1 Introduction

There are, we might be tempted to suppose, three protagonists: a subject, an object, and a relation of cognition that connects them. The subject gets to know the object, and the object becomes known by the subject. Getting to know the object is a complex process.¹ A first and naive approximation of that process might be the view that holds that within the subject certain presentations occur,² these being some form of mental duplication amounting to something like a photographic copy of the object that the subject seeks to know. The more exact the photographic duplication, the more adequate the cognition of the object.

That viewpoint is false, for at least two reasons. Firstly, cognition cannot be confined to instances of photographic mirroring, as in that case how would we get to know such abstract objects as Hilbert spaces? What would the copies of these objects be?

Secondly, the totality of what counts as getting to know an object cannot be equated solely with the adequacy of that object’s presentation. Presentations furnish the basic elements of cognition: they are the beginning of the cognition process, and as such do not themselves exhaust the entire cognition process. Amongst the components omitted by such an account there is, at the very least, the final result of cognition: i.e., the making of a judgment.

It is, in a certain sense, judgment that is the decisive factor (Ingarden, 1972), with the ineluctable role of the subject being to validate cognition. This is because the judgment we make about an object we seek to know constitutes the crowning moment of that object’s cognition. Hence, the correct conclusion in this respect is that cognition does not create a photographic copy of the object of knowledge. But what, then, does it amount to?

Let us use the following analysis as a first approximation of the object’s presentation, construed as the basis of cognition (Twardowski, 1977). The presentation of an object consists of three strongly interlinked components: the process (act) of presentation, the content of presentation and the object of presentation. The object of presentation is presented through the content of the presentation in the act of presentation. Our viewing the object of presentation through the content of the presentation is something to be analyzed via the decomposition of both object and content into their respective parts. The relationship between these parts can then be analyzed.

The relation obtaining naturally between some part of the content of presentation and some part of the object of presentation will be a certain correspondence. Should this be absent, the content of the presentation will not target the object, and the object of the presentation will not be adequate to the content of the presentation. We might expect to arrive at an understanding of that relation through observation and analysis of the results of their division into their respective parts: i.e. by differentiating the parts of the object of presentation and of the content of presentation. The key issues we aim to reflect on are the following: How do the parts of a presentation correspond with those of the object of presentation? How many parts of the content of presentation correspond with those of the object of presentation, and vice versa? In what way do the parts of the object of presentation correspond with those of the content of presentation? How many parts of the object of presentation correspond with the parts of the content of presentation? Our analysis will be carried out in the context of this sort of understanding of what correspondence amounts to.

The structure of the present article is therefore as follows: picking up from where Twardowski (1977) left off, I aim to render in more precise terms the concept of an object, to differentiate its parts, and to spell out in detail the relation of correspondence between the object and content of presentation. Next, I formulate and seek to justify my main thesis, to the effect that the presentation of complex objects is always a simplifying one, in the sense of one that omits some parts of the object, but – what is more – at the same time also an enriching one, in that it introduces into the object of presentation some parts which the latter does not itself have. The validation of this thesis proceeds via not one but two paths: through analysis of cognitive experience, and formal analysis of an object and content understood abstractly. The experience-based analysis is mainly based on the contribution of Twardowski himself, while the formal analysis aims to enhance our understanding the complexity of cognition through topological modeling, and in particular through the notion of types of dimension as introduced by Fréchet.

2 The Object and Content of a Presentation

Everything that is something is an object – that is, anything that can be presented. The totality of objects is coextensive with all that is something. In this wide sense, an object can be either real, like the sadness of some person, or unreal, like an angel or a square. It can exist – an example of an existing object would be the Academy of Young Scholars and Artists in 2016 – or not exist, like the Academy of Young Scholars and Artists in 2005, which is also an object, but a non-existent one. To put it briefly, “everything which is not nothing, but which in some sense is ‘something,’ is an object” (Twardowski, 1977, p. 35).

Objects can be possible, and they can be impossible. An apple lying on the table in front of me is a possible object (and one existing in reality), while a square circle is an example of an impossible object. Objects are not limited to things – to assert that they are would surely be a questionable view, as things are only one sub-category of the category of objects. V(D)J recombination, or the creation of a stage character by an author, are not things, but they are objects; the same goes for the Stoic postulate of the premeditatedness of evil, mannerism, the measure of disorder, and many other objects about which the authors of texts included in this volume write.

