Analyzing the philosophy of travel with Schopenhauerian argument maps

Emily Thomas's seminal book The Meaning of


| I N T RODUC T ION
Identifying a philosophy of travel as a separate discipline that can claim equal importance with bioethics or philosophy of race may initially be difficult.However, this branch becomes serious at least at the moment when we realize that ethical arguments come into play to decide whether a certain journey should be undertaken or not: What reasons are there for philosophers to fly to a conference (when they can exchange ideas via video conference)?Can we with good reasons oblige students to travel abroad if the trip may be dangerous?Are there compelling reasons to undertake a travel scholarship to a country that has just been hit by a huge natural disaster or where there are political riots?
Reflecting philosophically on travel and on the above-mentioned questions is certainly not commonplace, but it is also not as unusual as it might seem at first glance.In the last hundred years, the expression "philosophy of travel" has come up a few times.Consider, for

| SCHOPEN H AU ER'S A RGU M EN T M A P FOR T R AV ELI NG
The Schopenhauers were a family of travelers; it cannot be said otherwise.Johanna Schopenhauer published numerous travel reports in the first half of the nineteenth century (Martin, 2004a).The mother of the philosopher Arthur Schopenhauer took her son on many of these journeys, and he continued his mother's intention to travel until the 1830s.The Schopenhauers traveled to various European countries over long periods of time, and Johanna's account of her travels to England and Scotland in particular became a bestseller in nineteenth-century Germany.Numerous women in German-speaking countries during the late eighteenth and early nineteenth centuries undertook many journeys and successfully wrote travel literature, some of which was philosophically motivated, such as the works of Sophie von La Roche, Rahel Varnhagen von Ense, Friederike Brun, and others (Foster, 1990;Maurer, 1990).
20416962, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/sjp.12516by Cochrane Germany, Wiley Online Library on [26/05/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Johanna had no philosophical interest, as she explicitly stated.Whereas in her work, above all, one finds concrete reports on the landscape, on cities and sights, as well as on customs and traditions in individual concrete countries (Martin, 2004b), in Arthur's work there are several passages in which he reflects philosophically on travel as such.He laments the fleeting nature of travel impressions or the fact that constant travel can only provide a superficial acquaintance with the character of people.Arthur Schopenhauer, however, is also of the opinion that "novelty and the complete strangeness of the objects" (Schopenhauer, 1911-1942, II, p. 421) serve as an impetus to travel at all.He shares this thesis with Thomas, who advocates travel based on otherness or encountering the unfamiliar in several places (Thomas, 2020a, esp. ch. 1).
One passage in Schopenhauer's philosophical writings goes beyond the aforementioned musings on travel, offering a complex argumentation analysis on the subject.This argumentation analysis is found in § 9 of the main work Die Welt als Wille und Vorstellung (The World as Will and Representation), published in 1818.In this paragraph, Schopenhauer outlines two disciplines of theoretical philosophy, namely, logic and eristic.Logic is a monological discipline that is primarily concerned with examining the validity of arguments.Eristic, on the other hand, is a dialogical discipline that focuses not on the validity but on the persuasiveness of an argument (Chichi, 2002).Following Kant's famous distinction, Schopenhauer also calls logic "analytic" and eristic "dialectic."Both disciplines are closely related as Schopenhauer's eristic presupposes knowledge from logic.
Prior to the mid-2010s, Schopenhauer's logic and eristic were seldom taken seriously.This was due to the fact that the above-mentioned § 9 only comprises a total of just under ten pages.Schopenhauer contends that his ordinary readers do not really need to concern themselves with these topics, since everyone has already acquired an instinctive mastery of logic by learning the grammar of their mother tongue (Schopenhauer, 2010, p. 69).Consequently, logic is only of interest to academic philosophers.
What did gain prominence in the twentieth century was an unfinished manuscript by Schopenhauer on eristic, known today under the title Die Kunst Recht zu behalten (The Art of Being Right).This title is misleading, however, as Schopenhauer is not concerned with an art as an instruction, but with a descriptive doctrine in order to protect oneself from dishonest discussion partners (Hordecki, 2018).Therefore, a more appropriate title of the manuscript is Eristische Dialektik (Eristic Dialectics).
In the mid-2010s, however, the manuscripts of the so-called Berlin Lectures that Schopenhauer wrote in the 1820s were examined more closely for the first time.Schopenhauer wrote these for an academic audience with the intent of extensively exploring logic, as it was the most important discipline of academic philosophy alongside the philosophy of law (Schopenhauer, 1911-1942, IX, p. 72).The result is an approximately 150-page manuscript on logic and eristic that sheds new light on both § 9 of the main work and the unfinished manuscript on Eristic Dialectics.Of particular interest are the diagrams Schopenhauer employs throughout the Berlin Lectures, which are better explained than those in his more well-known writings on logic and eristic.Among other things, this makes the argumentation analysis of traveling, which is found in § 9 of The World as Will and Representation, more comprehensible.
