Written and collected by Zia H Shah MD, Chief Editor of the Muslim Times
Results from the 2020 PhilPapers survey, with responses from nearly 1,800 philosophers (mainly from North America, Europe, and Australasia), to questions on a variety of philosophical subjects and problems, revealed that 38% believe in platonism or abstract objects, 42% in nominalism and 20% in others.[1]
Two thirds to three fourths of top mathematicians are thought to be platonists.
Why do they believe in abstract objects?
The belief in abstract objects among philosophers and mathematicians is rooted in the desire to explain the nature of mathematical entities and the truths they represent. This belief is often associated with Platonism, a view that posits the existence of abstract, non-physical objects that are independent of human thought and language. Several key reasons underpin this perspective:
1. Ontological Commitment
Philosophers like Willard Van Orman Quine and Hilary Putnam have argued that our best scientific theories are committed to the existence of abstract mathematical entities. This is known as the Quine–Putnam indispensability argument, which suggests that because mathematical entities are indispensable to our scientific theories, we ought to accept their existence.
2. Objectivity and Universality
Mathematical truths exhibit a level of objectivity and universality that suggests they are not merely human inventions. For instance, the statement “2 + 2 = 4” holds true regardless of human opinion or cultural context. This universality implies the existence of abstract objects that transcend individual minds.
3. Explanatory Power
Belief in abstract objects provides a robust framework for explaining the consistency and applicability of mathematics. By positing that mathematical entities exist in an abstract realm, philosophers and mathematicians can account for the effectiveness of mathematics in describing the physical world.
4. Epistemic Access
Some argue that humans have a form of epistemic access to abstract objects through intuition or intellectual insight. This perspective suggests that mathematical discovery is akin to uncovering truths about a realm of abstract entities, rather than merely inventing useful fictions.
5. Avoidance of Paradoxes
Belief in abstract objects helps avoid certain paradoxes and inconsistencies that arise in nominalist or strictly formalist accounts of mathematics. By accepting the existence of abstract entities, philosophers can provide more coherent explanations for various mathematical phenomena.
In summary, the belief in abstract objects among philosophers and mathematicians is motivated by considerations of ontological commitment, the objectivity and universality of mathematical truths, their explanatory power, epistemic access, and the desire to avoid paradoxes. These factors contribute to the view that abstract entities exist independently of human thought and play a crucial role in our understanding of mathematics and the world.
I believe that abstract objects cannot exist except in the mind of a consciousness. So, the ontological necessity of abstract objects to me leads to God and should lead others, who do not have prior ideological commitment.
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