As a preliminary consider the definitions of *validity* and *jointly logically consistent* provided by the authors of *forall x: Calgary Remix*.

Here is their definition of "valid" (page 8):

An argument is valid if and only if it is impossible for all of the premises to be true and the conclusion false.

Here is their definition of "jointly logically consistent" (page 72):

A1,A2,...,An are jointly logically consistent iff there is some
valuation which makes them all true.

Derivatively, sentences are jointly logically inconsistent if there is
no valuation that makes them all true.

Consider the question: *Can you make a valid inference invalid by adding extra premises?*

Arguments are valid or invalid. Sets of premises can be jointly logically consistent or jointly logically inconsistent. Adding premises to a set of premises used in a valid argument may make the larger set of premises jointly logically inconsistent but that does affect the validity of arguments using a smaller set of premises.

On page 265 they have a chart answering questions about validity of an argument and consistency of premises. In summary, an argument is valid if we can give a proof using the premises and reaching the conclusion. It is invalid if we can find an interpretation where all of the premises are individually true but the conclusion is false.

Consider this an example. Let "P" and "Q" be premises. Try to derive "P ∧ Q". Here is the proof:

The two premises are assumed in lines 1 and 2. By using the conjunction introduction rule (∧I), I reach the goal in line 3.

Suppose I add ¬P to the premises to see if this expanded set of premises affects the validity of this argument. Since I am not using ¬P in the proof the proof checker shows that it does not.

Although the particular argument remains valid, something changed. I can easily find an interpretation for the first argument using "P" and "Q" as premises, but I will not be able to find any for the second argument using "P", "Q", and "¬P".

How would I be able to tell if the premises are jointly consistent or not? That is also answered on page 265. To show the premises are jointly consistent I need to provide an interpretation where all of the premises are true. Note, it says nothing about the conclusion of an argument. To show the premises are jointly inconsistent I need to prove that these premises lead to a contradiction. In other words, to show that the premises, "P", "Q", and "R", are jointly inconsistent, I would need to prove this argument: "P, Q, ¬P ∴ ⊥"

Here is that proof using contradiction introduction (⊥I):

In summary Peter Smith's question attempts to help the reader distinguish between the validity of an argument and the joint consistency of a set of premises.

References

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

Think about the definition of validity:

ifthe premises are true,thenthe conclusion is true as well. To show that an argument is invalid, you need to find an interpretation that makes the premises true but the conclusion false. If you start with a valid argument, can you add further premises that make all of the premises true but the conclusion false? – possibleWorld – 2017-06-03T13:02:31.253In classical logic no, but you can make a sound argument unsound by adding false premises. The difference between soundness and validity is usually ignored colloquially, but logical validity is neutral on the truth of the premises, it only cares whether inference would preserve that truth. Contradictory premises, however, would make any argument from them unsound. Moreover, in classical logic due to the law of explosion

– Conifold – 2017-06-04T22:03:48.560anythingcan be validly inferred from contradictory premises.Your intuition is captured by non-monotonic logics:"

– Conifold – 2017-06-04T22:07:12.387The term “non-monotonic logic” (in short, NML) covers a family of formal frameworks devised to capture and represent defeasible inference, i.e., that kind of inference in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information". In the light of new premises some of the original premises may be defeased (annuled), i.e. become untrustworthy, thus invalidating the original argument.In a nutshell, the def of

validityof an argument is: every "model" of the premises (i.e. every interpretation satisfying them) is also a model of the conclusion. If we "add" a new premise, we restrict the number of models (because the new premise will "cut off" all the previous models that do not satisfy it): thus, it cannot invalidate a valid argument. – Mauro ALLEGRANZA – 2017-06-05T09:28:05.453