In his examination of dialectical eristic, Schopenhauer takes the example of traveling to show that arguments can be formulated for both positions, for and against.The argumentation processes are as complex as they are small-step, but they are similar in that one argues either in one direction or in the opposite.Schopenhauer uses logic diagrams to demonstrate how complex and diverse these argumentation processes can be (Moktefi, 2020).He distinguishes between six different diagrams used in logic to test the validity of arguments and in eristic to outline the course of arguments.Figure 1 illustrates how concepts are represented as circles, whereby Schopenhauer himself speaks of "spheres."The circles indicate the relationship between two concepts to each other or to a third concept and can therefore be called relational diagrams (RD).
In order to understand the goal of the eristic dialectic, we have to take a look at Schopenhauer's ethics: Schopenhauer assumes that reason is neutral (Schopenhauer, 2010, pp. 112-113).It can be used for good or for bad.The latter is reminiscent of the Frankfurt School's realization that there is an instrumentalization of reason and that reasoning and logical arguments can be directed toward not only purposes that benefit all, but also toward selfish or immoral purposes (Brunero, 2020).Representatives such as Max Horkheimer or Alfred Schmidt have frequently noted their affinity to Schopenhauer (Michaelis, 2023).For Schopenhauer, it is true that if reason is used for the good and the moral, the discussion partners argue purely logically, that is, they make an effort to exchange valid arguments.However, if reason is instrumentalized for the worse and the immoral, the discussion partners will focus solely on persuading the other side to accept their argument, regardless of its validity.
In any case, Schopenhauer's eristic dialectic is not a normative art of being right, as it has often been misunderstood, that is, it is not a guide to bad but profitable argumentation (Chichi, 2002;Gutenberg et al., 2020).Rather, Schopenhauer understands himself as an Enlightenment philosopher who wants to give his reader a proven means of recognizing invalid or nonnecessary arguments in dialogue (Lemanski, 2022, p. 158ff.).All the arguments that eristic dialectic examines do not necessarily have to be accepted.They represent opinions that may or may not be shared by others.If they are not shared, the dishonest dialogue partner may even use tricks to make the arguments appear valid after all (Chichi, 2002).These tricks are usually woven into the dialogue as sophisms or stratagems, but according to Schopenhauer they depend on a merely cursory inspection of the relationships between conceptual spheres, which can then be determined as lying on either one side or the other according to the speaker's intentions.This generally happens in the following way: if the sphere of the concept under consideration lies only partly within a second sphere, but also partly within a third, completely different sphere, the first concept is declared to be completely contained within the second, or completely contained within the third, whichever suits the speaker's purpose.(Schopenhauer, 2010, I, p. 72) An unfair opponent would therefore proceed by presenting an argument using RD5 as if it were an argument in that RD2 are involved (cf. Figure 1).The unfair opponent thus represents a partial semantic intersection of two concepts (RD5) as if one concept were a proper subset of the other (RD2).Therefore, it is possible to speak of a replacement of RDs.In many cases, this is unproblematic as both speakers could agree about a nonnecessary argument.However, in cases where opinions differ about a fact and one speaker convinces another by presenting this fact as necessary, although it is not, and the opposing side allows itself to be deceived by this, an eristic argument occurs.According to Schopenhauer, this is made possible at all by the fact that concepts have a certain affinity, whereby one can reach an argumentative goal via longer paths: Schopenhauer (1911-1942, IX, pp. 269-284).I am not aware of anyone so far who has traced the essence of all sophistic reasoning and persuasion back to this, the most fundamental ground of their possibility, or shown how this possibility lies in what is most characteristic of concepts, i.e., in reason's own method of cognition.Since my presentation has led me to this point, I would like to make the issue even more clear (although it is not hard to comprehend) using the schema presented in the following table.This table [i.e., Figure 2] is intended to show how conceptual spheres overlap each other in such a multitude of ways that there is enough elbow-room to pass from one concept to any given other one at will.(Schopenhauer, 2010, I, p. 73) Schopenhauer does not give much more information on this subject in § 9 of The World as Will and Representation.He states that the whole subject is not particularly important.However, he revised his opinion in the following years, as he intended to write a whole treatise on the subject by the beginning of the 1830s.This is the above-mentioned manuscript Eristic Dialectics.However, he stopped working on it, as he could no longer endure the wickedness of mankind that it exposes.Here, in The World as Will and Representation, the only example available can be called an argumentation analysis of traveling: I have chosen the concept of travel as an explanatory example.Its sphere overlaps with four others so that a persuasive speaker may pass at will into any of them; these in turn overlap other spheres, many overlap two or more other spheres at once, and the speaker can continue plotting a course through them as he wishes, treating it as the only way, and finally ending up, according to his original intention, with either good or evil.The only requirement is to follow the spheres outwards from the centre (the main concept given) to the periphery without going backwards.Such a piece of sophistry can be dressed up either in continuous speech or as a rigorous syllogism, as the weakness of the listener suggests.(Schopenhauer, 2010, I, p. 73) This puts all the important information about this argumentation analysis of traveling on the table.Schopenhauer did not provide any further written material on the argumentation analysis of travel, believing that Figure 2 should speak for itself.This figure depicts a large collection of RDs that, like a map, indicate certain paths that go "from the center (the main concept given) to the periphery" with "good" on the left and "evil" or "bad" on the right.Even though Schopenhauer explains to his general audience that the topic is not so significant, he elaborates on it further in the Berlin Lectures (Schopenhauer, 1911-1942, IX, pp. 363-366), draws several more diagrams on eristic, and even shortly before his death, Schopenhauer comes back to the topic and revises the diagram of traveling with a new strand of argumentation (Lemanski, 2023).
