pair of black shoes on sand
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Often times we encounter terms in our everyday language which are not clearly defined and could encompass somewhat of a grey area. This ambiguity or vagueness does to a certain make us question where the boundaries and limitations are between one category and another. One common example that is utilized to demonstrate the issues with the Sorites Paradox is the difference between the definition between a grain of sand and a mound of sand. While we can all come to the consensus that one grain of sand does not constitute a mound nor does two or three.  However, when does a gathering of multiple grains of sand from a mound? If we have a precise number that operationally defines how many grains of sand composes a mound of sand, we eliminate the murky nature of the term “mound”[1].


As you could surmise you could certainly see how this premise is applicable to a myriad of other scenarios other than the defining number of grains of sand that are the minimum to qualify under that definition. One common criticism of Libertarianism is the lack of a clear distinction of boundaries in regards to policy. While I would tend to disagree due to the fact that the Non-Aggression Principle and the Constitution provide some clear parameters, I do not want to get this blog entry to far into the topic of politics. This example is merely to illustrate how the concept can be applied in a practical sense. Similar to my blog on free will, this will be a cursory overview of the Sorites Paradox with me providing some commentary.



The Sorites Paradox is defined as the paradoxical argument that transpires due to the indeterminacy on the parameters of how a specific term or label is applicable. This problem is primarily engendered by a lack of sharp delineation. It should be noted that this paradox is applicable to names, verbs, and adverbs. The paradox’s name Sorites derives its name from Soros which roughly translates to a heap in Greek. The logician   Eubulides of Miletus created the problem known as “The Heap” where if one grain of sand is not a heap and two grains are not a heap, where do you delineate a grain of sand from a heap? This was one of many puzzles devised by Eublides to address this semantic conundrum. Another well known of these puzzles was known as “The Bald Man Problem” If having several strands of hair on your head you are still bald at what point are you no longer bald? [2]



If we have a predicate with no real operational definition or well-defined boundaries how can we remedy this issue? The thing is when looking at the defining terms of weight and measurements it is clear to see how there is very little vagueness.  An excellent example would be how in regards to measurements after twelve inches the length would be then be measured in feet and attributed the label of measuring one foot. The same is applicable to weight, after an object, entity, etc. weighs sixteen ounces it can then be referred to as one pound. As is evident with the example of weights and measures is that you circumvent the vagueness through sharp delineation by the fact that these terms are defined by parameters that are quantified. The fact that you can objectively determine one category from the other is due to the fact each is clearly segregated on numeric grounds. There is little debate whether sixteen ounces would be considered a pound. However, how do we make delineations when the predicate or term itself does not do not have an inherent quantification connected to the definition?


There are several ways to approach resolving this paradox, the first resolution will be from the Epistemic paradigm. Essentially, this view if we can clearly define the predicate by clear definition then one of the contingencies must be incorrect other than the first one. Obviously, one grain of sand is not a pile, heap, or mound. Many critics of this approach would counter by stating, which of the other contingencies do we reject?  This is certainly a valid consideration. However, holders of this perspective support this paradigm on the premise that we are ignorant of the defining variables that sharply separate a concept such as liberty that is difficult to quantify. Therefore, there is a dividing line, however, we are unaware of where it is [3].


Then there is the Supervaluationism perspective which has a set of parameters for what defines a specific predicate. If the entity meets some of the criteria for the predicate it is considered to be true. However, if it meets all of the variables qualifying it for specific predicate it is Super-true and actually fitting the description of the predicate, making it appropriate to be label as such. The reason for this is that if it applies to all measures of the definition of the predicate then it will always be true. Either or not someone who is 5’10” is tall is extremely relative, yet someone who is 8′ tall would always be considered tall, making that statement super true. So in other words, if a predicate is applicable in all situations it is ultimately true making it equivalent to be true in the eyes of this paradigm. Because if it is always true there is little debate about whether or not the noun, adjective, adverb, etc is appropriate [4].


Please note that this argument for resolution is far from being invulnerable from the being dismantled by criticism.  For one the fact that the perspective states that a statement can be true and false at the same time,  X number of grains of stand = a mound, yet a collection of -X number is not. This perspective utilizes sharpening to have a predicate be applicable to the extent to which it is true. However, the law of excluded middle comes into play here. Due to the fact that there are “borderline” instances that this perspective broadly glosses over and doesn’t acknowledge. In a sense, it does not address the purgatory cases, where the predicate lies between two distinctions and cannot be neatly placed in either. A second issue is how it attempts to characterize “vagueness” because it does precisely define the vagueness by either (+,+ as Super-true), (+,- Prenumbra), (-,- Negative). It would appear as if the vagueness has been precisely defined, so it is really still ambiguity? The third issue with this approach is the fact that it suffers from the problem of higher-order vagueness. The reason for this is the fact that there is a sharp division by sharpening or adjusting the predicate to fit into Super-true, Prenumbra or true, and negative category. In some ways, the distinction between the three classifications is just as ambiguous as the predicate. Then we slide into a slippery slope of questioning if we could extend the range of borderline case for one of the three specific classifications of truth for the application of the predicate. [5]


