Jan Hartman

The concept of certainty and its correlates: truthulness and evidence 
(an introductory analysis)

This paper is giong to be published in 2004 by Rodopi in
Poznan Studies in the Philosophy of the Sciences and the Humanities in the volume under my editorial care and devoted to Jan Woleński

1.	Assumptions underlying the analysis of the certainty of knowledge

Two venues can be adopted in order to analyse the certainty of knowledge: the autonomous and the instrumental approach.  The autonomous approach means that the issues related to the certainty of knowledge arouse our cognitive curiosity. In effect they are considered because of the value of study itself. We feel the need of finding out what entity is endowed with the property of “certainty”. What is the nature of this property? Can it be graded?  On the other hand, in the instrumental approach to the analysis of “certainty”, the interpretation of this property’s nature is subordinated to the possible application of obtained knowledge about certainty to assess individual cognition results, or to formulate certain methodological directives for the scientific procedure. In the instrumental approach to the study of certainty, the results would be satisfactory only in the case when – on the basis of inherent criteria – the very analysis is found to provide certain knowledge (about certainty), i.e. the relation is reflexive. 
It would be prudent to tackle the issue of certainty from the autonomous viewpoint. Thus, we would not need to prove that our solutions are reflexive. The reflexivity means that they could be applied to themselves. They would be certain according to the interpretation of certainty that they offer. It does not mean that we plan to ignore the peculiarities resulting of the fact that the words “certain” or “true” appear in the statements formulating (on the basis of meta-theory or any level of meta-language) the cognitive evaluation of individual cognition acts, or statements expressing cognition results. To the contrary, the iterative character of the statement such as:  “it is certain that” (“it is certain that it is certain that it is certain...”), “it is obvious that” or “it is true that” and the related redundancy quality (“inflation” allowing to leave out the predicate i.e. “deflation” without the loss of the semantic nucleus of communication, its cognitive value or credibility) is characteristic for such predicates. It belongs to their crucial attributes responsible for the extreme difficulty of the study of truth, evidence (obviousness) and certainty. Nothing significant can be said in the study of these problems, without the exposition of the notions of iterability, redundancy, and reflexivity (the statement proclaiming the truthfulness, certainty or evidence of another statement or judgement inherent in it, shows itself as true, certain or obvious, or otherwise devoid of the capacity to communicate its sense) of epistemological predicates at stake and their mutual relations. The crucial ideas underlying present study (specified in part III) have been inspired by the above conviction, which can be precisely formulated in following assumed conditions: 
1.	No ultimate or universal statements can be made about the sense and object of the predicates “true”, “obvious” and “certain”, since they are mutually relative. They form a dynamic and changeable functional entity (changing in effect of the applied discourse type, the assumptions and preferences selected by the language user). The functional character of this entity results of its epistemological features, i.e. knowledge-generation and knowledge-transfer, as well as explanatory and persuasive characteristics. In general, such functions can be defined as pragmatic. In consequence, this functional entity can be described only. Besides, it can be shown that various strategies of applying relevant words (either consciously or unconsciously – as it is the case in explicit “concepts of truth”, consequently or not quite consequently – the latter being more frequent) lead to various conceptual configurations, and in various venues display the same set of peculiarities (reflexivity, redundancy, iterability).  
