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\title{An Historical Discourse on Phenomenological Platonism}
\author{Simone Testino}
\date{June 2023}
\begin{document}
\maketitle
\begin{abstract}
Parmenides definitely played a crucial role in the formation of the platonic thought and therefore my analysis will start from a couple of his verses, which I comment on, referring to E. Husserl. After this analysis of text I will consider the subject more conceptually, aiming to show that Platonism can be well interpreted in a phenomenological way.
\end{abstract}
\section{Parmenides in Two Verses}
I have two aims in this section: first I want to give an intuition of the Parmenidean \textgreek{εἶναι} through just two verses and their analysis\footnote{Original sentences have been taken from \emph{Parmenide, Sulla Natura}, Bompiani, G. Reale 2021 and I used the vocabulary \emph{GI}, Vocabolario della Lingua Greca $3^a$ Edizione, Franco Montanari. Books that helped the interpretation are \emph{Storia della Filosofia Greca e Romana}, G. Reale, Bompiani, 2018 and \emph{Platone, Alla ricerca della sapienza segreta}, G. Reale, i Fari, 2019 and \emph{La Filosofia dai Greci al Nostro Tempo}, E. Severino, Rizzoli, 2021.}; secondly I want to sketch a connection between Parmenides and Husserl in order to provide reasons to believe that even the Platonic groundings in Parmenides have at least a very phenomenological taste. Such a palatable intuition will then become a concrete thesis when I analyse the two definitions of \emph{objectivity} and see how Platonic realism relates to the phenomenological conception.
\subsubsection*{I. The Circularity}
\begin{quote}
\textgreek{Ξυνόν δέ μοί ἐστιν, ὁππόθεν ἄρξωμαι· τόθι γὰρ πάλιν ἵξομαι αὖθις.}\footnote{Parmenides, B. 5}
\end{quote}
Only after having well captured the Parmenidean picture, one can actually read in such brief sentences the whole system. The sentence begins in a weak adversative (\textgreek{δέ}) since the author well knows that what he'll state is against common sense. He affirms that \emph{to him} (\textgreek{μοί}) it is \textgreek{ξυνός}, which denotes the \emph{least significance of something}, often translated as \emph{common to many} or \emph{indifferent}; the object of this is \textgreek{ὁππόθεν ἄρξωμαι}, where the first word denotes a \emph{starting point}\footnote{Remark: for a more proper translation one should consider it as an adverb, not a noun}, though as often happens in many languages, and in Greek even more, locative locutions are mostly to be understood metaphorically, this will be of most significance for the interpretation; the following verb, \textgreek{ἄρξωμαι}, which comes from the well known word \textgreek{ἀρχή}, is a declination of the verb \textgreek{ἄρχω} denoting sometimes, like the Latin \emph{duco}, the action of \emph{command} and \emph{being in control} but also \emph{being the first} both in significance and time (we shall again notice that locality is one of the many meanings that \textgreek{ἄρξωμαι} as \textgreek{ὁππόθεν} have); the mediopassive voice shifts the meaning to the one involving less action by the subject, we shall here therefore understand it as \emph{to begin} (for more precision, one might identify it, the mediopassive voice only, with the deponent Latin verb \emph{orior}). The next sentence begins recalling \textgreek{ὁππόθεν}, we can here simply translate \textgreek{τόθι} as \emph{there} and \textgreek{γὰρ} adds emphasis to his statement. On the other hand, \textgreek{πάλιν} has two main meanings which can be reassembled in the German distinction between \emph{wieder} and \emph{wider}, the precise meaning is remarked by repetition by the last word \textgreek{αὖθις} denoting recurrence, it may be interpreted as never ending. The verb \textgreek{ἵξομαι} which comes from \textgreek{ἵκω}, or \textgreek{ἱκνέομαι} it mediopassive voice; in order to understand better its meaning we can compare it with another Greek verb meaning \emph{to come}, namely \textgreek{ἔρχομαι}: our verb has a more passive meaning, denoting that this \emph{return to the starting point} is not in the will of the author but instead imposed by more powerful strengths.\\
The interpretation I want to give to this sentence in order to let it span the whole Parmenidean system is the following: one should completely drop the locative and instead consider every dimension of the being so that time will recur on every predicate we can assert and therefore all that is, will be and has been is all part of \textgreek{ἕν}; and time itself is, not ruler of \textgreek{πάντα χωρεῖ}\footnote{All that changes, moves, becomes, from Heraclitus, Fr. 402.a}, instead anything but part of it.\\
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\subsubsection*{II. The \textgreek{νόημα}}
In order to have a deeper understanding of the limits (if they shall be called so) and the context of what \textgreek{εἶναι} denotes, one should understand its relation to \textgreek{νοεῖν} which is captured in the following passage:
\begin{quote}
\textgreek{[...]τὸ γὰρ αὐτὸ νοεῖν ἐστίν τε καὶ εἶναι.}\footnote{Parmenides, B. 3}
\end{quote}
This brief passage ends an unknown sentence with a crucial equality: the well known (yet unclear) \textgreek{εἶναι} with \textgreek{νοεῖν}. Two are the words that form Greek into English could be simply translated with the verb \emph{think}: the just met \textgreek{νοέω} or \textgreek{φρονέω}. The former has in Greek a broader meaning, can be translated as \emph{feel}, \emph{acknowledge}, \emph{know}, \emph{understand} and, not least, \emph{see}\footnote{Remarking the hypothesis on the strong bond present in the Greek culture between thought and visual perception.}. On the other hand \textgreek{φρονέω} ranges over a way narrower set of meanings, all referring solely to mental activities, from proper actions of the mind, like \emph{think} or \emph{understand} to some states like \emph{have something in mind}, \emph{being wise} or, more generally, \emph{have mental faculties}.\\
The interpretation of such a passage requires certainly a solid knowledge of the context, there are definitely too many ways to interpret such a statement if taken by itself. In order to do so, I want to relate this passage to a couple of paragraphs by E. Husserl in which he gives his (\emph{offenbar}) interpretation of the verse.