As far as we know today, Schopenhauer is the first to have designed this form of diagram to analyze the concept of travel.He also designed other diagrams of the same form to analyze other subjects in a similar way.As already enumerated in the introduction, there are various logics that have revisited and continued Schopenhauer's diagrammatic idea.The first adaptation of Schopenhauer's diagrammatic type can be found in Denzinger's work as early as the 1820s.At the end of the 1890s, Höfler and Meinong also refer to the travel example in their logic.In the twentieth century, Schopenhauer's diagrams fell into oblivion.For the nineteenth century, therefore, we can assume that Schopenhauer's approach was taken seriously, as it was often adapted by his contemporaries.Since Schopenhauer worked most intensively with these diagrams and all mentioned authors attribute them to him, I will refer to them as Schopenhauerian diagrams or Schopenhauerian argument maps.

| DI AGR A M S , M A P S , A N D GR A PH S
In Section 2, I provided a brief overview, using a few quotations, of the argumentation analysis of travel that Schopenhauer proposed.The distinguishing feature of this argumentation analysis is that it is based on diagrams.
As we have seen, Schopenhauer revisited the diagrams he developed in logic and employed them in eristic, creating large maps.In fact, Schopenhauer's approaches to this have already been associated with both terms, "diagram" and "map."However, both are retrospectively applied terms: neither Schopenhauer nor any of his successors in the nineteenth century speaks of diagrams or of maps by referring to Figure 2. When Schopenhauer indicates Figure 2, he only uses the topic-neutral term "table," as we have seen in the quotes given in Section 2. What we refer to as "diagrams" or "RDs" are in his words "schemes," "circles," or, even more frequently, "spheres," without giving a more precise explanation of these terms.
It has been argued from various directions so far that the RDs are "diagrams" (Moktefi, 2020) and that Figure 2 is a "map," or, more precisely, an "argument map" (Lemanski, 2023).Other authors even speak of Figure 2 being a map showing one or more "graphs" (Bhattacharjee & Lemanski, 2022).A philosophy of diagrams, maps, graphs, or the like did not exist in Schopenhauer's time, and it will probably not be possible to compile it from Schopenhauer's remarks.Schopenhauer himself does not use the term "diagram" in any text known to us, and he speaks of maps only very rarely.The beginnings of graph theory had already been laid with Euler, whom Schopenhauer read, but the term was not in common use.
In Section 2, we accepted that the diagrams presented in Figure 1 are referred to as RDs.Therefore, it is reasonable to extend this acceptance to the inclusion of diagrams in Figure 2.While we may refer to Figure 2 as a "large diagram," the question arises whether it is appropriate to label it as a "map" or even a "graph."In this section I would like to support the existing theses that Figure 2 is a map and that it can be interpreted as a graph.To do so I will use the definition of maps that can also be found in Thomas.However, it is important to note that I will only support the existing theses from the perspective of the philosophy of traveling.A comprehensive discussion of why Figure 2 is a map from a modern perspective would require more detailed definitions of maps.But that would go beyond the scope of this section.
Thomas's second chapter delves into maps and tackles some definitions.Her first preliminary definition of what constitutes a map is as follows: (1) a "map is a 'visual representation' of 'any part of reality'" (Thomas, 2020a, p. 14).This definition, according to Thomas, is not perfect, but it emerges from her critique of a geography textbook that claims that maps are a picture that represents Earth's surface or parts of it.However, Thomas proves that maps do not have to be pictures and that they can represent much more than just Earth or just surfaces.In the course of the chapter, however, further theses are added to (1) that soften this definition (p.17ff.).A few of Thomas's central theses are worth highlighting: (2) "maps are seeking to persuade or influence their readers" (p.17); (3) the center of the map is significant; (4) maps represent social constructs; (5) there is a choice of what is important and elements are valued differently; (6) maps are a means of communication; (7) maps are not things but processes (in the sense of metaphysics); and (8) maps depend on the human mind.