2.	The application of the concept of truth, evidence and certainty is always more or less directly related to the intention of the legitimisation of proclaimed statements. This fact leads to important consequences that must be always remembered. Firstly, the words “true”, “certain”, “evident”, applied in situations when a threat of falsity (of some type) appears, always serve to some degree the persuasive  (i.e. rhetoric) function. Nietzsche and some of his contemporary followers managed to build a complete theory of truth on this basis. A crucial result of this theory consists in a convincing demonstration that the persuasive feature reflects the imperfect nature of all knowledge available to humans. In some ŕ rebours way, it is compensated by assurances (however legitimate, but offering no more than just assurance) that “given statement is true rather than false”, “it is certain, rather than dubious”, “it is obvious, rather than unclear or non-obvious”.  In a proverbial way this situation can be summarised by the statement that God does not need the concepts of truth, certainty or evidence. Secondly, the natural use of the terms “true”, “certain” and “evident” is linked to legitimisation of statements. In consequence, the special way of using these words pertinent e.g. to the formulation of the theories of truth, certainty and evidence must be related to the procedure of statement legitimisation and the reflection over the problem of legitimacy. In result, the problem of the perspectives of judgement legitimisation  (i.e. the issue of the possible ultimate legitimisation of knowledge – Letzbergündung – and scepticism) supplements naturally the problem of truth (certainty or evidence), as long as the latter question is formulated radically, i.e. in expectation that the cognisance of the essence of truth is accompanied by the cognisance of the ultimate perspectives of human ascertainment in relation to formulated statements. In this radical formulation of the issue of truth (radical though also natural, since the claim of absolute certainty is natural in all situations when any claim to the ascertainment of the truth of given statement appears) the difference is partly obliterated between the above defined autonomous and instrumental approaches. The certainty, evidence and truth of the theory of truth must have possibly many common points with the properties discussed in this theory. Its criterion-generating value is always desirable. Similarly, in the natural application of language, it is desirable to get explicit knowledge about the meaning and the bases of statements claiming that given judgement is true, certain or evident. 

II.	The specification of issues related to the certainty of knowledge and correlate properties

The selection of the problem of certainty as the foundation on which the epistemological concept can be built, embracing all the inherently inter-related issues connected with the certainty of knowledge, its truth or evidence, is essentially arbitrary.  To some degree, it is justified by the fact that the awareness, and the following philosophical conceptualisation, of our natural claims to the truth of cognisance results lead the philosopher – always eager to persuade ultimately himself and others about the defended position – to everyday encounters with the problems of knowledge legitimacy, and thus directly also with the issue of certainty. Having perpetrated this partly arbitrary and partly justified choice, let us try to define the problem domain, where the reliable concept of certainty/truth/evidence should be localised. The ambition of present study is to offer only a very rough outline of such concept. However, if this rough outline were to be developed into detailed analysis, the questions to be answered (i.e. the minimum number of questions, since very many other ones could be formulated) should include the following: 

1.	What does it mean that an act or cognitive procedure yields certain (or true, or evident) knowledge? Is it exclusively and always knowledge? 
2.	What does it mean that a judgement and a statement formulate knowledge that is certain?
3.	Is the certainty (or evidence, or truth) an experience (mental object), a property or a relation? 
4.	Is the certainty (or evidence) of knowledge a warranty of its essential value (truthulness?) in general, or is it the ultimate cognition value in itself? 
5.	Do the criteria of statement certainty exist, and if so, are they different from the criteria of statement truthulness? (Can evidence be interpreted as a criterion?) 
6.	Is the formulation “certain (or true) knowledge” not a pleonasm? Is it possible for knowledge to be uncertain (untrue) and remain knowledge? 
7.	The iterations of the type “it is certain that it is certain that...” or “it is certain that it is true that it is certain that...” etc. – are they purely redundant (inflationary), or do they define any values? 
8.	What is the opposite of certainty? What does it mean that the opinion, statement or cognitive experience, contain uncertain elements?  In particular, do “uncertainty” and “mere possibility” denote the same quality? 
9.	Does the notion of certainty belong to the vocabulary of pragmatic rationality, referring to the criteria of accepting statements and opinions? Alternatively, is it a strictly epistemological entity referring to the value of opinions in their relations to the world or other opinions? In the former option, would it be different from the notion of truthulness? 
10.	Is the experience of cognitive certainty a cognition act in itself? If so, what are the given elements in such act? To what object is it related? 