The object of presentation is viewed through the content of presentation, in the act of presentation, where this is similar to the way a painter records a topic on a canvas through the picture, in the act of painting. Within this analogy, the topic corresponds with the object (e.g., the landscape), the picture corresponds with the content, and the act of painting corresponds with the act of presentation (cf. Twardowski, 1977, p. 13). The object of the presentation and the content of the presentation are not the same. One difference between them, for example, is that they can exist in different ways. The presentational content of an ideal or non-existing object is not ideal or non-existing. The content of the presentation of a non-existing object, should it be presented, exists independently of the non-existence of the object to which it pertains.

Object and content are to be discussed as the object and content of a particular presentation. Therefore, if we think only about some object, it will each time be the object of a certain possible presentation. Something similar goes for the content: if we discuss some specific content, that will be the content of a particular possible presentation. However, to render things more concise (in places where doing so will not engender inconsistency), we will use the terms object and content with the additional specification that they are the object or the content of a specific presentation. The context will decide whether the topic is one and the same presentation or, perhaps, many presentations.

3 Material Constituents and the Form of the Object

Anything which can be distinguished in an object independently of the very mode of distinguishing we call its part. Parts of a smartphone are a processor, a battery, a touch screen, etc. Parts of that type may be specified differently (albeit more narrowly) as pieces or parts in the usual sense. Nevertheless, in a smartphone, we can also discern that the battery cover covers the battery, that the touch screen is on the other side of the battery cover. In this way, parts of another type are distinguished: namely, relations between parts construed in the usual sense.

According to Twardowski (1977, p. 46ff), all of the parts of an object in the usual sense go to make up the material (German: Stoff) of an object, while all of the parts in the sense of relations distinguished in an object go to make up the object’s form. Obviously, the material of an object is so strongly interwoven by different relations with the object’s form that, in many cases, it is impossible to separate these effectively. An object’s material and form are abstracta of that object, and even though they are initially inseparable, to distinguish them is to do so in thought.³

4 The Material Constituents of the Object

The material (or matter) of an object is the totality of its parts in the usual sense of the term “part”. Parts are divided into simple ones, such as those that do not have parts, and complex ones, in which further parts can be distinguished. A simple object is an object that does not have parts; a complex object is an object with parts. The object’s parts, viewed in terms of their mereological order, may be located within it more proximally or more distally: the more proximal part of a smartphone is its touch screen, while its most distal part is the technology from which it was made – for example, its capacitive sensing screen technology. The fact that a part is a more proximal or more distal one furnishes the basis for distinguishing the order of parts (Twardowski, 1977, p. 47). First-order parts are parts of an object, but their parts are second-order parts, parts of second-order parts are third-order ones, etc. Breaking down an object into mereological orders (degrees or levels) is, of course, relative. A kilo may be broken down into 100 decagrams or 1000 grams: it is hard to say which parts of a kilo are more proximal and which more distal if we are not apprised of the particular rule for carrying out such a procedure.

The order of the parts is just one of the rules for dividing something up into parts of a whole. The next rule of division is the way in which parts can be parts of an object (Twardowski, 1977, p. 48). As parts of particular objects, duration and extent may be their parts only in one way. The Academy of Young Scholars and Artists cannot have duration in three different ways – it was established and lasts, so as long as it exists, it will last. At the same time, the redness of a red pen is a part of that pen in a different way than redness conceived as a part of a spectrum’s red band.⁴

The third way of dividing an object, alongside order and being a part in one or multiple ways, is division in terms of the dependencies pertaining to the existence of the object’s parts (Twardowski, 1977, pp. 48, 49).⁵ The latter are often tied to one another existentially: i.e. they are entangled in such a way that if one part exists, then the other has to exist too. That is the case with the redness and the extent of the apple lying on a table about which I wrote earlier: its redness cannot exist without the extent of its surface, and vice versa. The surface cannot exist without a specific colour. Colour in that sense is connected with extent, and there is an unbreakable relation of coexistence.

5 The Object’s Form

The object’s matter, as we have seen, is already incredibly complicated. However, the true complexity of an object is revealed in its form: that is, in the relations in which an object and its parts are involved. Following Twardowski, these relations are called the “formal constituents” of an object. We should also emphasize that Twardowski treats the relations of an object with other objects as a part of that object.

