Epigraph:
بَدِيعُ السَّمَاوَاتِ وَالْأَرْضِ ۖ وَإِذَا قَضَىٰ أَمْرًا فَإِنَّمَا يَقُولُ لَهُ كُن فَيَكُونُ
He is the Originator of the heavens and the earth, and when He decrees something, He says only, ‘Be,’ and it is. (Al Quran 2:117)
Have they been created from nothing, or are they their own creators? Have they created the heavens and the earth? In truth they put no faith in anything. (Al Quran 52:35-36)
This article is not written by AI or a robot but by Zia H Shah MD
In this article I have borrowed extensively from Encyclopedia Britannica and Stanford Encyclopedia of Philosophy.
Different numbers, which are infinite and all the mathematical formulas and equations are among abstract objects.
One doesn’t go far in the study of what there is without encountering the view that every entity falls into one of two categories: concrete or abstract. The distinction is supposed to be of fundamental significance for metaphysics (especially for ontology), epistemology, and the philosophy of the formal sciences (especially for the philosophy of mathematics); it is also relevant for analysis in the philosophy of language, the philosophy of mind, and the philosophy of the empirical sciences.
The abstract/concrete distinction has a curious status in contemporary philosophy. It is widely agreed that the ontological distinction is of fundamental importance, but as yet, there is no standard account of how it should be drawn. There is a consensus about how to classify certain paradigm cases. For example, it is usually acknowledged that numbers and the other objects of pure mathematics, like pure sets, are abstract (if they exist), whereas rocks, trees, and human beings are concrete. In everyday language, it is common to use expressions that refer to concrete entities as well as those that apparently refer to abstractions such as democracy, happiness, motherhood, etc. Moreover, formulations of mathematical theories seem to appeal directly to abstract entities, and the use of mathematical expressions in the empirical sciences seems indispensable to the formulation of our best empirical theories (see Quine 1948; Putnam 1971; and the entry on indispensability arguments in the philosophy of mathematics). Finally, apparent reference to abstract entities such as sets, properties, concepts, propositions, types, and possible worlds, among others, is ubiquitous in different areas of philosophy.
Though there is a pervasive appeal to abstract objects, philosophers have nevertheless wondered whether they exist. The alternatives are: platonism, which endorses their existence, and nominalism, which denies the existence of abstract objects across the board. (See the entries on nominalism in metaphysics and platonism in metaphysics.) But the question of how to draw the distinction between abstract and concrete objects is an open one: it is not clear how one should characterize these two categories nor is there a definite list of items that fall under one or the other category (assuming neither is empty).
The first challenge, then, is to articulate the distinction, either by defining the terms explicitly or by embedding them in a theory that makes their connections to other important categories more explicit. In the absence of such an account, the philosophical significance of the contrast remains uncertain, for the attempt to classify things as abstract or concrete by appeal to intuition is often problematic. Is it clear that scientific theories (e.g., the general theory of relativity), works of fiction (e.g., Dante’s Inferno), fictional characters (e.g., Bilbo Baggins) or conventional entities (e.g., the International Monetary Fund or the Spanish Constitution of 1978) are abstract?
It should be stressed that there may not be one single “correct” way of explaining the abstract/concrete distinction. Any plausible account will classify the paradigm cases in the standard way or give reasons for proceeding otherwise, and any interesting account will draw a clear and philosophically significant line in the domain of objects. Yet there may be many equally interesting ways of accomplishing these two goals, and if we find ourselves with two or more accounts that do the job rather well, there may be no point in asking which corresponds to the real abstract/concrete distinction. This illustrates a general point: when technical terminology is introduced in philosophy by means of examples, but without explicit definition or theoretical elaboration, the resulting vocabulary is often vague or indeterminate in reference. In such cases, it usually is pointless to seek a single correct account. A philosopher may find herself asking questions like, ‘What is idealism?’ or ‘What is a substance?’ and treating these questions as difficult questions about the underlying nature of a certain determinate philosophical category. A better approach may be to recognize that in many cases of this sort, we simply have not made up our minds about how the term is to be understood, and that what we seek is not a precise account of what this term already means, but rather a proposal for how it might fruitfully be used for philosophical analysis. Anyone who believes that something in the vicinity of the abstract/concrete distinction matters for philosophy would be well advised to approach the project of explaining the distinction with this in mind.
Let us read again the most important line above:
Though there is a pervasive appeal to abstract objects, philosophers have nevertheless wondered whether they exist. The alternatives are: platonism, which endorses their existence, and nominalism, which denies the existence of abstract objects across the board.