11.	The certain knowledge: is it necessarily unchangeable, subject to no correction (e.g. from the viewpoint of interpretation form)? 
12.	What is the relation between the notions of a priori necessity, analytical truthulness, and certainty?  The notion of certainty when referred to formal sciences and analytically true statements: can it be identified with the notion of certainty when referred to empirical cognition acts? Is the latter application possible at all? 
13.	The certain knowledge: is it exclusively obtained in scholarly research? Alternatively, can it be reached in everyday cognisance experience or in any other field of cognitive activity? 

III.	The theses 
(i)	Certainty is neither the property of cognitive experience nor the property (feature) of the cognising subject or judgements or tasks.                           Certainty is not a property in the strict meaning of this term (though in some essential way it is related both to experience and judgements). The way in which the property can constitute the substratum to which it pertains is quite different from the relation between certainty and the certain. For instance, the hypothetical deprivation of a given judgement of its certainty does not modify its properties, as it would occur in the case of similar operation performed on its syntactic structure (belonging to the group of judgement properties). Certainty seems to “penetrate” the certain in way comparable to existence “penetrating” the existing (while not being its property). Also being recognised, certainty “penetrates” the related experience in which we become sure of the existence of something.
(ii)	The essence of certainty (and truthulness) cannot be pondered in abstraction from the consideration of the certain conceived in its content, i.e. in abstraction from the question: what do we know ultimately and certainly?  These problems essentially partake in the fundamental aspirations of human reason (science), which can be seen as the effort to achieve general ontology (or metaphysics). Yet, in epistemology we are excused for limiting our analysis to the context of the formation and formulation of knowledge. I believe that in this specific epistemological context certainty ought to be conceived as a semiotic (pragmatic) relationship between the following statements: “The statement p proclaims certain knowledge” (equivalent to the statement “it is certain that p”, i.e. C(p)), and p. This relationship can be summarised as follows: if the statement proclaiming the truth of p is true, any further analysis of the truthulness of p is redundant. Of course the corroboration of above relationship is tantamount to the finding of truth in p since the corroboration of the truth of p is the only way to test the truthulness of the statement: “it is true that p”. The semiotic analysis of the terms “true” and “evident” is similar to the above consideration of the term “certain”. 
(iii)	The definition (ii) is consciously an explanation of ignotum per ignotum type. The justification is that the word “certain” (similarly to the term “existing” and especially the term “is”) has no definite meaning, while the way (and purpose) of its usage is such that the term is meant to lead us, or more precisely, persuades us to focus on the content of a certain cognitive experience or the content of a certain statement, which is meant to certify its validity per se (i.e. by its very content). Similarly, the existence (and the “is” word used to communicate this condition) is often subject to such deictic reference to “the thing in itself”, which is meant to proclaim itself, i.e. reveal its existence. From the object viewpoint such “self-testimony of given thing” or its “self-justification” is tantamount to so-called ontic truth, or simply the reality. From the subject’s viewpoint the confirmation of experience validity (through the course of experience itself, or through immanent reflection “I cannot be mistaken as to the fact that I do see something being red in hue”, which can be generalised into an epistemological law to the effect that “it is not possible to be mistaken about the content of current cognitive experience”) is related to the mind’s self-assurance (or the “aperception unity”, if we were to use a more sublime term). 