Among the formal parts, Twardowski (1977, p. 50) distinguishes two types: primary and secondary. (Twardowski speaks about “primary formal constituents” and “secondary formal constituents”.) The primary formal parts are the relations between the parts and the object as a whole, while secondary formal parts are relations obtaining among the particular parts themselves.

Relationships between the parts of an object and the object as a whole come in two kinds. Once the parts create a whole, and the whole binds them together (for example, causally) and encompasses them, they can be considered relationships in the strict sense; meanwhile, at other times the parts can be just somewhat similar to a whole, or looked at separately may be smaller/larger than the whole, in which case Twardowski considers such relationships to be primary formal constituents only in an extended sense. Parts of a given whole, to be capable of being similar to the whole to some degree, must first be its constituents.

Primary formal constituents in the strict sense stand in an ontological relationship of founding with primary formal parts in the extended sense, and such founding itself constitutes a further level of multiplying relations. Because the relata of the founding level are relations (primary formal constituents), it can be said that they are secondary-level relations. Relations between relations of the second level will be those of the third level, etc.⁶ In the case of some objects that analysis could go on endlessly. Such indefinite entangling of formal constituents is the key to answering the question about the core of the relation that binds the parts into a whole (see Twardowski, 1977, p. 56).

Formal secondary constituents of an object are those whose relata are the particular parts of an object, but not the object as a whole. The type of secondary formal constituents depends on its relata. When the relata are the material parts of an object, the secondary formal constituents are spatial relations between the material parts of, say, a smartphone.

The relata of these relationships may also be the primary formal constituents: i.e. the relations between the parts and the totality of the object. The differences between the ways in which the totality possesses the material parts can be compared as part and parcel of the analysis of the relations between the primary formal constituents. What is also to be taken into consideration as part of that analysis is the causal dependency obtaining between the different relations of an object and the object as a whole. If a smartphone has the right amount of RAM and a fast processor, it will also probably possess the feature of reacting quickly to the needs of a demanding user. We should add here that for Twardowski, the totality of secondary formal constituents, whose relata are primary formal constituents and those on the basis of which we can causally derive all remaining primary formal constituents in the discussed object, make up the essence [German: Wesen] of that object (Twardowski, 1977, p. 57).

6 Presentations Are Also Objects

The different types of parts of objects have been distinguished above in general terms. We should also point out that presentations can themselves be objects of presentations, as when I present a stage character right before the play. If such presentations are also objects, the types of parts distinguished above are also valid for them. Therefore, presentations may be broken down into material and formal parts, and it is possible to determine their further levels ad infinitum.

7 Adequacy

Since we are concerned with what it means to come to know an object, and the primary part of cognition is presenting an object, we are bound to be keenly interested in relationships between the contents of presentations and the objects of presentations. The object of a presentation is related to the presentation just because they are disclosed to us within one presentation. However, that aspect of their relationship does not have the same significance as how the presentations correspond with the content. To express it more precisely: in what manner do adequate parts of a presentation correspond with the object’s parts (such that the particular object and that particular content refer to the same object), and vice versa? To be even more precise, our question is whether any formal and material part of the content of the presentation corresponds with a formal and material part of the object, and whether each formal and material part of the object corresponds with a formal and material part of the content.

That issue forms part of the classic philosophical problem of the essence of veracity. From amongst the products issuing from our cognition of an object, we can distinguish those that do and those that do not “hit” the object, those that do and those that do not correspond with it, those that describe the object as being how it is and those that describe it as how it is not, those that are harmonious with the object and those that are not, and those that are consistent with other presentations of it and those for which such consistency with others is not possible.

Each of the dichotomies listed above corresponds with a particular tradition of grasping the problem of truth. The analysis presented here pertains to the base level of the problem of veracity, because presentations, according to the view presupposed by our thesis, make up exclusively the basis of cognition. Moreover, cognition is understood here as the activity of an individual subject (even if it is slightly extended by, for example, online computational tools – see Smart, 2022), while the group aspect of cognition is omitted here (even though the results of scientific cognition have, to be sure, a social dimension – see Fleck, 1979; Hutchins, 2012), as is the theoretical aspect, in the sense that we are not aiming to deal with the question of what it means for a particular scientific theory to be true.

