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  1. Muhammad Ikhwan Azlan
    MyJurnal
    The role of mathematics as a foundation of other
    sciences is well acknowledged since the dawn of
    modern science. This fundamental and important
    role is then not only limited to the natural and
    physical sciences but also further extended to
    the social domains of humanities. This article
    reviews the many definitions of mathematics as
    put forth by philosophers and mathematicians,
    how these definitions are understood, and how they subsequently influence the development
    of mathematics itself as well as other disciplines
    influenced by mathematics. These definitions
    are: mathematics as the science of teaching
    and learning (ʿulūm al-taʿālim); mathematics as
    abstraction or the construction of abstracts;
    mathematics as logic; mathematics as a formal
    system; mathematics as the science of quantity and
    structure, mathematics=ontology; and mathematics
    as intellectual exercise (riyāḍiyyāt). Based on the
    aforementioned definitions, this article attempts
    to analyse the ontological status of mathematics
    and mathematical objects based on the degrees of
    existence (marātib al-wujūd) framework which orders
    existence into five levels, namely essential existence
    (wujūd dhātī), concrete existence (wujūd ‘aynī), mental
    existence (wujūd dhihnī), verbal existence (wujūd lafẓī),
    dan formal or written existence (wujūd khaṭṭī).
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