(iv)	The property of self-supporting of the validity by the content of experience or statement itself is defined as its evidence, while in strict consideration  (when the terms “validity” or “general application” are used) the validity (or general applicability) is attributed to the statement or experience as its inherent (substantial) property. On the other hand the evidence relates to the relation occurring between the valid statement and the subject cognising its content (which becomes evident for the subject and ipso facto valid). Similarly, the definition of relation occurring between the content of valid statement or experience on the one hand and its referred object on the other, is the truthulness. Yet, the conceptual and language strategies serving the description of a given epistemic situation can vary significantly (i.e. divergent ontologies describe the relation of cognising subject, the subjective acts, their content, the subject and the object of cognition). Similarly, various strategies can be applied when using the terms and words, which are meant to “contribute jointly” to explain the complex meanings related to the legitimacy claims of cognisance. In my opinion, no reasons can be identified to argue about the validity of selected definitions of truth or certainty conceived in abstraction. Rather, it should be studied whether a given theory describes satisfactorily and comprehensively the epistemic relations. The precise definition of such concepts as “truth”, “certainty”, “evidence”, etc. provides but one of the methodological means for construction of epistemological theory. It is misused when such solutions are considered crucial for given research position and defining its characteristics. In alternative formulation:
(v)	All such quality definitions as certainty, evidence, truthulness (in various ethnic variations and relying on different philosophical concepts) acquire meaningfulness within statements that project selected relations between them. Such relations reflect the ontic relationships between the relevant beings (subject, act, content, object, etc.). In consequence, the serious epistemological discussion cannot avoid the area of cognising subject ontology.  It is worth noticing that one of the epistemological terms (e.g. certainty) must always play the role of intentional or focal “functor” – directing the attention to the own content of statement or experience, as self-corroborating, while other terms are used in sentences that express epistemic evaluations (e.g. “truthulness evaluations”) of other sentences. 
(vi)	In result, the statements formulated in iv above concerning the concepts of certainty, truth, validity and evidence have but relative value, since the present theses do not go beyond the status of the concept selected from many other possible concepts delineating the application strategy of mentioned terms. Yet, this strategy has one outstanding quality. It allows the clear understanding that the concepts of truth, certainty, etc. always belong to a certain complex concept system allowing to formulate statements at least both in primary and second-order language (i.e. they belong to the reflective discourse). Thus, also the substantial correlates of such predicates as “certain” or “true”, and consequently “truth” or “certain knowledge” shall always have the character of conceptual projects, derived from definite philosophical theories. Ultimately, these conceptual projects will have been developed within the framework of theory pertaining to exactly this type of notions, i.e. the particular “theories of truth” or the “the concepts of evidence”. 
(vii)	If it is possible to discuss truth or certainty etc. only in terms of concepts pertaining to particular “theories of truth” or “theories of certainty” etc., it is useless to cherish aspirations of absolute nature and transcending the limits of particular theories. The essence of truth and certainty cannot be understood “in general”. They must be conceived “on the grounds of a specific theory”. Emphatically, the above statements cannot be reduced to relativism (formulated as follows: “truth and certainty are always predicates having the sense conceived within the limits of definite theory of truth and certainty, ergo absolute truth does not exists”). Instead, it is the consequence of statements offered in (i) above. When the concept of certainty and the related concept of truth are considered, at some point a reference to the “very thing”, i.e. the individual content of experience or statement must appear. One of the terms in the group: “truth”, “evidence ”, “certainty” must adopt the role of “intentional functor”. In effect, the concept definition will necessarily include a redundancy, ignotum per ignotum, or another form of auto-reference. 
IV.	Discussion of exemplary statements aspiring to certainty 
The concept of certainty appears in various paradigmatic contexts. To some degree, the application rules of the predicate “certain” (and the correlated predicates “true”, “obvious”, “valid”) are biding also on the ground of philosophical analysis. In such analysis transition is made from standard statements, containing the studied terms, to a special type of statements, which form the theory of something (e.g. the theory of certainty, etc).  The statements in which problems are formulated and studied in a particular way must legitimise the ultimate declarations, which form the theory. In reverse direction: the theory must shed a new light upon the sense of these introductory statements  (supplement or comment it, and in specific cases even undermine it). That is why it is useful to study some characteristic statements, or communication situations, in which the term “certain” appears (alongside the related terms quoted above). The discussion of such examples shall be guided by the understanding of the certainty of knowledge that has been outlined in the offered theses, providing also the introductory verification (or perhaps only self-promotion) of their correctness and operational character. 