8 Addition and Subtraction of the Object’s Parts: Simplification and Enrichment of the Presentation of the Object

Let us repeat our central question: it concerns whether each formal and material part of a presentation’s content corresponds with a formal and material part of the object, and whether each formal and material part of the object corresponds with a formal and material part of the content of the presentation. That question, to be sure, is actually composed of many more detailed ones. Further levels of formal and material parts are discernible with each subsequent step. To successfully take the analysis in that direction, one would have to have appropriately complex and abstract structures at hand, which would model the structure of the content and the object (Wójtowicz & Skowron, 2022). We know that despite many attempts, such general structures have yet to be discovered. Below, though, we propose an overall topological understanding of the objects of interest to us.

Let us, then, try to answer that question not in an entirely general way, but on the basis of particular cases. Take, for instance, a concrete smartphone along with all its parts. Alongside those parts of a smartphone we have already mentioned, we should add the more complex relations it enters into with other objects: i.e. proximal spatial relationships, such as how it is located relative to other objects, and how it enters into network relationships with them. When it is connected to the Internet, it connects up with many other objects, including other smartphones, service providers’ servers, internet websites, etc. The network of relations which it is involved in is incredibly varied, and having regard, perhaps, to the accumulative proliferation of orders of parts, endlessly rich. However, the question is whether, within the content of the presentation of a smartphone, examples of all the relationships just listed will be encountered? The answer to this is a negative one. When I present a smartphone to myself, I do not take into consideration all the relationships in which it is involved.

What is more, it is not just relationships that are omitted in the content of the presentation: I also do not consider its material parts, because I omit both duration as a part of a smartphone, as well as further mereological and temporal levels of its persistence, not thinking all the time about its beginning and end. I also omit many secondary formal components, such as the processor’s location and the motherboard, which is seldom a component of the content of a smartphone’s presentation.⁷

Until now, we have been talking about complex objects, in that we have distinguished their parts. The analysis up to now has not included cases of simple objects, that by definition do not have parts. Examples of simple objects are Leibniz’s monads, a pure subject, or God. The content and object of presentation of simple objects are most probably related in the following way: that they are the content and object of one presentation. Do any other relationships obtain?

If we assume a proper breakdown into parts as described above, it would have to be said that there are no other relationships in force. This is because they cannot be said to be completely identical, as they are different objects. If anyone comes to know these objects at all, then this is not via a process having presentation as its basis. The importance of presentations decreases to the benefit of such intangible tools of cognition as intuition (for example, of the eidetic sort), and symbolic and abstract cognition.

Nevertheless, complex objects are often presented as simple objects.⁸ In moments of strong subjective tension – for example, under stress, or being suddenly blinded by a bright flash – we tend to present complex objects as simple ones. The content of the presentation of a flash in a moment of surprise is not complex: we do not differentiate its parts, we do not analyze its colour or intensity – the content tends to be simple. States of tension or surprise are a violation of our standard mode of maintaining a certain poise, or relative peace and quiet, yet in those states a simplification of objects occurs. It might be conjectured that simplification is a cognitive strategy typical for subjects engaged in coming to know an object.⁹ Cognition is, in large part, a matter of filtering what is available to the subject. It is impossible to contain in the content of a presentation all parts of the object of presentation. Attempts to fully specify an object, in which strict mutual adequacy between the parts of the content and the object is achieved, generally prove unsuccessful.

When we present complex objects as simple, we subtract some parts from them, and simplify them. A process that is the reverse of simplification is the conferral of additional internal diversity, which occurs inter alia in cases of optical illusion or vivid psychedelic hallucinations. The content of presentation of the image below includes more parts than the image itself. The grey spots which, when we look at the entire image, appear in the places where the white edges of the grid cross-sect, are a part of the presentation, but they are not a part of the object. This illusion is called the Herman grid illusion, and is one of many known illusions of that type.

Another example is furnished by the content of presentation of objects such as a legal driver without a driving license. Within the content of that presentation, it is natural to include a driving license. It is impossible to present to yourself a legal driver without a driving license without presenting some form of driving license. The driving license, although not part of the object, is a part of the object’s presentation. There are many cases of such indubitable enrichment of objects in terms of content. More subtle examples are contributed by transcendental philosophy which, while examining the preconditions for our cognitive capacities, points to certain accessories needed by the subject (for example, sensual forms such as time and space), as well as some creative aspects of cognition involved in creating an object. However, pursuing a transcendental analysis would take us too far away from our main task here.