\begin{quote}
Die ersten Keime eigentlicher vernunftkritischen Problematik, die wir vor allem uns etwas näherbringend müssen, einer Problematik, die nicht auf Wahrheit und Sein, nicht auf Theorie und Wissenschaft im Sinn eines theoretischen Systems gerichtet ist, sondern eben auf das Vernunftbewußtsein selbst, treten uns im Altertum bei Parmenides und vor allem in wirksamer negativistischer Form in der Sophistik entgegen. Ihr Skeptizismus hinsichtlich der Wahrheit und des Seins als Korrelates der Wahrheit hat seine Parallele in einem Skeptizismus hinsichtlich des Erkennens, nämlich hinsichtlich der Möglichkeit eines auf Seiendes im Sinne einer bewußtseinstranszendenten Objektivität gerichteten Erkennens.\\
Gegen die Parmenideische These von der "Identität" von Denken (noein) und Sein, deren Sinn offenbar der war, daß das im "vernünftigen" Denken Gedachte und das wahrhaft Seiende unabtrennbare Korrelate sind, endet Gorgias, indem er das Sein im natürlichen Sinn als objektives (bewußtseinsjenseitiges) Sein versteht, ein: Denken ist Vorstellen, Vorstellen ist aber nicht Vorgestelltes.\footnote{E. Husserl, \emph{Phänomenologie und Erkenntnistheorie}, 1916, Kapitel II, 6}
\end{quote}
This passage outlines a debate I regard as very central in the whole ancient philosophy, though in ancient times it remained very clouded, there were not yet the means to shed light upon the essence of the question. This brings me to make a jump in time but trying to keep the focus as closed as possible to the original Platonism.
\section{Plato, Gödel and Husserl on Reality}
Before getting into the core of the topic I need to define those words that will be necessary to state the question properly; in fact the following are two very different attempt to define objectivity which will show particular features of the metaphysical context they are inserted in.\footnote{The upcoming distinction has been sketched both in E. Husserl, \emph{Phenomenologie und Erkenntnisstheorie}, 1916, Kapitel II, 6 but also in Tieszen, R., 2011, \emph{After Gödel: Platonism and Rationalism in Mathematics and Logic} Oxford and New York: Oxford University Press. That this lays in the very centre of both writings is though not surprising: as I will later better explain, Phenomenology has been of great influence in later Gödel's philosophy who, probably more than any (or most explicitly), synthesised Platonism and Phenomenology. For more, see: \url{https://plato.stanford.edu/entries/goedel/goedel-phenomenology.html}}
\subsection{Objectivity Defined}
Before distinguishing two very different definitions of objectivity, I want to list a couple of remarks that hold for both: first I have to make clear what \emph{can} be objective, namely the domain of our predicate and I think that this is a feature that the two definitions, at a first sight\footnote{I will later give a reason why one shall not believe so, though, for now, it is simpler to assume their domains to be the same.}, have in common. They both are predicates on propositions, namely those that we call true or false\footnote{That is to say that the domain of objectivity is the same as the one of truth. One can alternatively regard objectivity as being a predicate on definitions of truth, as one might notice in the following definitions by E. Husserl, though no relevant difference will occur for the coming reasoning.}. One might alternatively say that those are predicates on events or on objects, though I see no relevant differences for the next stages and I want to stick with the following writings, which regard objectivity as being predicate on propositions.
\subsubsection*{Transcendental Objectivity}
\begin{quote}
[...] eine Wahrheit, die "Objectives", nämlich außersubjektive Gegenstände, betrifft.\footnote{E. Husserl, ibidem}
\end{quote}
Those propositions whose truth we regard as being \emph{outside} of the \emph{subject} are to be called transcendental objective. Both words \enquote{subject} and \enquote{outside} are to be better clarified, I'll avoid to make a proper excursus on what we should call a \enquote{subject}, I just refer to the Descartes consciousness as being made solely by \emph{res cogitans}. Though \enquote{outside} really captures the idea of objectivity and is to be understood as a sort of independence of the truth from the subject. As anyone would notice from the just stated sentence, objectivity is, in this context, a synonym of \enquote{real} from the well known theories on realism\footnote{First of all, it is common to see realism as a theory on events and not on propositions (or definitions of truth), this particularly holds when one considers that realism must be defined through causality (independence can be understood as \enquote{there being no causal relation}), which usually has events as domain, for more see: \url{https://plato.stanford.edu/entries/causation-metaphysics/}}. The philosophical object that most of all is to be considered \emph{outside} of the subject, is definitely the \emph{noumenon} by Kant and similarly any form of materialism.