Thomas's argumentation in this chapter can be examined critically.For example, there is evidence that not only humans possess a cartographic ability, as Elisabeth Camp (2009), for example, has argued.So there are good reasons why (8) is not true, even if Schopenhauer as an idealist would certainly have sympathized with it.Moreover, it is not always clear how the individual qualities relate to each other; ( 5) and ( 6) are likely to be dependent on (4), although in my opinion this is not made sufficiently clear in Thomas's text.However, we also have to take into account that not every definition comes from Thomas herself but has also been taken from the literature.
Nevertheless, one can work well with the definitions and properties (1)-( 7) given by Thomas for the time being.We first give a rough overview of how ( 1)-( 7) apply to Figure 2 and then discuss some points in more detail.
1. Figure 2 is a visual representation of a certain part of reality.If we consider arguments as part of reality, then we can interpret Schopenhauer's Figure 2 as a map in the sense of Thomas's provisional definition.This is provisional in the sense that anything that is part of reality can, by definition, be a map.Therefore, we need to revisit this point and discuss narrower definitions beforehand.2. Figure 2 aims to convince us that arguments of dialectical eristic can be presented as Schopenhauer did with his spheres.A self-application argument occurs in the process: Schopenhauer does not only want to convince us as readers with Figure 2, but also to represent convictions in argumentative transitions themselves.3. The center is also significant in Figure 2, as this is the starting point of the argument, as Schopenhauer explicitly states in one of the quotes given in Section 2. We start in Figure 2 with the concept in the center, that is, travel, and then follow the course of RD5 to the periphery, either right or left.So there are elements in Figure 2 that are more important than others.Schopenhauer marks the center by drawing the circle in some of his maps thicker and larger than all other circles in the vicinity or by capitalizing the central term.4. Figure 2 represents social constructs; it shows conceptual relations and thus also shows conceptual boundaries as they are understood by at least one argumentation partner (or an observer of an argumentation).5. Figure 2 also gives a selection of what is important, and elements are evaluated differently.
For example, we can imagine that there are lines of argumentation that are not represented by Figure 2, for example, the question of whether it is ethical to travel to a country when there is a famine there.This may be a more important argument for some travelers than the fact that travel is gained through new experiences.6. Figure 2 is at least one means of communication between Schopenhauer as the author and us as readers.This is already evident in the fact that Schopenhauer does not give a verbal argument, but only the map.It alone is intended to show us how one can argue either for or against travel.Furthermore, Figure 2 can also serve as a means of communication between two people who want to agree on a course of argument.For example, let us think of a lawyer and his client.The lawyer could use Figure 2 to show his client what consequences could follow if his client concedes individual partial arguments.But it could also facilitate intrapersonal communication, where I want to be clear about certain arguments myself.7. Figure 2 is also a process.This can be observed very well in the fact that Schopenhauer, in his old age, changed the map in such a way that he added several conceptual spheres (urn:nbn:de:hebis:30:2-259336). Figure 2 is therefore also not unchangeable, it can be modified in various ways.
(1)-( 7) indicate that it is possible to read Figure 2 as a map.Definition (1), however, has proved problematic, as Thomas herself suggests, since everything that is a part of reality becomes a map somehow.However, Schopenhauer's verbal description draws attention to the fact that Figure 2 bears a resemblance to a road map; through the RD2, several terms are depicted in their relation in such a way that they produce chains of RD2 that look like a "way" to "follow," to "pass," to "go," or "to continue" as quoted in Section 2. Later interpreters, such as Moktefi, have also taken up this metaphorical designation of the map by speaking of "routes" or "paths" (Moktefi, 2020, p. 123).These ways, according to Schopenhauer, lead from the center to the periphery (Schopenhauer, 2010, p. 73).This is reminiscent of maps where we observe traffic roads leading from the capital to the rural areas or leading from the main railway station to the individual city districts.A common feature between road maps, transit maps, and Schopenhauer's Figure 2 has been worked out by Bhattacharjee and Lemanski (2022).Graph theory provides a mathematical theory that indicates abstractly as edges and vertices what the aforementioned maps indicate concretely through roads and residential areas, railway lines and stations, or conceptual relations and concepts.I want to take up this graph-theoretical approach here as well and interpret the center as a source vertex and the periphery as a sink vertex (Figure 3).Using this approach, I translate the concrete map of Figure 2 into an abstract graph in Figure 3.In doing so, it is possible to overlay Figure 3 on Figure 2 and see that each edge corresponds to a concept and each vertex to a concept relation.Such an overlay can be seen, for example, in Figure 4 or Figure 6.Of course, it is possible to arrange the graph with the same elements in a completely different way.And at first glance it may seem confusing that Figure 3 does not show a connection in the center.However, as Bhattacharjee and Lemanski have demonstrated, Figure 3 is the most effective translation of Figure 2.
