Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript is excellent.

There are just a few minor points to take into account:

1. In the abstract, it would be advisable to improve slightly a formulation slightly. 'It is argued that mathematical assumptions underlie the ways that in which Russell and Popper portray the metaphysics of Plato and Hegel'. 

2. On p. 1, the name 'Heraclitus' should be written according to its established form in English.

3. References 67–69 and 73 should also include page citations.

4. A slight improvement also in the final sentence: "Hegel would thus begin to be regarded as a 'philosopher of freedom'".

Author Response

Of course, I am delighted with the reviewer's general comments and am grateful for the specific points made.

Comment 1: In the abstract, it would be advisable to improve slightly a formulation slightly. 'It is argued that mathematical assumptions underlie the ways that in which Russell and Popper portray the metaphysics of Plato and Hegel'. Reply: Changed as suggested.

2: On p. 1, the name 'Heraclitus' should be written according to its established form in English. Reply: Changed as suggested

3: References 67–69 and 73 should also include page citations. Reply: these have all been added.

4: A slight improvement also in the final sentence: "Hegel would thus begin to be regarded as a 'philosopher of freedom'". Reply: This has been reworded.

Reviewer 2 Report

Comments and Suggestions for Authors

I enjoyed reading this paper. I've made a few comments on the manuscript, these are just suggestions.

Comments for author File: Comments.pdf

Author Response

I was very grateful for the care taken in reviewing this manuscript. In relation to specific issues raised:

Page 4, notes 1 and 2, I have corrected the labelling of Figure 2 so as not to misleadingly describe it as a “Sierpinski triangle”.

Page 5, note 1. I have deleted the comma after “r1”.

Page 10, note 1. I have rewritten the confusing sentences, explaining “hexagram” and elaborating on the six-pointed “Star of David” and its relevance.

Page 11, notes 1 and 2. I have retained figure 5, but changed it in ways to show its relation to the earlier “hexagram” of Pascal’s theorem as well as the earlier “pentagram” in figure 3. Also, incorrect figure numberings have been corrected throughout.

Page 16, note 1. I have more explicitly described the role of the converging blue lines in Figure 7 in the way suggested.