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The Herman grid illusion (Source: http://en.wikipedia.org/wiki/Grid_illusion, Accessed: 06.04.2023)

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It can be the case that certain parts of the object do not correspond with any parts of the content, and vice versa. Although such a deficiency with respect to adequacy may have negative consequences, the idea that it wholly undermines the cognitive effectiveness of subjects engaged in coming to know an object would seem like an overly hasty conclusion. It seems that small differences pertaining to parts within the object should correspond with small differences pertaining to parts within the content of presentation – at least in respect of that presentation’s “hitting” the object. The situation is similar with significant differences – with greater and more noticeable differences within the content – at least if assume that in a certain way we are, for example, asymptotically approximating to the object as we come to know it. If the relationships described here in terms of differences as to the content and the object do not make reference to the entire content and object, they certainly will obtain between selected parts of these.

Cognition exhibits a certain purposive character, which is that as we go through the process of coming to know something, we at the same time yearn for that which is being cognized to be accessible to us in full. Distortions, though undesirable, are an inherent component of the “adjusting” of the content to the object. They may be presumed to form a part of the conditions of possibility of cognition – in that the idea of a capacity for complete coherence with respect to cognition can, as we have seen, be quickly challenged.¹⁰

9 The Search for a Model of Object and Content¹¹

As we have noted already, the problem of adjusting the model or the material to achieve adequacy as regards both the object and the content remains open. We know that despite many imperfections, correspondence takes place between parts of the content and parts of the object. In order to examine the nature of these correspondences, we must in some way imitate, or assign a structure to, such contents and objects. We know that there can be no relation of photographic mirroring between these structures, and also that in the process of presenting them many simplifications and diversifications will arise – as what, collectively, we call “distortions.”

Within the content of its presentations, a subject somehow adjusts the parts to its properties and capabilities. It constructs certain presentations (cf. Jernajczyk, 2014) that amount to distortion, but which nevertheless do not become severed from the basic condition that a particular content should correspond with a particular object of presentation. Some, even if erratic, adequacy on the part of the content of the presentation still remains. Sometimes it is strict adequacy, while at other times it may be absent altogether. The strictness of this adequacy will consist in the following: that small changes in an object can be expected to compel equivalent small changes in the content, and vice versa. The contents of the presentation will be distorted, yet the process of distorting is not entirely unconstrained. It maintains “partial continuity,” so to speak. So what does it consist in?

As an attempt at responding to the question concerning the structure of adequacy of the content’s parts, we propose to model the structural aspect of both the content and the object with the help of topological spaces.¹² On such a basis, we believe that it will be possible to examine and model the nature of such distortion.

10 Dimensional Types Pertaining to Contents and Presentations

Assuming that certain topological spaces furnish a formal representation of the object of presentation and the content of presentation,¹³ we may define the phenomenon of “partial” continuity of distortion in the following way.

The relation of being-a-part is expressed with the help of set theory – the relation of mutual containing between sets. Homeomorphic objects have the same types of dimension. However, the reverse phenomenon does not occur, and objects of the same type may not be homeomorphic. The elementary example is a closed interval (an interval with limit points) and a straight line. They are not homeomorphic. A straight line, contrary to the interval, is not compact. However, if we consider an interval included in the closed interval, but this time without limit points, i.e. an open interval, it is homeomorphic with the straight line. And going in the other direction: if we take a closed interval which is a part of a straight line, it is homeomorphic with the initial closed interval. The real straight line and the closed interval have the same type of dimension, although they are not homeomorphic.

To sum up: if object G is homeomorphic with a certain part of object H, and object H is not homeomorphic with any part of object G, we say that object G has a smaller type of dimension than object H, which we record as dG < dH. If, between any objects X and Y, there is neither dX < dY nor either dY < dX or dX = dY, then we say that X and Y are incomparable in terms of their dimensional types.

An example of a sequence of objects with a growing dimensional type is shown in Figure 16.2.