Figure 3 is a disconnected directed graph, that is, a forest including four trees (Diestel, 2005, sec.1.5).Here, each intersection of an RD has been interpreted as a vertex and the connections between them as edges: v1, v9, v13, and v17 are the source vertices where "traveling" is related to another concept; v8, v12, v23, and v30 are the source vertices where a concept leads to "good" and v16, v39, and v44 are the source vertices where a concept leads to "evil."Thus, the vertices do not indicate concepts but relations between at least two concepts.And relations between concepts are expressed linguistically in propositions or judgments: for example, v1 stands for the proposition "traveling is healthy," v2 for "healthy is invigorating," and so on.
Thus far, it has been argued that Figure 2 is a map because it bears a resemblance to maps due to the properties elaborated by Thomas.We have also noticed by the use of metaphors and by the translation into graph theory that it is also possible to establish a similarity between Figure 2 and certain maps, namely, road maps or transit maps.However, as Figure 2 does not depict roads or rails, it would be misleading to call it a "road map" or similar.Instead, Figure 2 represents a multitude of concepts.In this respect, it is possible to consider Figure 2 as a "concept map," showing semantic relations between concepts.
As we have seen above, not only can semantic overlaps between concepts be read, but the vertices can also be translated into propositions such "traveling is healthy."Some concept maps can do that too.However, a number of propositions add up to whole arguments.For example, in Figure 3 an entire argument is either a tree or, in the tree beginning with v17, a subgraph of a tree.In other words, Figure 2 depicts how one can argue that a central concept such as traveling is either good or bad.Thus, Figure 2 can do more than a concept map and can for various reasons be called a "Schopenhauerian argument map" (Lemanski, 2023).
The exact designation of Figure 2 may not carry significant weight, but discussing its definition certainly offers more precise insights into Schopenhauer's methodology and the functioning of maps, particularly argument maps.Although Schopenhauer knew maps, he did not explicitly point out the similarity between them and Figure 2.However, it becomes apparent that using the term "map" is justified, and describing Figure 2 as an argument map makes sense.Schopenhauer's choice of the example of traveling in his brief explanation of the diagram type may not have been a coincidence, as the diagram itself displays various travel routes.Nonetheless, we must keep in mind that Schopenhauer used his argument map to illustrate other concepts and topics in eristic dialectics.
Anyway, since our aim is to analyze the philosophy of travel with the Schopenhauerian argument maps, it is advantageous that Schopenhauer and other authors used "travel" as a starting point to describe the diagram type.The exact advantages of this map type, however, remain to be explored in the next section.In Section 3 it was argued that Figure 2 is a kind of map.It has certain similarities with concept maps, but it also shows entire propositions and argumentation processes.In this respect, the description "argument map" fits best, even though Schopenhauer's map introduces a distinct type of this genre.A central property of many argument maps is that they can be read as graphs (Lemanski, 2023).This holds true for Figure 2, as demonstrated in Figure 3. Consequently, I concur with prior scholars who have also interpreted Figure 2 as a graph.Both forms of representation, diagrams, and graphs, have their respective strengths and weaknesses, and they also have advantages and disadvantages over the verbal representation found in Thomas.The aim of this section is to identify these strengths and weaknesses more precisely, not for the sake of comparison, but to develop an improved argumentation analysis of traveling in Section 5.

F I G U R E 3
Figure 3 has advantages over Figure 2, but also disadvantages: One advantage is that by indexicalizing the vertices and edges we can state linguistically exactly which element on the map we mean.We no longer have to rely on indeterminate labels, such as "the third circle to the right of 'traveling,'" but we can say directly whether we mean e13 or v42 (or indeed a completely different circle).That we cannot simply denote Figure 2 by the words given in the circles is already evident from the fact that we have several words that appear at different positions in the diagram, for example, "enriching" is given at e7 and e16.
One could argue that Figure 3 is somewhat akin to a syntactic version of Figure 2, which in turn can be considered a semantic version of Figure 3. Nevertheless, Figure 2 has the advantage of providing a visual representation of a large amount of information.We only encounter circles and words in Figure 2, but by understanding how to read the argument map, numerous propositions of various arguments soon pop up before the mind's eye.