1.	“I have seen him a moment ago, so certainly he will not answer your phone call at his home telephone now (he is not at home)”.  This statement reflects the simple empirical impossibility: no one can cover such long distance in such short time. What is meant here by certainty is such an evaluation of probability that denies that the event is “only possible” and claims this event is impossible: “It is impossible that your phone call finds him at home now.”  The truth of the former part of the compound statement (“I have seen...”) guarantees the exclusion of condition defined in latter part (the relevant person being at home now); it is beyond any reasonable measure of probability. It is characteristic for this type of statements that they reject 
a priori all chance of negation. Though essentially some probability does exist that in future certain processes shall develop quite differently from the past experience.  The “possibility of miracles” cannot be absolutely excluded.  This indifference to the possibility of miraculous event (which would undermine the unshaken belief in empirical observation based on incomplete induction reasoning relying on innumerable amount of past cases) should not be seen as pure rejection of negligible probability. Instead, it is tantamount to the conviction that any events other than the foreseen one are absolutely out of question. This sort of a priori certainty rejecting all negation is an experience. Yet, it seems to contain a significant epistemological claim, which can be paraphrased as follows: “the certainty that a cube of sugar dissolves in a cup of hot tea is unshaken by any imagination (possible in a nightmare) that something different might occur. Essentially it boils down to my own certainty about my personality, integral and sensible character of my own experience, memory and orientation in world.” The certainty of statements similar to above example depends on a certain functional quality that can be attributed to human mind (i.e. our cognitive life). This quality is expressed most significantly in the fact that our mind is prone to believe in its faculties, relies on its own convictions and provides authority for itself. This functional quality can be seen as the mind’s self-assurance. It is to this self-assurance that we appeal by adding the ascertaining functor (“it is certain that...”,  “surely...”) to the statement “he will not answer your call now”. The message receiver is sent the persuasion signal that he/she would better forego any attempts to verify the truth of offered statement and trust the assurance. Why should the assurance be trusted? It is because the person formulating the assurance signals also his/her self-awareness: the message receiver would obviously share this conviction if he/she partook in the sender’s experience (knowledge). 
2.	“It is certain that people often say things they do not truly believe in.”  Again, this general judgement clearly rejects all attempts of negation and is impermeable to all efforts to undermine its correctness or even clarity. The foundations of this statement could be specified as follows: “everyone is aware of this fact – from own experience and contacts with other people”. Again, this statement refers to the mind’s reliance on self-assurance, and characteristically declines of direct justification, which is claimed to be redundant. The content of this statement is sufficiently clear for everyone. All reasonable persons would also consider it significant and contributing to the knowledge essentially necessary for individuals and the society. Yet, in a sense, it is a non-scientific statement. Especially this (extremely natural) formulation seems extremely non-scholarly. What is the meaning of this “certainty outside the realm of science” or “certainty in the matter that does not fall directly into the domain of science”? Should it be surmised that, for some unclear reasons, scholarly research has abandoned a certain area of rational expectations, which are both important and certain? Could it be that the excessively obvious certainty of such judgements, i.e. their triviality, resulted in such abdication of science. If this were the case, would it not be honest to undertake the effort aiming at the listing or classification of resulting consequences – which need not be necessarily trivial? The development of the strictly formal lore of mathematics had relied on the ordering and development of a certain category of simple and certain judgements. 
