diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index e2a74ea6f5351..ddb2f01898ec7 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1012,6 +1012,26 @@ def _reduce(self, name: str, *, skipna: bool = True, **kwargs):
         ------
         TypeError : subclass does not define reductions
         """
+        pa_type = self._data.type
+
+        data_to_reduce = self._data
+
+        if name in ["any", "all"] and (
+            pa.types.is_integer(pa_type)
+            or pa.types.is_floating(pa_type)
+            or pa.types.is_duration(pa_type)
+        ):
+            # pyarrow only supports any/all for boolean dtype, we allow
+            #  for other dtypes, matching our non-pyarrow behavior
+
+            if pa.types.is_duration(pa_type):
+                data_to_cmp = self._data.cast(pa.int64())
+            else:
+                data_to_cmp = self._data
+
+            not_eq = pc.not_equal(data_to_cmp, 0)
+            data_to_reduce = not_eq
+
         if name == "sem":
 
             def pyarrow_meth(data, skip_nulls, **kwargs):
@@ -1033,8 +1053,9 @@ def pyarrow_meth(data, skip_nulls, **kwargs):
             if pyarrow_meth is None:
                 # Let ExtensionArray._reduce raise the TypeError
                 return super()._reduce(name, skipna=skipna, **kwargs)
+
         try:
-            result = pyarrow_meth(self._data, skip_nulls=skipna, **kwargs)
+            result = pyarrow_meth(data_to_reduce, skip_nulls=skipna, **kwargs)
         except (AttributeError, NotImplementedError, TypeError) as err:
             msg = (
                 f"'{type(self).__name__}' with dtype {self.dtype} "
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index a7c243cdfe74f..af3952a532113 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -566,10 +566,24 @@ def test_reduce_series(
                 f"pyarrow={pa.__version__} for {pa_dtype}"
             ),
         )
-        if not pa.types.is_boolean(pa_dtype):
+        if pa.types.is_string(pa_dtype) or pa.types.is_binary(pa_dtype):
+            # We *might* want to make this behave like the non-pyarrow cases,
+            #  but have not yet decided.
             request.node.add_marker(xfail_mark)
+
         op_name = all_boolean_reductions
         ser = pd.Series(data)
+
+        if pa.types.is_temporal(pa_dtype) and not pa.types.is_duration(pa_dtype):
+            # xref GH#34479 we support this in our non-pyarrow datetime64 dtypes,
+            #  but it isn't obvious we _should_.  For now, we keep the pyarrow
+            #  behavior which does not support this.
+
+            with pytest.raises(TypeError, match="does not support reduction"):
+                getattr(ser, op_name)(skipna=skipna)
+
+            return
+
         result = getattr(ser, op_name)(skipna=skipna)
         assert result is (op_name == "any")