However, this advantage of Figure 2 also brings problems.As Moktefi has shown, the reading of the RDs in eristic does not always coincide with the reading of the RDs in logic (Moktefi, 2020, p. 123).For example, let us look in Figure 2 at the relationship between the concepts "profitable" and "useful," that is, e5 and e7.Both have no intersection and would therefore have to be read like RD3, that is, as contradictory concepts.However, this is probably not Schopenhauer's intention, since-following the general folk ontology-he would probably admit that both concepts have a strong commonality.What Schopenhauer probably wants to point out, however, is that a mediating concept such as "enriching" is needed to explain the relationship between "profitable" and "useful." That said, there are definitely concepts that are in RD3 relation and are contradictory: "good" and "evil" or "enriching" and "losing," for example.Not all circles in RD3 relation therefore depict oppositional concepts, but some do.As a rule of thumb, all concepts that are either to the left or to the right of the central concept "traveling" in a tree are not oppositional concepts, but if one concept is to the left and one is to the right of "traveling," then they might be.This ambiguity of RD3 can initially make the map more challenging to interpret.However, as Thomas suggests, we humans are accustomed to quickly interpreting syntactically ambiguous information correctly on maps (Thomas, 2020a, p. 14ff.).For instance, even on a black-and-white map, we can quickly identify that some lines are national borders, others are roads, and still others are contour lines.
One can criticize Schopenhauer's map even further, particularly with regard to the repetition of concepts and the directionality of the graph.For instance, some concepts occur twice and in such a way that they produce the same propositions and even longer chains of propositions.This is the case, for example, with e6 and e7 in comparison with e25 and e26.However, we must admit that we have all made an acquaintance with the fact that similar or the same propositions can arise in different argumentation processes.Another point of criticism, however, concerns the directionality and the cycle of Figure 3.The interpretation of Bhattacharjee and Lemanski goes back to a directed graph, because Schopenhauer said in the last quotation cited in Section 2 that one should "not go backwards," but always in a straight line from the center to the periphery.However, this should not correspond to our intuition, since we often pick up a thread of conversation again, revisit accepted arguments, and then build alternative ones.The directionality of the graph may correspond to Schopenhauer's understanding of argumentation processes, but probably not to the general one.
This problem leads us directly to the fact that some subgraphs of Figure 3 may be cycle-free, but one contains several cycles if the graph is interpreted in a nondirectional way (Diestel, 2005, sec. 1.3).Suppose two persons, p and q, are in a discussion: p wants to argue that traveling is useful and tries the path from v17 to v30.q accepts several arguments, most recently e20, but then not e21.So v25 seems unreachable for p for now.But now p can choose the strategy of going out to e28 in order to then get to v25 via e27.So we have a cycle here, and this might be more in line with our intuition about the course of conversations, because after all, after rejecting an argument from our discussion partner, we do not directly start again at the beginning of the dialogue.Furthermore, it is strange that Schopenhauer includes cycles in some subgraphs, but not in others.
As we have seen so far, Schopenhauer's argumentation analysis of traveling has its advantages and disadvantages.The last-mentioned points of criticism are motivation enough to offer some considerations in this section that could improve Schopenhauer's argumentation analysis of traveling.The last points of criticism were obvious: the cycle, the directionality of the graph, the repetition of concepts and propositions, and the ambiguity of the RDs.
One advantage of Figure 2 is certainly the harmonization of complexity and readability: Schopenhauer's circle diagrams give a lot of information in a small space.If the logic diagrams are also combined with graphs, there are good possibilities for describing relations on the one hand, but also for sketching conversation paths precisely, on the other.
These advantages can be demonstrated, for example, by pointing to numerous arguments in Figure 2 that Thomas also develops in her book by interpreting quotes from individual philosophers.For example, Thomas gives several arguments why travel is good because: it increases our knowledge (Thomas, 2020a, pp. 6, 73); itprepares us for public duties (p.29); it promotes science (p.42); one stores experience(p.50); it enhances prestige (p.73); it is enriching (p.74); it produces peace of mind (p.125); or it is exhilarating (p.184).However, Thomas also brings out arguments against traveling, for example, that traveling increases desires (p.75), is risky and loss-making (p.75), or is dangerous (pp. 78, 112ff., 131ff.). Figure 4 presents both positively and negatively connoted concepts.
Schopenhauer thus seems to make almost as many arguments with one diagram as Thomas does in her whole book.A diagram is worth more than thousand words, says a famous thesis (Larkin & Simon, 1987).By presenting the above-given page references in Figure 4, one can even read Schopenhauer's diagram as a map showing an orientation about the location of arguments in Thomas's book.By perusing the diagram as a navigational tool, one can easily identify the exact sections of Thomas's book where each argument is discussed.In this case, Figure 4 has a similar function to an index map.
Nevertheless, these observations are unjust if they are perceived as a disadvantage of the book rather than an advantage of the diagram.The diagram lacks the eloquence of the book; it cannot even map the precise rhetoric of a proposition; and in terms of content it lacks further arguments, such as the inconvenience of travel (Thomas, 2020a, p. 84) or the aspect of environmental pollution (p.181), which Thomas presents in more detail.However, one point is not clear at first glance: namely, regarding the contextualization of the arguments and validity.