3.	“It is certain that two times two is four”. The claim of the validity and certainty of this statement is individually legitimised in the act of consciousness in which the summation of two and two is effectuated. The certainty that we cherish in relation to such arithmetic thesis, and which we can check applying our own mind faculties, again seems to have the characteristics of the mind’s self-assurance. The mind furthers its infallibility by finding the certainty of the truth of proposed statement as being obvious. Even if the language proclaiming such knowledge expires, even if the skill of translating the phrase “two plus two equals four” into any other language is lost, the essential truth of this statement shall remain intact. Human mind is absolutely certain of this truth. It seems that this certainty is closely related to the conviction about correctness of the mind’s functioning in the addition of two and two yielding four. This certainty can be shown through such expressions of the epistemic value of the thesis “two plus two equals four” as “true”, “evident”, “undeniable” or “certain”, enjoying the characteristic freedom of choice. Whichever predicate is finally used, it will fulfil the function of directing the speaker’s and the interlocutor’s attention at the very content of mental process (or – perhaps – a single act) in which the counting is realised. What is more, the use of the term “certain” (or any other of above-mentioned predicates) in this case has no persuasive function, in contrast to the empirical statements discussed in previous sections. It is not necessary to omit, replace or simplify the procedure of proof. The statement of the type “it is certain that two plus two is four” is made in such conditions and circumstances that no one experiences any doubt about its truth.  It even seems that one of the functions of the term “certain” consists in underlining this pragmatic background, this exceptional circumstances of some conversation. Present example illustrates well our thesis about the functional interdependence of the terms and notions defining a given epistemic situation. This interdependence leads to the situation that the adopted strategy of “role allocation” (through definition) to such terms as “truth”, “evidence” or “certainty” should be evaluated from the viewpoint of the relevance of the whole strategy, rather than the relevance of particular terms. It means that in various concepts, which equally well reflect the essence of cognitive situation, the definitions of truth, certainty or evidence may be quite divergent. The philosophical concepts of truth (certainty, evidence) have inherited this terminological instability from the everyday language usage. The comparative analysis of the following statements is instructive:
“I am sure that p is true, since it is evident”
“p is evident for me, since it is obviously certain”
“It is obvious for me that p is true, since it is certain”
“It is true that p is obvious and therefore it is certain”
“p is obviously certain, and therefore its truthulness is undeniable”. 
The analysis of the above and other similar statements defining essentially the same situation in everyday language (which need not be devoid of some reflective, theorising aspirations), can show us the ways leading to particular strategic decisions related to the definitions of truth, evidence and certainty, based on philosophical theories. 
4.	“It is certain that I am, since I think”. In the case of this statement (let us call it cogito in short) it is not certain whether it should be conceived as a universally valid general thesis, or a record of a certain material experience.  If former approach is adopted, it is yet no certain whether it should be formulated in the way: “whenever someone thinks, he/she exists”, or rather  “this subject exists that thinks (the thinking subject or res cogitans) whenever anyone reads or hears and understands the present statement”. Independently of the intention of subject expressing the cogito thesis, and independently of the fact whether it is attributed with validity within the given reflection act, in which the necessity is found for the existence of the subject currently experiencing the consciousness act (the act of “thinking”), or else with general validity, it is clear that the truth of this thesis is legitimised in a particular reflection act revealing the ego-logic structure of mental acts. The realisation of the mental act or process reveals its belonging to the subject that performs it, or provides its substratum. It means that the certainty of cogito statement is strictly related to the experience consisting in the understanding of its content as including the aspect of self-reference. This statement referring to all consciousness acts (i.e. all “thinking”) refers in particular to this act in which the utterance and its understanding occurs. In different wording, a certain version of cogito statement, reflecting its crucial quality of self-reference, is as follows: {I think that (I think and therefore I am) and therefore I am}. It is easy to observe the iteration that can be continued indefinitely, while preserving the a priori conviction about the validity (certainty) of statement. In this aspect, the similarity is revealed between cogito statement and the certainty of any other statement in which the record of a mental experience is contained, i.e. where the act of definite nature is recorded, for instance: “I can see a red surface”, “I do not like you”, “It seems to me that I am but an object of someone’s imagination, while truly I do not exist”. One cannot be mistaken about the occurrence or the content of an experience, since the unmistaken self-revelation of a thing as occurring and having definite content is the very essence of cognitive experience. This condition relates also to cogito statement. I cannot be mistaken about the fact that I think (the cognitive experience occurs). I cannot be mistaken about the fact that I experience the evidence of the cogito thesis. I cannot be mistaken as to the fact that cogito seems certain to me. Thus, it appears that cogito thesis is but a particular case, and also a certain generalisation, of the epistemological law claiming the undoubted character of the occurrence of cognitive act (in its self-revealing structure, including the assumption of the act subject), in its given content. Let us observe that the above quoted abstract formulation of this law is both such a specific case and a generalisation. Similarly to cogito, though much more clearly theoretically, it is a kind of the infinite sum of statements of a given type. For the given epistemological thesis, the following statements will be concerned: “I cannot be mistaken that I currently experience the observation, which contains the quality of red hue”, “I cannot be mistaken that I currently experience the recollection which contains the picture of my being a pharaoh”, etc. For cogito these statements will be qualified as the type: “I perceive something, therefore I am the perceiving self (the perceiving I)”, “I remember something, therefore I am the remembering self (the remembering I), etc. 
