# What do you call this fallacy that relies on dubious transitivity?

Is there a formal name for this kind of fallacy that relies on transitivity between parts and whole? Some examples:

The government is fundamentally white supremacist. Bernie Sanders supports the government. Therefore Bernie Sanders supports white supremacy.

Or

The military is protective of our country. Within our country are prisons containing convicted murderers. Therefore the military is protective of convicted murderers.

Or

Baby farts a lot. Daddy loves baby. Therefore daddy loves farts.

• Well, second example is bad one, because government really protects prisoners as well, exactly because of this argument. In other cases I think it's some kind of faulty generalization. Jun 29, 2018 at 16:54
• @rus9384 I think it may be technically true but the implication is something scurrilous. But I modified the example slightly to make the false implication more obvious. Jun 29, 2018 at 17:00
• Well, it changes nothing and if you study the law, you'll know that government really protects all it's inhabitants, including convicted prisoners. Also, if government doesn't protect them, then why do policemen in prisons stop prison riots? Jun 29, 2018 at 19:34
• The way you phrase the question sounds close to the fallacy of division, inferring that something is true of a part from it being true of a whole. Loving or supporting X does not imply loving or supporting everything about X. Jun 29, 2018 at 20:26
• Just removing the logic tag, since this is entirely an argumentation question. Jul 1, 2018 at 8:23

## 2 Answers

I think 1 and 3 are false dilemmas, just phrased unusually.

You could rephrase them to "Either you love farts or you don't love your baby" or "You are either against white supremacy or you support the government"

In fact I think #2 is a truism, generalised to "P is a subset of C, A protects all C therefore A protects P"

I'd say that a version of the fallacy of division is at work :

A is a part of B

B has property X

Therefore A has property X.

In the Bernie Saunders example :

1 Bernie Saunders supports the government (A supports B)

2 The government is fundamentally white supremacist (B has property X = is white supremacist).

3 Therefore Bernie Saunders supports white supremacy (A has property X = is white supremacist).

One thing that's wrong here is that if Bernie Saunders supports the government this does not entail that he supports all its policies; he may support all of them but supporting the government only need entail supporting some of its policies. Whiter supremacist policies need not be among the policies Bernie Saunders (specifically) supports when he (generally) supports the government. Compare : a Republican might support Donald Trump's administration without supporting its treatment of illegal Mexican immigrants or its tariff policy.

Also there is the possibility that even if BS supports all the government's policies he does not realise that some of them, even the fundamental ones, are white supremacist. In this case it would be only a half-truth to say that he supports white supremacy : his actions de facto support it but he does not know this and he does not accept a white supremacist agenda intentionally since white supremacy has no place in his value system.

I realise this only tackles one of your examples but you did offer a set of 'or's.