At first glance, the disadvantage of Schopenhauer's diagram relates to the fact that the arguments are not contextualized as in the book.For instance, Thomas identifies the philosopher who originated or expounded on a particular argument and offers insights into their reasons for doing so.The propositions in the book also contain indicators of what constitutes data, warrant, or claim, following Toulmin's DWC-model.Schopenhauer refrains from such contextualization but instead offers the context of possible courses of conversation that leave room for multiple variations in the formulation and use of concepts.
In Section 4, we have observed that each form of representation for argumentation analysis of traveling has its own set of advantages and disadvantages.In verbal-propositional form, we already find quite good approaches for an argumentation analysis of "traveling" in Thomas.Schopenhauer and his successors, however, developed complex processes of argumentation that are not found in Thomas.Nevertheless, these diagrammatic representations also have their shortcomings, and it is necessary to transcend Schopenhauer's ideas in order to analyze the concept of traveling in a more precise manner.
The first step towards surpassing Schopenhauer's ideas is to ask how diagrams and graphs can be verbalized.Let us take an example from Thomas (2020a, p. 6), which contains arguments by several philosophers such as Montaigne and Descartes that travel is good or useful because it brings new experiences.In contrast, Schopenhauer offers a more nuanced approach.While he, too, acknowledges that one can argue that travel is good, he gives the concepts of usefulness and experiences a smaller role in a more differentiated argument.A possible course of argumentation in which p introduces the aforementioned concepts to q could be reconstructed and verbalized as follows: This example is a verbalized form of the Schopenhauerian argument map or at least a section of it, going from v17 to v30.Such a verbalization of parts of Schopenhauer's eristic has been done before by Fouqueré and Quatrini (2012), interpreting the individual propositions as actions (K).Although this verbalization could be analyzed and discussed in all its facets over several pages, we are more interested in presenting an example of how to analyze certain arguments given in Thomas by applying an improved Schopenhauerian argument map.
First, let us examine which actions (K) we also find in Thomas. In Thomas (2020a, p. 6), K1, K7, K9, and K12 are given in more abstract terms.If we disregard the intermediate steps K10 and K11, which only serve to justify why "useful" and "good" are in an RD2 relation, Schopenhauer's progression through actions K2-K5 is more small-step.In contrast to the diagram (Figure 2), however, it is yet possible to use the verbalized form of the example to distinguish between data, warrant, and claim: K1 and K7 are data that become a claim in K10 because they are backed up by K3-K5, K7, and K9.
To make it clear how p aims to convince his discussant q that "useful" and "good" are in an RD2 relationship, it makes sense to use diagrams.However, since the diagrams cannot represent the course of the conversation, it is helpful to superimpose graphs on the diagram, that is, to combine Figure 2  Moreover, we can improve Schopenhauer's maps by dividing the diagrammatic elements into data, warrant, and claim, as Toulmin's scheme does.Since each action is an edge in the graph, the edges can also be distinguished by their shape to be able to assign who performed which action.An example of such an enhancement can be obtained from Figure 5. Here, K1-K5 have been depicted: the actions of p are a straight edge; the actions of q are sinuous.Data are represented as vertices in completely gray intersections and warrants in intersections that are hatched.This example should suffice to demonstrate that Schopenhauer's maps can be improved in many ways.
Furthermore, it remains important to improve one step that is not clear enough in Thomas's verbal and in Schopenhauer's visual presentation: all arguments are not necessary; they are dialectical in nature, so they can be accepted or not.Thomas's book, for example, is a treasure trove of arguments, but the author wisely does not place too much emphasis on any of them.There exist compelling arguments in support of traveling as well as arguments against it.RD2 between "useful" and "good" can be understood as an argument that p uses to convince q that this is a necessity: in all possible worlds, what is useful for p is also what is good.But whether q accepts this is another question.In this respect, we would do well to introduce a valued graph, where the transition from one proposition to the next is assigned an absolute value.This would indicate how high p's expectation is that q accepts the argument.Such a fictitious value could be added to Figure 5.But this would have to be elaborated in more detail.
Finally, we have to go beyond Schopenhauer on one point.So far in this section, we have been less concerned with content and more with form.But if we look at the concepts and the represented propositions in Figure 2, we notice the following: each route in Figure 3   represents a certain theme, a kind of thematic strategy to reach the sink vertex.These represent different positions or isms that can be found in practical philosophy today; v8 and v30 could be described as a positive approach to utilitarianism, whereas v25 and v26 point to a political dimension, but v5, v6, and v7 more to an economic one.The directed subgraph with the sink vertex v12 appears hedonistic, while v23 seems to be stoic in character; v16 is negative-economic, v44 antistoic, and v39 can be described as utilitarian in the sense of risk ethics.In this case, it would be a position that is risk-averse and sees no benefit in traveling in balance with the risks involved.
