Make Part look like Section and make Section look like paragraph; but with all the numbering preserved?

Question

So I am trying to write a book summary, a few pages long. Is there any way to make part look just like section, except preserving the Roman numbering for part; and make section look just like paragraph, except preserving the Arabic numbering for section? I tried with the following commands:

\let\part\section
\def\thesection{\Roman{section}}
\let\section\paragraph
\def\theparagraph{\arabic{paragraph}}

In some way, it worked for part; but it doesn't work for section, as once let section behave like paragraph, I can't add any numbering to it anymore...

Edit: I also need to make sure numbering of the paragraph-ized section not affected by the section-ized part; i.e., make the section numbers continue regardless of parts

Answer 1

Not sure what it is that you want but why not just use \section and \paragraph while changing the style of their numbering?

\documentclass{article} % ????
\usepackage{lipsum}

\usepackage{chngcntr} % for changing how counters get incremented
\counterwithout{subsection}{section} % continuous subsection numbering
\counterwithout{subsubsection}{subsection} % continuous subsubsection numbering
\counterwithout{paragraph}{subsubsection} % continuous paragraph numbering

\renewcommand{\thesection}{\Roman{section}}
\renewcommand{\theparagraph}{\arabic{paragraph}}

\setcounter{secnumdepth}{4} % number \paragraph in document
\setcounter{tocdepth}{4}    % put \paragraph in ToC

\begin{document}
\tableofcontents
\section{First section}
\lipsum[1]
\paragraph{First paragraph}
\lipsum[2]
\paragraph{Second paragraph}
\lipsum[2]
\section{A section}
\lipsum[1]
\paragraph{A paragraph}
\lipsum[2]
\end{document}

In response to your comment I have added code so that paragraph numbering is continuous.