The validity of the cogito, and the thesis about the doubtless character of experience in its precise content, has purely tautological character. It can be reduced to the validity of stating the following identity: the conscious experience is a conscious experience, i.e. it is what it is.  Yet, it is not a purely banal tautology, since it opens the broad field of intellectual practice consisting in continuous co-ordination of each cognition act to the subject’s self-cognition. It is the field of reflection philosophy and the exploitation of the tautology I = I.  This philosophy relies on the pragmatic functions of certification, conviction, and truth awareness, which are fulfilled by the terms: “true”, “certain” or “evident”. They are used and developed, providing the basis for the “thinking of thinking”, i.e. the intellectual activity subordinated to the absolute self-legitimisation in itself. The semiotic qualities of the predicate “certain” and its correlates enable such activity and stimulate it. For instance, the formulation that cogito is an evident, true and certain statement is a method of abridged description of its specific qualities as tautology: the reflexivity, iterability and redundancy. The explanation of this thesis, illustrating the above-defined concept of certainty, should provide an appropriate concluding element of present discussion: 
Cogito as an iterable thesis: I think that I think... therefore I am. It is the simplest form of reflective penetration of the consciousness act occurring in my self, showing me its evidence, i.e. directing me to its self-presenting content (which is the cogito thesis). 
Cogito as a reflexive thesis. A number of cogito expositions are possible showing the self-applicability of this thesis:
-	[I think: (I think therefore I am)], therefore I am; [{[I think: (I think therefore I am)] therefore I am}] therefore I am and further higher order iterations;
-	I think that [(I think therefore I am) therefore I am]; and iterations of this formula;
-	[I think that (I am because I think)] therefore I am; and iterations of this formula.
All these reflexivity formulas corroborate cogito, i.e. they show the truthulness of this thesis when applied to itself. 
Cogito as redundant thesis. Its redundancy (inflationary character) consists in mutual excess of both parts: “I think” and “I am”.  The simple contemplation (inwards reflection) of the occurrence of consciousness act is reducible to 
“I think, I think, I think...”.  The subject of this contemplation exists through its occurrence, i.e. its existence mode and its very existence rely on reflection. Yet, the purely existential reflection (having also the contemplative character): “I am, I am, I am...” fulfils exactly the same function.  It is exactly equivalent whether I say: “I am, I am, I am...” or 
“I think, I think, I think...”. It is exactly this indifference that is expressed by the cogito thesis. This indifference means also the “doubtless character”, or certainty of cogito “thesis”, since the simple identity expressed by the formula “I am, I am, I am...” and “I think, I think, I think...” is not a statement (having different subject and predicate) and therefore cannot be evaluated by the categories of “doubted or undoubted status”. Cogito ergo sum is an undoubted formula in the sense that this category does not fall in the field of “doubted or undoubted”, and in the very strict wording it is impossible to put it in doubt.