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edited Nov 14, 2020 at 16:39

Either the word " this" ( used as subject in the conclusion) refers to something or not.
If it does not, the alledged conclusion has no meaning and therefore is not a proposition. In that case , there is no question as to the validity of the " argument" for there is no argument. For an argument is a sequence of genuine propositions. ( More precisely, it is couple/ ordered pair having as first member a set Gamma of premises, and as second element a single proposition playing the role of conclusion).
If " this" has a meaning it means " this argument" or " the argument having ' London is in England' and 'Beijing is in China' as premises" .

In that case the conclusion means " The argument having as premises .... is an an argument". Hence it is a tautology.

Any argument having a tautology as conclusion is valid, whatever the premses may be. Since there is no way to make a tautology false, there is, a fortiori, no possible case in which the premises are true and the conclusion false.
Conclusion : if one allows metalangage in an argument, this argument is valid, and is not a counterexample to the validity criterion set forth in the book referred to.

Either " this" refers to something or not.
If it does not, the alledged conclusion has no meaning and therefore is not a proposition. In that case , there is no question as to the validity of the " argument" for there is no argument. For an argument is a sequence of genuine propositions. ( More precisely, it is couple/ ordered pair having as first member a set Gamma of premises, and as second element a single proposition playing the role of conclusion).
If " this" has a meaning it means " this argument" or " the argument having ' London is in England' and 'Beijing is in China' as premises" .

In that case the conclusion means " The argument having as premises .... is an an argument". Hence it is a tautology.

Any argument having a tautology as conclusion is valid, whatever the premses may be. Since there is no way to make a tautology false, there is, a fortiori, no possible case in which the premises are true and the conclusion false.
Conclusion : if one allows metalangage in an argument, this argument is valid, and is not a counterexample to the validity criterion set forth in the book referred to.

Either the word " this" ( used as subject in the conclusion) refers to something or not.
If it does not, the alledged conclusion has no meaning and therefore is not a proposition. In that case , there is no question as to the validity of the " argument" for there is no argument. For an argument is a sequence of genuine propositions. ( More precisely, it is couple/ ordered pair having as first member a set Gamma of premises, and as second element a single proposition playing the role of conclusion).
If " this" has a meaning it means " this argument" or " the argument having ' London is in England' and 'Beijing is in China' as premises" .

In that case the conclusion means " The argument having as premises .... is an an argument". Hence it is a tautology.

Any argument having a tautology as conclusion is valid, whatever the premses may be. Since there is no way to make a tautology false, there is, a fortiori, no possible case in which the premises are true and the conclusion false.
Conclusion : if one allows metalangage in an argument, this argument is valid, and is not a counterexample to the validity criterion set forth in the book referred to.

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created Nov 14, 2020 at 16:33

Either " this" refers to something or not.
If it does not, the alledged conclusion has no meaning and therefore is not a proposition. In that case , there is no question as to the validity of the " argument" for there is no argument. For an argument is a sequence of genuine propositions. ( More precisely, it is couple/ ordered pair having as first member a set Gamma of premises, and as second element a single proposition playing the role of conclusion).
If " this" has a meaning it means " this argument" or " the argument having ' London is in England' and 'Beijing is in China' as premises" .

In that case the conclusion means " The argument having as premises .... is an an argument". Hence it is a tautology.

Any argument having a tautology as conclusion is valid, whatever the premses may be. Since there is no way to make a tautology false, there is, a fortiori, no possible case in which the premises are true and the conclusion false.
Conclusion : if one allows metalangage in an argument, this argument is valid, and is not a counterexample to the validity criterion set forth in the book referred to.