We see that the greater the dimensional type, the more complex the object. Simplification of objects, and the conferral of additional diversity upon them, relies in the content of presentations on ascribing a smaller type of dimension in the former case and an ever-higher type of dimension in the latter one. More precisely, if some part of the presentation’s content has a smaller dimensional type than the corresponding part of the object of presentation, then we say that that part of the content of presentation is a simplification. Meanwhile, a conferral of additional diversity on a particular part takes place when a part of the presentation’s content has a higher dimensional type than the corresponding part of the object of presentation. The content of presentation will be strongly simplificatory if each of its parts is a simplification in relation to each corresponding part of the object, and it will be strongly diversificatory if each part of that content amounts to a conferral of additional diversity in relation to the corresponding part of the object.

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A series of objects of progressively higher dimensional type

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The actual complexity of cognition depends on the premises present in advance as part of what constitutes its basis: namely, that during a presentation some parts of it will simplify parts of the object, and some will confer additional diversity on them. Presentation is a process, and as such is extended over time. One object corresponds with sequences of presentations. During that process, one part of the object may have a lower type than the corresponding part of the content, and another may have a higher type than its counterpart.

It is worth noting that even if contents can have either a simplificatory or a diversificatory impact on an object, they maintain the basic relationship between content and object responsible for the fact that some contents correspond with that particular object, and that the object is presented through that particular content. That relationship is based on the comparability of the dimensional types of the corresponding parts: i.e. that we can say that the first one is higher than the second, the second higher than the first, or that they are equal. When such comparability as to types of dimension does not occur, the contents of presentations fall short of the object. Cognition does not “reach out” successfully to its object. This thesis is an expression of the philosophical conviction that the contents of presentations, even if they distort the object by subtracting or adding something, still in some basic sense refer to the object and to some extent present it. That is a kind of epistemological optimism.

In order to carry out – in a reliable and detailed manner – an analysis of objects’ and contents’ presentations under the mantle of topology, we would have to formulate appropriate postulates regarding adequacy relating to the types of parts differentiated earlier, and to the parts of topological spaces: ones similar in form to the postulates of quantum mechanics. However, due to the scale of such an undertaking, that would exceed the scope of this paper.

11 On the Union of Presentation and Object

Some parts of the content of presentations do not fully correspond with parts of the objects of presentations and – vice versa – some parts of objects of presentations are not fully represented in the contents of presentations. Despite this, objects are somehow cognized. Therefore, there must be some parts of an object whose equivalents are parts of the content of the presentation of that object. These parts, given that they are responsible for cognition’s adequacy and its being “on target,” hold a particular cognitive significance, and for that reason have been picked out using a different name. Twardowski calls them characteristics (German Merkmale). A characteristic of an object is that part of it, which is at the same time a part of the content of the presentation of that object. In the words of Immanuel Kant: “A characteristic is that about a thing which constitutes a part of the knowledge of it” (quoted in Twardowski, 1977, p. 79).

Twardowski also posed the question of whether there are parts of the object of presentation that every object possesses. Amongst the natural candidates for that type of part, we find identity and unity. Identity, however, need not be a part of the object of presentation: it occurs, for example, in the set of contrary objects. On the other hand, unity is a part of each object. Each object of presentation is a homogenous totality, even when it is a complex object: it is one object, and it is presented as one object. Therefore, unity exists in every content of the presentation, which is why it is a characteristic of every object (Twardowski, 1977, p. 86).

12 In Place of a Conclusion

The process of cognition is complex. Right up to this point, we have focused exclusively on a certain phase of cognition relating to the presentation of the cognized object. We have also assumed that a presentation is important because it is a founding and enabling moment of cognition. It is on the basis of presentations that we are able to carry on with cognition. What is presented can be judged – that is the essence of cognition, but it might be both desirable and repellent.

Each and every cognition, so long as it does claim to be cognition, should culminate in the formulating and pronouncing of a certain judgment. Yet even though cognition may not always achieve a definitive completion in such terms, this need not mean that it is not then cognition – it will often have a certain value or cognitive power, albeit of a somewhat unfinished and incomplete kind. Nevertheless, it is worth noting that the process of cognition, right from its beginnings, is in danger of being simplified or rendered more internally diverse many times over, where this may subsequently lead to further distortions. In particular, when such a process culminates in the formulating and issuing of a judgment, some distortions present at its outset may engender distortions at its ending. Being aware of such impairments (or inherent properties?) of cognition, especially in terms of the cognition of complex objects, will then permit an adequate adjustment of the strength of assertion of the judgment made.