Critical Thinking: Fallacies from Relevance X

Posted by Hallee on Apr 1, 2010 in Critical Thinking, homeschooling |


Fallacies from Relevance

A fallacy from relevance occurs when the response to a conclusion or an argument is not relevant to the conclusion or argument. These are fallacies that ignore the point at hand and attempt to derail the argument by bringing irrelevancies into the arena of the debate. In this post, I will discuss the Fallacy of Division and Fallacy of Composition.

Fallacy of Division

A Fallacy of Division is committed by inferences based upon the fact that a whole has a property leading to a conclusion that a part of the whole also has that property.  While for some properties this is a legitimate form of inference, for most properties this line of inference is fallacious.


  1. Water is liquid.
  2. (Therefore:) H2O molecules are liquid.

This argument, in attributing liquidity, a macro-property of water, to its constituent microscopic parts, commits the fallacy of division. Though water is liquid, individual molecules are not.

Note, however, that an argument with the same logical form but inferring a different property — for example scale — say from the fact that a steak knife is smaller than a saber that every part of the steak knife is smaller than a saber, would not be fallacious.   The fallacy is mainly due to the property one infers based on the given facts.

The Fallacy of Division is the reverse of the Fallacy of Composition.

Fallacy of Composition

This pattern of argument is the reverse of that of the Fallacy of Division. The Fallacy of Composition is the fallacy of inferring from the fact that every part of a whole has a given property that the whole also has that property.  As with Division, it is not always fallacious, but one aught to exercise caution in making inferences pertaining to properties in this form.


  1. H2O molecules are  solid particles
  2. (Therefore:) water is solid

Of course, water can be solid in frozen form, but speaking of liquid or gaseous water vapor, this argument is fallacious.  Therefore, in the case of ice, it is so, but in the other two cases it is not so.  To infer that it is always so based upon the premise is fallacious.

Here is another example that pertains to distance:

  1. Every segment of the journey from here to there is less than one mile.
  2. (Therefore:) The entire trip is less than one mile.

Obviously, an journey consisting of many short segments may itself be much longer than a single mile.  While it may also prove true, it is not always true, and to infer it is always so based upon the premise is fallacious.

Just as with the Fallacy of Division, not all arguments of this form are fallacious. Whether or not they are depends on what property is involved in the premise and the conclusion. Some properties, such as distance or duration, may be possessed by every part of something but not by the thing itself. Others, such as being bigger than a bread-box, must be possessed by the whole if possessed by each part.


Where properties of Composition and Division can be used without fallacy is dependant upon the properties being investigated and the argument form.

For example, if I were to posit based on the property of duration:

  1. Every song on this album is less than one hour in duration
  2. (Therefore:) The entire album is less than on hour in duration.

I have a committed a fallacy of Composition.  Obviously, an album lasting much longer than one hour can be composed of songs each lasting less than one hour.  However, if I were to posit based on the property of duration in the reverse manner:

  1. The entire album is less than on hour in duration.
  2. (Therefore:) Every song on this album is less than one hour in duration

Now, while this argument takes the form of the Fallacy of Division, it is not fallacious.  Obviously, an album lasting less than one hour in duration is going to be composed of smaller parts which are also less than one hour in duration.

Simple logic pulls back the curtain on what is and is not fallacious in determining these properties.

One case where it is difficult for unbelievers to decide whether the fallacy of composition is committed concerns the Cosmological Argument, sometimes called the Argument for Contingency, which argues for the existence of an “unconditioned” or “non-contingent” or  “supreme” being — to whit, God — who is often described as the Uncaused Causer or the First Cause.  This famous argument is also traditionally known as an argument from universal causation, an argument from first cause, the causal argument, or the argument from existence.  In it’s most classical form, this argument was laid down by St. Thomas Aquinas in his most famous work entitled SUMMA THEOLOGICA.  Here is his Argument from Contingency:

  • (1) Many things in the universe may either exist or not exist. Such things are called contingent beings.
  • (2) It is impossible for everything in the universe to be contingent, for then there would be a time when nothing existed, and so nothing would exist now, since there would be nothing to bring anything into existence, which is clearly false.
  • (Therefore:) There must be a necessary being whose existence is not contingent on any other being or beings.
  • (I assert that:) This being is that whom we call God.

The premise of the argument takes the fact that the universe is contingent — in other words, might never have come into being — as ultimately concluding the existence of our Creator who brought the universe into being.  This most famous form of the argument is supported by centuries of logical work from Plato who posited a “demiurge” or supreme wisdom and intelligence as the creator of the cosmos in his work Timaeus, to Aristotle who put forth the idea of a First Cause or Prime Mover in his work Metaphysics, and even from Parmenides whose famous syllogism “nothing can come from nothing” is the foundation of another obvious syllogism, that being everything cannot come from nothing.

The summary of the first two parts of the argument which form the premise are:

  1. Everything in the universe is contingent (i.e. could possibly have never existed).
  2. (Therefore:) The universe as a whole is contingent (i.e. could possibly have failed to exist.)

It is clear that this part of the argument has the form of the Fallacy of Composition; what is not clear to nonbelievers is whether it really is fallacious or sound. So, must something composed entirely of contingent parts itself also have a  contingent property? Or might it be that the universe is necessarily existent even though each of its parts is not?

Believers argue that every system in the universe is composed of irreducibly complex and vastly interdependent and contingent systems of order, which strongly argues for design, and therefore a Designer.  Unbelievers argue for randomness, waste, chaos, and undirected non-contingent processes.  Considering the incredibly vast and ordered systems in the universe, all without waste and all in amazing balance, which conclusion do you find more plausible or sound?

Another controversial example concerns materialistic explanations of consciousness. The mind-brain identity theory suggests that consciousness is just electrical activity in the brain and nothing more. Opponents of mind-brain identity theory sometimes argue as follows:

  1. The brain is composed of unconscious neurons.
  2. (Therefore:) The brain itself is not conscious.

This argument takes on the form of the Fallacy of Composition and is clearly fallacious.  Since consciousness actually exists, it is certainly difficult to see how consciousness can emerge from purely material processes, but the mere fact that each part of the brain is unconscious does not entail that the whole brain is the same.  Believers understand that consciousness is that which we call our immortal souls, which is separate and distinct from our material bodies that are merely the mechanism that presently houses our eternal selves.  Those who have no faith believe that consciousness is merely accidental electrical impulses with neither meaning nor purpose.  Considering that you are able to comprehend what you just read, and that these expressions of ideas may have touched you on many intellectual, emotional, or even spiritual levels, which conclusion do you find more plausible?

brain toolsConclusion:

Recognizing truth is an essential survival tool for the mind, and ultimately, for the soul.  It is vital that believers weigh the so-called “wisdom” of the world on the perfect scale of authoritative scripture.  (I Corinthians 1:19-21)

Teaching our children the ability to recognize fallacies of this type, giving them the intellectual skill to deconstruct these types of arguments, will ensure that the arguments they, themselves, will one day make are at least valid and thoughtfully arrived upon. It will also assist them to investigate more deeply into the conclusions espoused by those in the world whose motives might not come from love and might not have been very carefully arrived at or well researched.

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