How are the academic philosophers divided on this issue of Platonism versus nominalism. Let us go to a recent poll of the Western philosophers, who on a different question were noted to be 75% atheists:
Abstract objects: Platonism 39.3%; nominalism 37.7%; other 23.0%.
For the sake of simplicity let us assume that half the top academic philosophers believe that abstract objects necessarily exist and half of them believe in nominalism and say they do not exist. When it comes to mathematicians, we know from other polls that 3/4th of them are Platonists.[1]
The whole of the poll and all the 30 questions can be reviewed in the following PDF file. Perhaps, each question is a goldmine for our future philosophical and theological discussions:
According to Encyclopedia Britannica:
A complete explanation of mathematical Platonism should begin with what is meant by an abstract object. Among contemporary Platonists, the most common view is that the defining trait of an abstract object is nonspatiotemporality. That is, abstract objects are not located anywhere in the physical universe, and they are also entirely nonmental, and yet they have always existed and they will always exist. This understanding does not preclude having mental ideas of abstract objects; according to Platonists, one can. For example, one can have a mental idea of the number 4. However, having a mental idea of the number 4 does not imply that the number 4 is just a mental idea. After all, people have ideas of the Moon, but it does not follow from that fact that the Moon is just an idea, because the Moon and people’s ideas of the Moon are distinct things. Thus, when Platonists say that the number 4 is an abstract object, they mean to say that it is a real and objective thing that, like the Moon, exists independently of people and their thinking but, unlike the Moon, is nonphysical.
I beg to differ here a little. If nothing exists at all, no universe, no humans, no consciousness, no God, a total blank, the abstract objects cannot exist:
Nothing comes out of absolute nothing: ex nihilo nihil fit!
This is examined in further details in a separate article: The best proof against atheism is to imagine what they profess: What if nothing exists, no God a total blank!
Again according to Encyclopedia Britannica:
Abstract objects are also, according to Platonists, unchanging and entirely noncausal. Because abstract objects are not extended in space and not made of physical matter, it follows that they cannot enter into cause-and-effect relationships with other objects.
Platonists also assert that mathematical theorems provide true descriptions of such objects. What does this claim amount to? Consider the positive integers (1, 2, 3,…). According to Platonists, the theory of arithmetic indicates what this sequence of abstract objects is like. Since ancient times, mathematicians have discovered all sorts of interesting facts about this sequence. For instance, the Greek mathematician Euclid proved more than 2,000 years ago that there are infinitely many prime numbers among the positive integers. Thus, according to Platonists, the sequence of positive integers is an object of study, just as the solar system is an object of study for astronomers.
On the one hand, it is impossible to deny the existence of mathematical abstract objects and on the other hand to imagine them freely unless guided by certain ideology without any consciousness, be it divine, human or extraterrestrial. Remember, half the philosophers believe in Platonism and half in nominalism and three fourth of mathematicians believe in Platonism. If we believe in mathematical heaven then the religious heaven is not too far: How Could Most Mathematicians Believe in Heaven, But Not in God?
I just read this paragraph in Reddit to refute Platonism:
Without the existence of beings able to conceptualize numbers, there is no reason to assume that ‘510’ exists. A dog may see 510 leaves on the ground, but without language or a mind capable (as far as we know) of mathematical logic, there is no reason to assume that ‘510’ is an inherent property of those leaves or that the dog has any concept of such things. Mathematics is a process used to describe relations between observed or abstract concepts, but there is no reason to assume that ‘510’ exists outside of the conceptual or physical objects they represent. Likewise, it is easy to imagine ‘510’ not existing at all; if we had decided on binary, rather than base 10, numerals, our conception of ‘510’ would be ‘0b111111110’ instead. Since computers think in this exact method, from the perspective of a computer’s ‘consciousness’ this is an equally true statement, and there is no reason to assume such a thing exists beyond the computer that processed the value.
If we believe in nominalism and mathematics and laws of nature do not exist, then how can we have a universe that we live in: The best proof against atheism is to imagine what they profess: What if nothing exists, no God a total blank!
Platonism or nominalism the necessity of God is inescapable: Video: Is God Necessary or Who Made God?
References
Categories: Highlight, Metaphysics, Philosophy, Quran, The Muslim Times, Theology
Richard Swinburne nicely articulates his views on nominalism in the above video. I do not agree with his position on Platonism, as outlined in my article above.