Final answer:
The argument presented by the student is not valid because it does not follow the Law of Syllogism or the Law of Detachment properly. The conclusion assumed a single cause for the paper burning without justification, leading to an error in deductive reasoning.
Step-by-step explanation:
The student asked whether the argument 'If there are ashes, then the paper burned. Conclusion: A flame burning the paper to ashes' is valid, if it uses the Law of Syllogism or the Law of Detachment. This argument is not valid because it assumes that a flame is the only thing that could have caused the paper to burn, which is not supported by the premises. The error in reasoning here is assuming a single cause without justification. In fact, the conclusion does not logically follow from the premises, making this argument an improper use of deductive reasoning.
A better deductive reasoning process would include premises that directly support the conclusion. For instance, if the premises were '1) If a flame is applied to paper, then the paper will burn. 2) A flame was applied to the paper.' then we could conclude, by the Law of Detachment, that the paper burned. However, that is not the case presented in the student's question.
The argument also incorrectly applies the concept of a disjunctive syllogism. A disjunctive syllogism has the structure '1) X or Y, 2) Not Y, 3) Therefore X', which does not fit the argument given. Therefore, the correct answer is A. No. This is an improper use of the Law of Syllogism.