Saturday, December 13, 2025

Composition Fallacy/The Fallacy of Division: Satire Und Theology Version

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Composition Fallacy/The Fallacy of Division

Preface

Originally published 20160609, slight revisions and additions 20251213.

PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.

Composition Fallacy

'The fallacy of composition occurs when it is claimed that what is true for individual members of a class is also true for the class considered as a unit.' (62).

'It is fallacious to suppose that what is true of the parts must also be true of the new entity they collectively make up.' (62).

'This must be a good orchestra because each of its members is a talented musician.' (62).

Pirie explains this is fallacious as members in the orchestra might not play and perform well in unison with others. (62).

For clarity with this weighty material:

Individual to corporate

I t C (My add)

Each member is a talented musician, therefore it must be a good orchestra. (My add)

I would opine that it can take less than each member to not be a good 'team player' to cause an orchestra not to be considered good sounding, it may simply take one or so 'bad apples.'

Pirie then uses the European football example of a club transferring in top players, that are soon transferred out because they do not fit in well with the team. (62).

Therefore I would not merely state:

As it has the best individual talent, therefore, Team Canada will win the 2016, World Cup of Hockey.

Consider:

According to experts and commentators, Team Canada has had the best individual talent almost every 'best on best' tournament, but wins most of the tournaments, not all of them.

In my view, other propositions are required to strengthen a related argument, although with changes in terminology.

Team Canada has excellent individual talent.

Team Canada has excellent individual skill.

Team Canada has players that have won together as a team.

Team Canada has several Stanley Cup champions.

Team Canada has several Olympic Gold Medalists in Ice Hockey.

Team Canada will have home ice advantage.

Therefore:

Team Canada could reasonably win the 2016 World Cup of Hockey in Toronto.

(Team Canada did win, 2025 note)

Blackburn defines this fallacy similarly:

'...arguing because something is true of members of a group or collection, it is true of the group as a whole. (71).

The following example is provided:

'J.S. Mill appears to argue that since each person desires just their own happiness, people together desire the common happiness.  (71).

Blackburn is contrast explains that nobody desires the common happiness. (71). Blackburn means based on Mill's philosophy, and that is reasonable.

My own view would be that almost all persons desire their own happiness (some mentally ill as possible exceptions), and some persons desire the common happiness.
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The Fallacy of Division

BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.
 
Blackburn helpfully explains the converse fallacy...

The fallacy of division is therefore stating:

Corporate to individual

C t I (my add)

'If something is true of a group, then it is also true of individuals belonging to it.' (71).

Example of fallacy:

Real Madrid won the UEFA Champions League, 2016, therefore it must have all the best players.


References:

GOODMAN, M. F. (1993) First Logic. University Press of America.

Logically Fallacious: Fallacy of Division

(also known as: false division, faulty deduction, division fallacy) 

Description: Inferring that something is true of one or more of the parts from the fact that it is true of the whole. This is the opposite of the fallacy of composition 

Example

His house is about half the size of most houses in the neighborhood. Therefore, his doors must all be about 3 1/2 feet high. 

Explanation: The size of one’s house almost certainly does not mean that the doors will be smaller, especially by the same proportions. The size of the whole (the house) is not directly related to the size of every part of the house.

Logically Fallacious also explains the compositional fallacy


(also known as: composition fallacy, exception fallacy, faulty induction) 

Description: Inferring that something is true of the whole from the fact that it is true of some part of the whole. This is the opposite of the fallacy of division.

Example

'Each brick in that building weighs less than a pound. Therefore, the building weighs less than a pound.'
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BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.

CONWAY DAVID A. AND RONALD MUNSON (1997) The Elements of Reasoning, Wadsworth Publishing Company, New York.

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy)

MILL, J. S. (1863) Utilitarianism. London: Parker, Son, and Bourn. 

MILL, J. S. (1972) Letter to Henry Jones (13 June 1868). In John M. Robson (ed.), Collected Works of John Stuart Mill vol. XVI. Toronto: University of Toronto Press. 1413–4.

PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.