consider this argument?

Question

Consider the argument:
If Company A does not control its spending, then it will suffer huge budget deficits.
Company A is suffering huge budget deficits.
Therefore, it is not controlling its spending.


a. Write the argument symbolically.




b. By considering its truth table or by Venn diagram, decide if the argument is valid or invalid.

Answer 1

company A controls its spending = p
company A suffers huge budget deficits = q

~p -> q
q
--------
~p

(~ = negation, --------- = mark for concluding the argument)

You do not use Venn diagrams for proofs in sentence logic, you only use them for syllogistic (and what you have here is sentence logic).

The argument is not valid. It is a classical wrong form of Modus Ponens, affirming in the premises the consequent (in our case, q) instead of the antecedent (~p). In the truth table, you get the faulty "possible world" if you assign to both p and q "true".


About ~p.
I have simply translated "Company A does not control its spending" as "not (Company A controls its spending)", both in the premise and in the conclusion. Which is, technically speaking, the right way to do it, since in symbolic logic the negation is a connective, so when you meet a negated sentence in the natural language, you should translate it as a negated sentence in the formal language as well. My explanation (or the original argument) had nothing to do with the law of contraposition (or some wrong variant of it), since, I repeat, ~p occurred both in the premise and in the conclusion. Translating "Company A does not control its spending" as simply "p" wouldn't have changed the main structure of the symbolic argument, it would just have made the formalization less accurate. The reason for the invalidity is more that, if p is a sufficient condition for q, there is no logical ground to conclude that q is a sufficient condition for p. This would just not be logical ;).

...Since I have just noticed - what on earth is this question doing in "Parapsychology"?!

Answer 2

jlb who answered this question previously has it 92% right.

p= "does not control spending"
q= "suffer huge budget deficits"

I would have written

p ----> q
q
________
p

This is a simple converse statement, which may be valid or invalid. jlb is right in that it's a bad Modus Ponens called "affirming the consequent".

"p implies q" or p ----> q. This statement is the conditional. The whole conditional may be itself "true" or "not true." But what matters in deductive logic is whether or not the statement is "logically equivalent."

The statement logically equivalent to p---->q is the contrapositive. The contrapositive is ~q ---> ~p.

The contrapositive of a statement is always logically equivalent to the conditional.

When you say q---> ~p, that is not a logically equivalent statement, even if it appears to be true! In fact, it might not be true, because there may be other causes to why Company A is suffering huge budget deficits, outside of their spending control. You can only talk about the contrapositives as true if the conditional was itself true. Converses and inverses may or may not be true, even if they appear to be true. The fact that they may not be true means you can never, ever rely on them with certainty. Lot of people look at them, say they must be true because they appear true, and they're actually wrong.

To answer your original question, you cannot say whether or not Company A is controlling its spending. It may or may not be.

This was actually a deep question and deductive logic applies to everything in life. You just can't be like Mr. Spock about it.

Skylor Williams

Answer 3

Not control ------> huge deficits

but huge deficits -/-/-/-/-/-/ > no control. That is a fallacy. (Converse). Huge deficits may come from other sources.

But it would be true to assert that if the company does NOT
have huge deficits, then it IS controlling its spending.
(Law of the contrapositive.)

Also, this is plain logic, having nothing to do with parapsychology or alternative thinking.

Answer 4

invalid, co A deficits may be due to theft, taxes, natural disaster.

Answer 5

I now feel really dumb....back to easier questions I go.......

Answer 6

How is Co. A doing in production and sales? More info please?