise together violates rule C1.

The last thing I will change is to move “therefore” to the main conclusion. This is simply a stylistic choice.

We now have this.

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Final Version

1. It is impossible for an object to complete an infinite series.

   1. To complete a series, an object must reach its end.

   2. An infinite series has no end.

   3. Therefore, it is impossible for an object to complete an infinite series. (This follows 1a. and 1b.)

2. [1/2, 3/4, 7/8, …] is an infinite series.

3. Therefore, an object cannot complete the series [1/2, 3/4, 7/8, …]. (From 1, 2)

4. To reach point B, an object must complete the series, [1/2, 3/4, 7/8, …].

5. Therefore, an object cannot reach point B. (From 3, 4)

6. But point B can be any arbitrary point (separated from A).

7. Therefore, no object can go anywhere. (From 5, 6)

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