The Boiling Frog

The boiling frog is a fable describing a frog being slowly boiled alive. The premise is that if a frog is put suddenly into boiling water, it will jump out, but if the frog is put in tepid water which is then brought to a boil slowly, it will not perceive the danger and will be cooked to death.

The boiling frog story is generally offered as a metaphor cautioning people to be aware of even gradual change lest they suffer eventual undesirable consequences. It may be invoked in support of a slippery slope argument as a caution against creeping normality. It is also used in business to reinforce that change needs to be gradual to be accepted. The story is often used as a metaphor for the inability or unwillingness of people to react to or be aware of sinister threats that arise gradually rather than suddenly.

The boiling frog story has been used as a way of explaining the Sorites Paradox. Sometimes known as the paradox of the heap, it is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?

Color_gradient_illustrating_a_sorites_paradox_with_labels

Continuum fallacy

The continuum fallacy (also called the fallacy of the beard, line-drawing fallacy or decision-point fallacy) is an informal fallacy closely related to the Sorites paradox. Both fallacies cause one to erroneously reject a vague claim simply because it is not as precise as one would like it to be. Vagueness alone does not necessarily imply invalidity. The fallacy is the argument that two states or conditions cannot be considered distinct (or do not exist at all) because between them there exists a continuum of states.

Narrowly speaking, the Sorites paradox refers to situations where there are many discrete states (classically between 1 and 1,000,000 grains of sand, hence 1,000,000 possible states), while the continuum fallacy refers to situations where there is (or appears to be) a continuum of states, such as temperature – is a room hot or cold? Whether any continua exist in the physical world is the classic question of atomism, and while Newtonian physics models the world as continuous, in modern quantum physics, notions of continuous length break down at the Planck length, and thus what appear to be continua may, at base, simply be very many discrete states.

As an example, if a person (Fred) has no beard, one more day of growth will not cause him to have a beard. Therefore, if Fred is clean-shaven now, he can never grow a beard (for it is absurd to think that he will have a beard some day when he did not have it the day before).

For the purpose of the continuum fallacy, one assumes that there is in fact a continuum, though this is generally a minor distinction: in general, any argument against the sorites paradox can also be used against the continuum fallacy. One argument against the fallacy is based on the simple counterexample: there do exist bald people and people who are not bald. Another argument is that for each degree of change in states, the degree of the condition changes slightly, and these “slightly” build up to shift the state from one category to another. For example, perhaps the addition of a grain of rice causes the total group of rice to be “slightly more” of a heap, and enough “slightly” will certify the group’s heap status – see fuzzy logic.

A common first response to the paradox is to call any set of grains that has more than a certain number of grains in it a heap. If one were to set the “fixed boundary” at, say, 10,000 grains then one would claim that for fewer than 10,000, it is not a heap; for 10,000 or more, then it is a heap.

However, such solutions are unsatisfactory as there seems little significance to the difference between 9,999 grains and 10,000 grains. The boundary, wherever it may be set, remains arbitrary, and so its precision is misleading. It is objectionable on both philosophical and linguistic grounds: the former on account of its arbitrariness, and the latter on the ground that it is simply not how we use natural language.

A second response attempts to find a fixed boundary that reflects common usage of a term. For example, a dictionary may define a “heap” as “a collection of things thrown together so as to form an elevation.” This requires there to be enough grains that some grains are supported by other grains. Thus, adding one grain atop a single layer produces a heap, and removing the last grain above the bottom layer destroys the heap.

And so, relatively speaking, we have found ourselves back in the pot and the water is slowly getting hotter. At what point will we decide to jump out?
(It should be noted that the symbol for Gab is a frog)

A little fruit for thought! Also, here’s a song I use to get through the troublesome times :grinning:
Faith in God is the only true form of divination!

Ecclesiastes 4:12 - “Though one may be overpowered, two can defend themselves. A cord of three strands is not quickly broken”

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Its all about where we choose to “arbitrarily” place the zero [0] on the scale.

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Love Your Posts…

Kudos

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Fuzzy Logic

Fuzzy Math…

Good topic.

There’s the whole scenario of the heap just being too vast to properly make a proper assessment. I feel the gov uses this to their advantage.

If we set a boundary, for example 10,000 grains of sand is a heap but 9 999 isn’t, we have a
logistical issue at hand where it’s just too Impossible to discern anyway. Nobody is going to keep counting grains of sand because their too busy, too distracted, or maybe they just aren’t armed with the proper information. The gov is very aware of this.

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