\subsubsection*{Phenomenological Objectivity}
\begin{quote}
[...] Wahrheit, die an sich gilt.\footnote{E. Husserl, ibidem}
\end{quote}
Phenomenological objectivity is a predicate that we attribute to those propositions that, no matter what happens to us, we'll always regard them as true, it is absurd to deny them. In order to give a more precise description of this predicate, like I did previously when I connected transcendental objectivity with realism, I can now compare phenomenological objectivity with the predicate \emph{$x$ is believed by the subject to be necessary}. Here the role of the subject is crucial, since phenomenological objectivity refers to nothing but to what appears to the subject.\\
To conclude this section I note that the remark I made at the beginning is not quite right though, the domain of the two predicates seems to not be the same anymore. Both regard proposition, though, before investigating if it is objective or not, we're able to say if such a proposition could either be transcendentally objective or phenomenologically objective\footnote{What I’m implicitly meaning with this sentence is that the intersection of the domains of the two predicates is empty}: in fact the distinction between these two classes of propositions can be done independently from the definition of objectivity, they come from the very first bricks one lays to build the metaphysical structure, only \emph{trascendental}, propositions, those regarding \emph{noumenic} objects can be trascendental objective and solely those that have no more than a \emph{subjective} value can be phenomenologically objective. Though it is very practical to define these two words, since they will help me in distinguishing clearly the metaphysical systems that allow transcendentality and those which don't. Here that those definitions are laid down I can properly state the central question of the essay:
\begin{center}
\emph{Are propositions on Platonic Ideas transcendentally objective?}
\end{center}
\subsubsection{An Historical Remark}
There are many ways one could approach any question and therefore one should firstly clarify precisely in which sense she's answering it. Historically, I suppose, the former question is nonsense. The distinction, as I have sketched it, between phenomenological and transcendental objectivity is typical of the modern era:
\begin{quote}
Das Erkenntnisproblem im Sinne des besprochenen Transzedenzproblems [...] [wird] durch Descartes' \emph{Meditationes} inauguriert.\footnote{E. Husserl, ibidem, Ch. 2, 8}
\end{quote}
Therefore it makes no sense to ask if Plato actually meant his \textgreek{ὑπερουράνιον τόπον} to be the place where all propositions are phenomenologically or transcendentally objective. Several historical considerations, though, could be made, for example noticing the second verse I reported by Parmenides. Though this is not in my interest, I want to see how the shape(s) of Platonism(s) have changed during the centuries, while many enriching philosophical ideas came along. One of these steps in the evolution of Platonism can, in my opinion, be well observed in Gödel during the husserlian developments of Phenomenology.
\subsection{Gödelian Implications on Completeness}
It is not the case that the name of Gödel can't be written without the word \enquote{(in)completeness} next to it, in fact I have a good reason to talk about completeness here. Previously I introduced the two forms of objectivity as signs of a specific feature of the metaphysical structure they were defined in and now I'll use completeness for a similar purpose. In fact Gödel develops a very strong conception of completeness as the result of a certain internal structure which might answer our previous question.
\begin{quote}
Rationalism is connected with Platonism because it is directed to the conceptual aspect rather than toward the (real) world.\footnote{Wang, 1996, \emph{A Logical Journey: From Gödel to Philosophy (Representation and Mind)}, Cambridge, MA: MIT Press, 9.4.18}
\end{quote}
Such rationalism in the most Platonic sense is the one that gives Gödel the grounding to believe that the world, in a sense, is complete, in fact:
\begin{quote}
There are systematic methods for the solution of all problems (also art, etc.).\footnote{ibidem, p. 316.}
\end{quote}
And similarly:
\begin{quote}
I am under the impression that after sufficient clarification of the concepts in question it will be possible to conduct these discussions with mathematical rigour and that the result will then be [...] that the Platonistic view is the only one tenable.\footnote{\emph{Gödel Collected Works}, III: \emph{Unpublished essays and lectures}, S. Feferman, J. Dawson, S. Kleene, G. Moore, R. Solovay, and J. van Heijenoort, Oxford: Oxford University Press., p. 322}
\end{quote}
I deduce from these paragraphs that in order to get the proper realism that is proper of Platonism, there is no need at all to assume there to be some noumenic objects which are to be considered \emph{outside} of the subject; again, historically both affirming and negating this claim is nonsense, as I explained before, I remark that I'm not referring to the thought by Plato himself, instead what we can conceptually derive from it. Resuming the discourse, there's no need in Platonism of such noumenic objects, it can all be properly described by considering phenomenological objectivity instead of the more immediate transcendental objectivity.
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