Another potential perspective solution comes to form the paradigm of the Many-Valued Logic perspective. This philosophical stance is asserting that a sentence or train of logic is only as true as the truth of the variables that compose it. This perspective is a departure from classical logic in the sense that it holds the assumption that there can be multiple truth values. Which classical logic holds that there can only be one. [6] Similar to the previous perspective examined this view purports that the three classifications of truth are still valid,  Super-True, Prenumbra, and negative. However, a variation on this stance known as fuzzy logic supports the premise that there is an infinite range of truth it is merely a matter of degree. For a kind of morbid example, someone can be physically alive, yet clinically brain dead. Even when someone is deceased cognitively and are inanimate, their hair and skins cells are still alive (I am talking about pre-decomposition). I apologize for the gruesome example here, however, I personally feel that illustrates the premise of the assertions of fuzzy logic splendidly [7].


The final perspectives we will be examining for resolving this quandary is the Contextual perspective and embracing the paradox. In this stance, the assertion is that we can not clearly delineate or define vagueness, however, through this admission we can use it as a stepping stone of how to proceed. What do I mean by this?  Well, essentially we would have to create the parameters for those boundaries. The final approach is to merely embrace the paradox in the sense that we take the conditional statement and apply it in its totality.  We take the positive or negative condition and make it applicable to every scenario. For instance, everyone is tall. However, if everyone was short height wise obviously this would be an untrue statement. From my own personal perspective, the issue becomes if we treat it as an all or nothing application, we are negating the validity of the reciprocal condition, which may be valid in a specific circumstance. Embracing the paradox is far from a reasonable approach in my opinion because it obtusely applies a potentially untrue conditional statement without consideration for other invalidating contingencies. Even to the least rational of us would seem to be an outlandish approach towards remedying the issue of setting up clear boundaries.



As is evident from the entity of this blog entry the Sorites Paradox is a complicated problem that resembles a semantic minefield that needs to be guided with the utmost precision. As open-ended and mind-bending as grappling with the Paradox itself and attempting to compose conclusions, the solutions provided by professional academics are equally if not more perplexing. I paraphrased all of the solutions descriptions in hopes of relinquishing confusion. However, these solutions are very specific to a certain string of logic and can be a convoluted labyrinth in their own right. I really hope that this blog post was at the very least interesting and informative versus boring and befuddling. I have to be forthright here, the topic of the Sorites Paradox was more challenging than I anticipated. It really is a reminder of how nothing is quite as linear as it seems from the superficial level. It easy to over this problem and provide a quick fix solution, however, the unwitting and rash who attempt this will end up in a logical or semantic pitfall. To purport you have the solution without extensive research would be intellectually dishonest, erroneous, and even kind of foolish. To believe that you have a concrete answer when philosophers have been grappling with this issue for thousands of years is supremely arrogant. I personally believe that at this point in human history we do not have a clear-cut solution, odds are we never will. I do not mean to sound judgmental towards those who believe hastily they have the magic bullet for this problem, however, you, in my opinion, were seduced by the illusion of simplicity that this philosophical puzzle carries.


This paradox, if anything teaches such a lesson about being unassuming. The reason why I purpose this is that it is really easy to fall into the “seductive illusion of simplicity”. A phrase I just coined, unless I am inadvertently is plagiarizing this from someone else. If so please let me know immediately!!! This illusion transpires when a seemingly simple question requires a more complex solution, yet due to the appearance of simplicity, we are eager to provide a rash solution. Similar to the misapplication of Occam’s Razor, which I will cover sometime down the road, is an intellectual pet peeve of mine. Actually to some extent is related to the concept of Occam’s Razor the more I think about it. Folks sometimes the simplest answer is not always the best or the correct answer. Especially for such an intellectually controversial topic and subject matter. My personal opinion on this one is if you have to attempt to address it try a mixture or combination of the elements of the solutions listed previously. While it may not be possible to resolve the paradox at the present time if you must attempt it you will need a basic semantic or logic based paradigm to approach it.  It seems like it would be easy to remedy this issue by providing a detailed operational definition to the predicate to control for the variable of ambiguity blurring the lines between categorical predicates. However, I know better than to assert this two promptly without proper evaluation of the veracity of such suggestions. While I would not assert this to be a solution it may be an interesting method to explore.



3 thoughts on “SORITES PARADOX

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