Figure 6 shows this described assignment in the diagram in the form of seven clusters.The fact that argument clusters can be depicted to show the isms or positions means that Schopenhauer probably did not create the individual trees arbitrarily, but rather imagined certain argumentation partners who represented certain positions or isms.If one wants to apply Schopenhauer's argument maps to other subject areas outside the philosophy of travel and plan possible courses of argumentation with the help of these maps, one could question which arguments to attribute according to which positions or isms and thus argumentation maxims.
However, Figure 6 also demonstrates that entire themes are missing that Schopenhauer did not depict in his map, but of which Thomas offers some, for example, the environmental-ethical aspect that speaks for or against traveling or the gender perspective.This also highlights that Schopenhauer's example is incomplete from a contemporary viewpoint and requires further supplementation.Furthermore, it demonstrates that Schopenhauer's map is not complete from today's perspective, as additional trees can be constructed to show the missing perspectives and topics.Overall, therefore, the argument maps from the nineteenth century complement each other very well with today's philosophy of travel, since the one displays and systematizes detailed arguments that the other overlooks, while the latter portrays a bunch of perspectives and positions that were not even in view in the nineteenth century.

| CONC LUSION A N D OU T LOOK
Schopenhauer's argument maps depict potential lines of argument in a dialogue and arrange them based on the interlocutors' stances toward a specific topic.In the case at hand, the topic relates to the essential query of whether one supports or opposes travel.Therefore, the discussion is not about whether to endorse a particular journey or not, but whether travel, in general, is good or evil, beneficial or harmful.As such, the argument maps offer a valuable contribution to the field of philosophy of travel, which has been relatively overlooked thus far.
In this article, I have tried to enrich the philosophy of travel with precisely this diagrammatic approach from the nineteenth century.At the same time, however, we have seen that this nineteenth-century form of argumentation analysis, while a profitable idea for constructing argument maps, needs to be greatly modernized.Therefore, Schopenhauerian argument maps give an important contribution both to the philosophy of travel, but also to the presentation and analysis of arguments.
Schopenhauer created a diagrammatic technique to map nonnecessary courses of argumentation.This is the basic objective of eristic dialectics.An argumentation analysis of traveling with Schopenhauer's argument maps has some advantages and disadvantages.Several disadvantages could be overcome by providing more precise reading instructions for the diagram and supplementing it with graphs.In addition, a proposal was made to include further graphical elements to adapt Schopenhauer's argument maps to those of Toulmin, among others.However, the improvement of Schopenhauer's method is not yet complete.Numerous improvements can still be imagined, for example, the calculation of the extent to which an argument is likely to be used.However, this depends on how Schopenhauer's maps are applied, whether for evaluating already existing argumentation processes, for representing actual discussion, or for planning potential arguments.
While a complete argumentation analysis of all arguments for and against traveling is beyond the scope of this article, the diagrammatic representation offers a more small-step approach than a verbal description.However, not all argumentative paths adopted by Schopenhauer were thematically complete or contemporary.Nevertheless, the method described here is sufficient for future research in the philosophy of travel to organize and discuss the arguments missing in Schopenhauer's work or to systematize Thomas's treasure trove of arguments more rigorously.
Furthermore, Schopenhauer's argumentation maps are not limited to the philosophy of travel alone.Schopenhauer already used maps of the same type to examine other concepts.The argumentation maps represent a universal method for describing, analyzing, or planning evaluations of various concepts and courses of argumentation.It is conceivable to exchange not only the concept of traveling and the related concepts, but also the target concepts.Instead of good and evil, it is certainly possible to use contradictory value concepts such as positive and negative, meaningful and meaningless, useful and useless, desirable and undesirable, and many others.

AC K NOW L E DGM E N T S
This paper is supported by the Fritz Thyssen Foundation (project: History of Logic Diagrams in Kantianism) and benefited from the ViCom-project Gestures and Diagrams in Visual-Spatial Communication funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-(RE 2929/3-1).Furthermore, I would like to thank the two anonymous reviewers for many valuable comments and suggestions for improvement.Open Access funding enabled and organized by Projekt DEAL.

20416962, 0 ,
Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/sjp.12516by Cochrane Germany, Wiley Online Library on [26/05/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License with Figure 3.This is because a directed graph can show the course of 20416962, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/sjp.12516by Cochrane Germany, Wiley Online Library on [26/05/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License actions.In this way we get the best of both depictions, that is, the information on the content from the diagram and the realization of the actual course of the dialog in the graph.

F
Example for an enhancement of Schopenhauer graphs.F I G U R E 6 Isms clustered in Schopenhauerian maps.